Enhanced collectivity along the N = Z line: Lifetime measurements in 44Ti, 48Cr, and 52Fe

NASA Astrophysics Data System (ADS)

Arnswald, K.; Braunroth, T.; Seidlitz, M.; Coraggio, L.; Reiter, P.; Birkenbach, B.; Blazhev, A.; Dewald, A.; Fransen, C.; Fu, B.; Gargano, A.; Hess, H.; Hirsch, R.; Itaco, N.; Lenzi, S. M.; Lewandowski, L.; Litzinger, J.; Müller-Gatermann, C.; Queiser, M.; Rosiak, D.; Schneiders, D.; Siebeck, B.; Steinbach, T.; Vogt, A.; Wolf, K.; Zell, K. O.

2017-09-01

Lifetimes of the 21+ states in 44Ti, 48,50Cr, and 52Fe were determined with high accuracy exploiting the recoil distance Doppler-shift method. The reduced E2 transition strengths of 44Ti and 52Fe differ considerably from previously known values. A systematic increase in collectivity is found for the N = Z nuclei compared to neighboring isotopes. The B (E2) values along the Ti, Cr, and Fe isotopic chains are compared to shell-model calculations employing established interactions for the 0 f 1 p shell, as well as a novel effective shell-model Hamiltonian starting from a realistic nucleon-nucleon potential. The theoretical approaches underestimate the B (E2) values for the lower-mass Ti isotopes. Strong indication is found for particle-hole cross-shell configurations, recently corroborated by similar results for the neighboring isotone 42Ca.

Mirror energy difference and the structure of loosely bound proton-rich nuclei around A =20

NASA Astrophysics Data System (ADS)

Yuan, Cenxi; Qi, Chong; Xu, Furong; Suzuki, Toshio; Otsuka, Takaharu

2014-04-01

The properties of loosely bound proton-rich nuclei around A =20 are investigated within the framework of the nuclear shell model. In these nuclei, the strength of the effective interactions involving the loosely bound proton s1/2 orbit is significantly reduced in comparison with that of those in their mirror nuclei. We evaluate the reduction of the effective interaction by calculating the monopole-based-universal interaction (VMU) in the Woods-Saxon basis. The shell-model Hamiltonian in the sd shell, such as USD, can thus be modified to reproduce the binding energies and energy levels of the weakly bound proton-rich nuclei around A =20. The effect of the reduction of the effective interaction on the structure and decay properties of these nuclei is also discussed.

Roles of nuclear weak rates on the evolution of degenerate cores in stars

NASA Astrophysics Data System (ADS)

Suzuki, Toshio; Tsunodaa, Naofumi; Tsunoda, Yuhsuke; Shimizu, Noritaka; Otsuka, Takaharu

2018-01-01

Electron-capture and β-decay rates in stellar environments are evaluated with the use of new shell-model Hamiltonians for sd-shell and pf-shell nuclei as well as for nuclei belonging to the island of inversion. Important role of the nuclear weak rates on the final evolution of stellar degenerate cores is presented. The weak interaction rates for sd-shell nuclei are calculated to study nuclear Urca processes in O-Ne-Mg cores of stars with 8-10 M⊙ (solar mass) and their effects on the final fate of the stars. Nucleosynthesis of iron-group elements in Type Ia supernova explosions are studied with the weak rates for pf-shell nuclei. The problem of the neutron-rich iron-group isotope over-production compared to the solar abundances is shown to be nearly solved with the use of the new rates and explosion model of slow defraglation with delayed detonation. Evaluation of the weak rates is extended to the island of inversion and the region of neutron-rich nuclei near 78Ni, where two major shells contribute to their configurations.

Algebraic Bethe ansatz for the sℓ (2) Gaudin model with boundary

NASA Astrophysics Data System (ADS)

Cirilo António, N.; Manojlović, N.; Ragoucy, E.; Salom, I.

2015-04-01

Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations.

The Hamiltonian Structure of Nonlinear Elasticity: The Convective Representation of Solids, Rods, and Plates,

DTIC Science & Technology

1986-12-01

paper, we consider geometrically exact models, such as the Kirchhoff-Love-Reissner- Antman model for rods and its counterpart for plates and shells. These...equivalent model, formulated as a constrained director theory - the so-called special theory of Cosserat rods - is due to Antman (1974] - see also...Anan and Jordan [1975], Anunan and Kenny [1981]. and Antman [1984] for some applications. The dynamic version along with the parametrization discussed

Constraint algebra in Smolin's G →0 limit of 4D Euclidean gravity

NASA Astrophysics Data System (ADS)

Varadarajan, Madhavan

2018-05-01

Smolin's generally covariant GNewton→0 limit of 4d Euclidean gravity is a useful toy model for the study of the constraint algebra in loop quantum gravity (LQG). In particular, the commutator between its Hamiltonian constraints has a metric dependent structure function. While a prior LQG-like construction of nontrivial anomaly free constraint commutators for the model exists, that work suffers from two defects. First, Smolin's remarks on the inability of the quantum dynamics to generate propagation effects apply. Second, the construction only yields the action of a single Hamiltonian constraint together with the action of its commutator through a continuum limit of corresponding discrete approximants; the continuum limit of a product of two or more constraints does not exist. Here, we incorporate changes in the quantum dynamics through structural modifications in the choice of discrete approximants to the quantum Hamiltonian constraint. The new structure is motivated by that responsible for propagation in an LQG-like quantization of paramatrized field theory and significantly alters the space of physical states. We study the off shell constraint algebra of the model in the context of these structural changes and show that the continuum limit action of multiple products of Hamiltonian constraints is (a) supported on an appropriate domain of states, (b) yields anomaly free commutators between pairs of Hamiltonian constraints, and (c) is diffeomorphism covariant. Many of our considerations seem robust enough to be applied to the setting of 4d Euclidean gravity.

Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

NASA Astrophysics Data System (ADS)

Cirilo António, N.; Manojlović, N.; Salom, I.

2014-12-01

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

Enhanced collectivity along the N = Z line: lifetime measurements in 44Ti, 48Cr, and 52Fe

NASA Astrophysics Data System (ADS)

Arnswald, K.; Reiter, P.; Coraggio, L.; Birkenbach, B.; Blazhev, A.; Braunroth, T.; Dewald, A.; Fransen, C.; Fu, B.; Gargano, A.; Hess, H.; Hirsch, R.; Itaco, N.; Lenzi, S. M.; Lewandowski, L.; Litzinger, J.; Müller-Gatermann, C.; Queiser, M.; Rosiak, D.; Schneiders, D.; Seidlitz, M.; Siebeck, B.; Steinbach, T.; Vogt, A.; Wolf, K.; Zell, K. O.

2018-02-01

Lifetimes of the {2}1+ states in 44Ti, 48,50Cr, and 52Fe were determined with high accuracy exploiting the recoil distance Doppler-shift method. The reduced E2 transition strengths of 44Ti and 52 Fe differ considerably from previously known values. A systematic increase in collectivity is found for the N = Z nuclei compared to neighboring isotopes. The B(E2) values along the Ti, Cr, and Fe isotopic chains are compared to shell-model calculations employing established interactions for the 0f 1p shell, as well as a novel effective shell-model Hamiltonian starting from a realistic nucleon-nucleon potential. The theoretical approaches underestimate the B(E2) values for the lower-mass Ti isotopes. Strong indication is found for particle-hole cross-shell configurations, recently corroborated by similar results for the neighboring isotone 42 Ca. A detailed manuscript has meanwhile been published in Physics Letters B [1].

Description of strong M1 transitions between 4^+ states at N=52 within the sdg-IBM-2

NASA Astrophysics Data System (ADS)

Casperson, R. J.; Werner, V.; Heinze, S.

2009-10-01

The interplay between collective and single-particle degrees of freedom for nuclei near the N=50 shell closure have recently been under investigation. In Molybdenum and Ruthenium nuclei, collective symmetric and mixed-symmetric structures have been identified, while in Zirconium, underlying shell-structure plays an enhanced role. The one-phonon 2^+ mixed-symmetry state was identified from its strong M1 transition to the 2^+1 state. Similar transitions were observed between 4^+ states in ^94Mo and ^92Zr, and shell model calculations indicate that hexadecapole excitations play a role. These phenomena will be investigated within the sdg-Interacting Boson Model-2 in order to gain a better understanding about the structure of the states involved, and to which extent the hexadecapole degree of freedom is important at relatively low energies. First calculations within this model, using an F-spin conserving Hamiltonian to disentangle symmetric and mixed- symmetric structures, will be presented and compared to data.

A revised MRCI-algorithm. I. Efficient combination of spin adaptation with individual configuration selection coupled to an effective valence-shell Hamiltonian

NASA Astrophysics Data System (ADS)

Strodel, Paul; Tavan, Paul

2002-09-01

We present a revised multi-reference configuration interaction (MRCI) algorithm for balanced and efficient calculation of electronic excitations in molecules. The revision takes up an earlier method, which had been designed for flexible, state-specific, and individual selection (IS) of MRCI expansions, included perturbational corrections (PERT), and used the spin-coupled hole-particle formalism of Tavan and Schulten (1980) for matrix-element evaluation. It removes the deficiencies of this method by introducing tree structures, which code the CI bases and allow us to efficiently exploit the sparseness of the Hamiltonian matrices. The algorithmic complexity is shown to be optimal for IS/MRCI applications. The revised IS/MRCI/PERT module is combined with the effective valence shell Hamiltonian OM2 suggested by Weber and Thiel (2000). This coupling serves the purpose of making excited state surfaces of organic dye molecules accessible to relatively cheap and sufficiently precise descriptions.

{ITALIC AB INITIO} Large-Basis no-Core Shell Model and its Application to Light Nuclei

NASA Astrophysics Data System (ADS)

Barrett, Bruce R.; Navratil, Petr; Ormand, W. E.; Vary, James P.

2002-01-01

We discuss the {ITALIC ab initio} No-Core Shell Model (NCSM). In this method the effective Hamiltonians are derived microscopically from realistic nucleon-nucleon (NN) potentials, such as the CD-Bonn and the Argonne AV18 NN potentials, as a function of the finite Harmonic Oscillator (HO) basis space. We present converged results, i.e. , up to 50 Ω and 18 Ω HO excitations, respectively, for the A=3 and 4 nucleon systems. Our results for these light systems are in agreement with results obtained by other exact methods. We also calculate properties of 6Li and 6He in model spaces up to 10 Ω and of 12C up to 6 Ω. Binding energies, rms radii, excitation spectra and electromagnetic properties are discussed. The favorable comparison with available data is a consequence of the underlying NN interaction rather than a phenomenological fit.

Neutron single-particle strengths at N =40 , 42: Neutron knockout from Ni,7068 ground and isomeric states

NASA Astrophysics Data System (ADS)

Recchia, F.; Weisshaar, D.; Gade, A.; Tostevin, J. A.; Janssens, R. V. F.; Albers, M.; Bader, V. M.; Baugher, T.; Bazin, D.; Berryman, J. S.; Brown, B. A.; Campbell, C. M.; Carpenter, M. P.; Chen, J.; Chiara, C. J.; Crawford, H. L.; Hoffman, C. R.; Kondev, F. G.; Korichi, A.; Langer, C.; Lauritsen, T.; Liddick, S. N.; Lunderberg, E.; Noji, S.; Prokop, C.; Stroberg, S. R.; Suchyta, S.; Wimmer, K.; Zhu, S.

2016-11-01

The distribution of single-particle strength in Ni,6967 was characterized with one-neutron knockout reactions from intermediate-energy Ni,7068 secondary beams, selectively populating neutron-hole configurations at N =39 and 41, respectively. The spectroscopic strengths deduced from the measured partial cross sections to the individual final states, as tagged by their γ -ray decays, are used to identify and quantify neutron configurations in the wave functions. While 69Ni compares well with shell-model predictions, the results for 67Ni challenge the validity of current effective shell-model Hamiltonians by revealing discrepancies that cannot be explained so far. These results suggest that our understanding of the low-lying states in the neutron-rich, semimagic Ni isotopes may be incomplete and requires further investigation on both the experimental and theoretical sides.

Modeling of thin-walled structures interacting with acoustic media as constrained two-dimensional continua

NASA Astrophysics Data System (ADS)

Rabinskiy, L. N.; Zhavoronok, S. I.

2018-04-01

The transient interaction of acoustic media and elastic shells is considered on the basis of the transition function approach. The three-dimensional hyperbolic initial boundary-value problem is reduced to a two-dimensional problem of shell theory with integral operators approximating the acoustic medium effect on the shell dynamics. The kernels of these integral operators are determined by the elementary solution of the problem of acoustic waves diffraction at a rigid obstacle with the same boundary shape as the wetted shell surface. The closed-form elementary solution for arbitrary convex obstacles can be obtained at the initial interaction stages on the background of the so-called “thin layer hypothesis”. Thus, the shell–wave interaction model defined by integro-differential dynamic equations with analytically determined kernels of integral operators becomes hence two-dimensional but nonlocal in time. On the other hand, the initial interaction stage results in localized dynamic loadings and consequently in complex strain and stress states that require higher-order shell theories. Here the modified theory of I.N.Vekua–A.A.Amosov-type is formulated in terms of analytical continuum dynamics. The shell model is constructed on a two-dimensional manifold within a set of field variables, Lagrangian density, and constraint equations following from the boundary conditions “shifted” from the shell faces to its base surface. Such an approach allows one to construct consistent low-order shell models within a unified formal hierarchy. The equations of the N th-order shell theory are singularly perturbed and contain second-order partial derivatives with respect to time and surface coordinates whereas the numerical integration of systems of first-order equations is more efficient. Such systems can be obtained as Hamilton–de Donder–Weyl-type equations for the Lagrangian dynamical system. The Hamiltonian formulation of the elementary N th-order shell theory is here briefly described.

Structure of p-shell nuclei using three-nucleon interactions evolved with the similarity renormalization group

DOE PAGES

Jurgenson, E. D.; Maris, P.; Furnstahl, R. J.; ...

2013-05-13

The similarity renormalization group (SRG) is used to soften interactions for ab initio nuclear structure calculations by decoupling low- and high-energy Hamiltonian matrix elements. The substantial contribution of both initial and SRG-induced three-nucleon forces requires their consistent evolution in a three-particle basis space before applying them to larger nuclei. While, in principle, the evolved Hamiltonians are unitarily equivalent, in practice the need for basis truncation introduces deviations, which must be monitored. Here we present benchmark no-core full configuration calculations with SRG-evolved interactions in p-shell nuclei over a wide range of softening. As a result, these calculations are used to assessmore » convergence properties, extrapolation techniques, and the dependence of energies, including four-body contributions, on the SRG resolution scale.« less

Porter-Thomas distribution in unstable many-body systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Volya, Alexander

We use the continuum shell model approach to explore the resonance width distribution in unstable many-body systems. The single-particle nature of a decay, the few-body character of the interaction Hamiltonian, and the collectivity that emerges in nonstationary systems due to the coupling to the continuum of reaction states are discussed. Correlations between the structures of the parent and daughter nuclear systems in the common Fock space are found to result in deviations of decay width statistics from the Porter-Thomas distribution.

Neutron single-particle strengths at N = 40 , 42: Neutron knockout from Ni 68 , 70 ground and isomeric states

DOE PAGES

Recchia, F.; Weisshaar, D.; Gade, A.; ...

2016-11-28

The distribution of single-particle strength in 67,69Ni was characterized with one-neutron knockout reactions from intermediate-energy 68,70Ni secondary beams, selectively populating neutron-hole configurations at N = 39 and 41, respectively. The spectroscopic strengths deduced from the measured partial cross sections to the individual final states, as tagged by their γ-ray decays, is used to identify and quantify neutron configurations in the wave functions. While 69Ni compares well to shell-model predictions, the results for 67Ni challenge the validity of current effective shell-model Hamiltonians by revealing discrepancies that cannot be explained so far. Furthermore, these results suggest that our understanding of the low-lyingmore » states in the neutron-rich, semi-magic Ni isotopes may be incomplete and requires further investigation on both the experimental and theoretical sides.« less

Effective operators in a single-j orbital

NASA Astrophysics Data System (ADS)

Derbali, E.; Van Isacker, P.; Tellili, B.; Souga, C.

2018-03-01

We present an analysis of effective operators in the shell model with up to three-body interactions in the Hamiltonian and two-body terms in electromagnetic transition operators when the nucleons are either neutrons or protons occupying a single-j orbital. We first show that evidence for an effective three-body interaction exists in the N = 50 isotones and in the lead isotopes but that the separate components of such interaction are difficult to obtain empirically. We then determine higher-order terms on more microscopic grounds. The starting point is a realistic two-body interaction in a large shell-model space together with a standard one-body transition operator, which, after restriction to the dominant orbital and with use of stationary perturbation theory, are transformed into effective versions with higher-order terms. An application is presented for the lead isotopes with neutrons in the 1{g}9/2 orbital.

gA-driven shapes of electron spectra of forbidden β decays in the nuclear shell model

NASA Astrophysics Data System (ADS)

Kostensalo, Joel; Suhonen, Jouni

2017-08-01

The evolution of the shape of the electron spectra of 16 forbidden β- decays as a function of gA was studied using the nuclear shell model in appropriate single-particle model spaces with established, well-tested nuclear Hamiltonians. The β spectra of 94Nb(6+) →94Mo(4+) and 98Tc(6+) →98Ru(4+) were found to depend strongly on gA, which makes them excellent candidates for the determination of the effective value of gA with the spectrum-shape method (SSM). A strong gA dependence is also seen in the spectrum of 96Zr(0+) →96Nb(6+) . This decay could be used for determining the quenching of gA in sixth-forbidden decays in the future, when the measurement of the spectrum becomes experimentally feasible. The calculated shell-model electron spectra of the ground-state-to-ground-state decays of 87Rb, 99Tc, and 137Cs and the decay of 137Cs to the isomeric 11 /2- state in 137Ba were found to be in excellent agreement with the spectra previously calculated using the microscopic quasiparticle-phonon model. This is further evidence of the robust nature of the SSM observed in the previous studies.

Towards a First-Principles Determination of Effective Coulomb Interactions in Correlated Electron Materials: Role of Intershell Interactions

NASA Astrophysics Data System (ADS)

Seth, Priyanka; Hansmann, Philipp; van Roekeghem, Ambroise; Vaugier, Loig; Biermann, Silke

2017-08-01

The determination of the effective Coulomb interactions to be used in low-energy Hamiltonians for materials with strong electronic correlations remains one of the bottlenecks for parameter-free electronic structure calculations. We propose and benchmark a scheme for determining the effective local Coulomb interactions for charge-transfer oxides and related compounds. Intershell interactions between electrons in the correlated shell and ligand orbitals are taken into account in an effective manner, leading to a reduction of the effective local interactions on the correlated shell. Our scheme resolves inconsistencies in the determination of effective interactions as obtained by standard methods for a wide range of materials, and allows for a conceptual understanding of the relation of cluster model and dynamical mean field-based electronic structure calculations.

Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model

NASA Astrophysics Data System (ADS)

Manojlović, N.; Salom, I.

2017-10-01

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.

Towards a First-Principles Determination of Effective Coulomb Interactions in Correlated Electron Materials: Role of Intershell Interactions.

PubMed

Seth, Priyanka; Hansmann, Philipp; van Roekeghem, Ambroise; Vaugier, Loig; Biermann, Silke

2017-08-04

The determination of the effective Coulomb interactions to be used in low-energy Hamiltonians for materials with strong electronic correlations remains one of the bottlenecks for parameter-free electronic structure calculations. We propose and benchmark a scheme for determining the effective local Coulomb interactions for charge-transfer oxides and related compounds. Intershell interactions between electrons in the correlated shell and ligand orbitals are taken into account in an effective manner, leading to a reduction of the effective local interactions on the correlated shell. Our scheme resolves inconsistencies in the determination of effective interactions as obtained by standard methods for a wide range of materials, and allows for a conceptual understanding of the relation of cluster model and dynamical mean field-based electronic structure calculations.

Impact of off-diagonal cross-shell interaction on 14C

NASA Astrophysics Data System (ADS)

Yuan, Cen-Xi

2017-10-01

A shell-model investigation is performed to show the impact on the structure of 14C from the off-diagonal cross-shell interaction, 〈pp|V|sdsd〉, which represents the mixing between the 0 and 2ħω configurations in the psd model space. The observed levels of the positive states in 14C can be nicely described in 0-4ħω or a larger model space through the well defined Hamiltonians, YSOX and WBP, with a reduction of the strength of the 〈pp|V|sdsd〉 interaction in the latter. The observed B(GT) values for 14C can be generally described by YSOX, while WBP and their modifications of the 〈pp|V|sdsd〉 interaction fail for some values. Further investigation shows the effect of such interactions on the configuration mixing and occupancy. The present work shows examples of how the off-diagonal cross-shell interaction strongly drives the nuclear structure. Supported by National Natural Science Foundation of China (11305272), Special Program for Applied Research on Super Computation of the NSFC Guangdong Joint Fund (the second phase), the Guangdong Natural Science Foundation (2014A030313217), the Pearl River S&T Nova Program of Guangzhou (201506010060), the Tip-top Scientific and Technical Innovative Youth Talents of Guangdong special support program (2016TQ03N575), and the Fundamental Research Funds for the Central Universities (17lgzd34)

An explicitly spin-free compact open-shell coupled cluster theory using a multireference combinatoric exponential ansatz: formal development and pilot applications.

PubMed

Datta, Dipayan; Mukherjee, Debashis

2009-07-28

In this paper, we present a comprehensive account of an explicitly spin-free compact state-universal multireference coupled cluster (CC) formalism for computing the state energies of simple open-shell systems, e.g., doublets and biradicals, where the target open-shell states can be described by a few configuration state functions spanning a model space. The cluster operators in this formalism are defined in terms of the spin-free unitary generators with respect to the common closed-shell component of all model functions (core) as vacuum. The spin-free cluster operators are either closed-shell-like n hole-n particle excitations (denoted by T(mu)) or involve excitations from the doubly occupied (nonvalence) orbitals to the singly occupied (valence) orbitals (denoted by S(e)(mu)). In addition, there are cluster operators with exchange spectator scatterings involving the valence orbitals (denoted by S(re)(mu)). We propose a new multireference cluster expansion ansatz for the wave operator with the above generally noncommuting cluster operators which essentially has the same physical content as the Jeziorski-Monkhorst ansatz with the commuting cluster operators defined in the spin-orbital basis. The T(mu) operators in our ansatz are taken to commute with all other operators, while the S(e)(mu) and S(re)(mu) operators are allowed to contract among themselves through the spectator valence orbitals. An important innovation of this ansatz is the choice of an appropriate automorphic factor accompanying each contracted composite of cluster operators in order to ensure that each distinct excitation generated by this composite appears only once in the wave operator. The resulting CC equations consist of two types of terms: a "direct" term and a "normalization" term containing the effective Hamiltonian operator. It is emphasized that the direct term is almost quartic in the cluster amplitudes, barring only a handful of terms and termination of the normalization term depends on the valence rank of the effective Hamiltonian operator and the excitation rank of the cluster operators at which the theory is truncated. Illustrative applications are presented by computing the state energies of neutral doublet radicals and doublet molecular cations and ionization energies of neutral molecules and comparing our results with the other open-shell CC theories, benchmark full CI results (when available) in the same basis, and the experimental results. Highly encouraging results show the efficacy of the method.

Transition sum rules in the shell model

NASA Astrophysics Data System (ADS)

Lu, Yi; Johnson, Calvin W.

2018-03-01

An important characterization of electromagnetic and weak transitions in atomic nuclei are sum rules. We focus on the non-energy-weighted sum rule (NEWSR), or total strength, and the energy-weighted sum rule (EWSR); the ratio of the EWSR to the NEWSR is the centroid or average energy of transition strengths from an nuclear initial state to all allowed final states. These sum rules can be expressed as expectation values of operators, which in the case of the EWSR is a double commutator. While most prior applications of the double commutator have been to special cases, we derive general formulas for matrix elements of both operators in a shell model framework (occupation space), given the input matrix elements for the nuclear Hamiltonian and for the transition operator. With these new formulas, we easily evaluate centroids of transition strength functions, with no need to calculate daughter states. We apply this simple tool to a number of nuclides and demonstrate the sum rules follow smooth secular behavior as a function of initial energy, as well as compare the electric dipole (E 1 ) sum rule against the famous Thomas-Reiche-Kuhn version. We also find surprising systematic behaviors for ground-state electric quadrupole (E 2 ) centroids in the s d shell.

A revised MRCI-algorithm coupled to an effective valence-shell Hamiltonian. II. Application to the valence excitations of butadiene

NASA Astrophysics Data System (ADS)

Strodel, Paul; Tavan, Paul

2002-09-01

In Paper I of this work we have sketched an improved MRCI algorithm and its coupling to the effective valence-shell Hamiltonian OM2. To check the quality of the resulting OM2/MRCI approach, it is applied here to the excited valence states of all-trans butadiene. As is explained by a review of previous theoretical work, proper descriptions of these states posed severe problems within correlated ab initio treatments but seemed to be trivial within simple correlated pi-electron models. We now show that an extended MRCI treatment of the correlations among all valence electrons as described by OM2 closely reproduces the experimental evidence, placing the vertical 2 1Ag excitation by about 0.2 eV below the 1 1Bu excitation. By an analysis of sigma]-[pi interactions we explain the corresponding earlier success of correlated pi-electron theory. Exploiting the enhanced capabilities of the new approach we investigate the potential surfaces. Here, OM2/MRCI is shown to predict that the 2 1Ag state is energetically lowered about four times more strongly than the 1 1Bu state upon geometry relaxation constrained to the C2h symmetry. We conclude that OM2/MRCI should be well-suited for the study of excited state surfaces of organic dye molecules.

Model of Anisotropic Magnetization of In(1-x)Mn(x)S: Comparison to Experiment

NASA Astrophysics Data System (ADS)

Garner, J.; Franzese, G.; Byrd, Ashlee; Pekarek, T. M.; Miotkowski, I.; Ramdas, A. K.

2004-03-01

Calculations of and experimental results for the anisotropic magnetization of the new III-VI dilute magnetic semiconductor, In(1-x)Mn(x)S, are presented. The model Hamiltonian incorporates the interaction of the incomplete shell of Mn 3d-electrons with the crystal lattice within the point-ion approximation. Other terms in the Hamiltonian include the Zeeman interaction, the spin-orbit and the spin-spin terms. It is assumed the Mn atoms do not interact with each other (this is the singlet model, which is appropriate when x is small, here 2%). The temperature- and field- dependent magnetization is found from the energy eigenvalues of the Hamiltonian matrix, which was expressed in terms of an uncoupled angular momentum basis set. Magnetization versus temperature results are found for several field values, B, pointing along various directions relative to the underlying dilute magnetic semiconductor crystal lattice. In addition, the magnetization versus field is computed for several fixed temperatures and for various B-field directions and magnitudes. Overall, the agreement of this simple model with the experimental data is very good except at low temperatures (< 20 K) and high fields (> a few Tesla). It would be useful for quantitative comparison purposes to have optical absorption data in order to better fix the crystal potential parameters that are input parameters in the theory. In addition, the model could be improved by going beyond the point-ion approximation to better model the covalent bonds in the crystal.* Supported by UNF Research Grants, Research Corporation Award, CC4845, NSF Grant Nos. DMR-03-05653, DMR-01-02699, and ECS-01-29853 and Donors of the American Chemical Society Petroleum Research Fund PRF#40209-B5M, and a Purdue Univ. Academic Reimbursement Grant.

Three-cluster dynamics within an ab initio framework

DOE PAGES

Quaglioni, Sofia; Romero-Redondo, Carolina; Navratil, Petr

2013-09-26

In this study, we introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method. Energy-independent nonlocal interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to amore » 4He+n+n description of 6He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the no-core shell model. Differences between the two calculations provide a measure of core ( 4He) polarization effects.« less

Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian

NASA Astrophysics Data System (ADS)

Ripoche, J.; Lacroix, D.; Gambacurta, D.; Ebran, J.-P.; Duguet, T.

2017-01-01

Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei. In their best current level of implementation, their accuracy is of the order of a few percent error on the ground-state correlation energy. Recently implemented variants of these methods are operating a breakthrough in the description of medium-mass open-shell nuclei at a polynomial computational cost while putting state-of-the-art models of internucleon interactions to the test. Purpose: As progress in the design of internucleon interactions is made, and as questions one wishes to answer are refined in connection with increasingly available experimental data, further efforts must be made to tailor many-body methods that can reach an even higher precision for an even larger number of observable quantum states or nuclei. The objective of the present work is to contribute to such a quest by designing and testing a new many-body scheme. Methods: We formulate a truncated configuration-interaction method that consists of diagonalizing the Hamiltonian in a highly truncated subspace of the total N -body Hilbert space. The reduced Hilbert space is generated via the particle-number projected BCS state along with projected seniority-zero two- and four-quasiparticle excitations. Furthermore, the extent by which the underlying BCS state breaks U(1 ) symmetry is optimized in the presence of the projected two- and four-quasiparticle excitations. This constitutes an extension of the so-called restricted variation after projection method in use within the frame of multireference energy density functional calculations. The quality of the newly designed method is tested against exact solutions of the so-called attractive pairing Hamiltonian problem. Results: By construction, the method reproduces exact results for N =2 and N =4 . For N =(8 ,16 ,20 ) , the error in the ground-state correlation energy is less than (0.006%, 0.1%, 0.15%) across the entire range of internucleon coupling defining the pairing Hamiltonian and driving the normal-to-superfluid quantum phase transition. The presently proposed method offers the advantage of automatic access to the low-lying spectroscopy, which it does with high accuracy. Conclusions: The numerical cost of the newly designed variational method is polynomial (N6) in system size. This method achieves unprecedented accuracy for the ground-state correlation energy, effective pairing gap, and one-body entropy as well as for the excitation energy of low-lying states of the attractive pairing Hamiltonian. This constitutes a sufficiently strong motivation to envision its application to realistic nuclear Hamiltonians in view of providing a complementary, accurate, and versatile ab initio description of mid-mass open-shell nuclei in the future.

Mean-field and linear regime approach to magnetic hyperthermia of core-shell nanoparticles: can tiny nanostructures fight cancer?

NASA Astrophysics Data System (ADS)

Carrião, Marcus S.; Bakuzis, Andris F.

2016-04-01

The phenomenon of heat dissipation by magnetic materials interacting with an alternating magnetic field, known as magnetic hyperthermia, is an emergent and promising therapy for many diseases, mainly cancer. Here, a magnetic hyperthermia model for core-shell nanoparticles is developed. The theoretical calculation, different from previous models, highlights the importance of heterogeneity by identifying the role of surface and core spins on nanoparticle heat generation. We found that the most efficient nanoparticles should be obtained by selecting materials to reduce the surface to core damping factor ratio, increasing the interface exchange parameter and tuning the surface to core anisotropy ratio for each material combination. From our results we propose a novel heat-based hyperthermia strategy with the focus on improving the heating efficiency of small sized nanoparticles instead of larger ones. This approach might have important implications for cancer treatment and could help improving clinical efficacy.The phenomenon of heat dissipation by magnetic materials interacting with an alternating magnetic field, known as magnetic hyperthermia, is an emergent and promising therapy for many diseases, mainly cancer. Here, a magnetic hyperthermia model for core-shell nanoparticles is developed. The theoretical calculation, different from previous models, highlights the importance of heterogeneity by identifying the role of surface and core spins on nanoparticle heat generation. We found that the most efficient nanoparticles should be obtained by selecting materials to reduce the surface to core damping factor ratio, increasing the interface exchange parameter and tuning the surface to core anisotropy ratio for each material combination. From our results we propose a novel heat-based hyperthermia strategy with the focus on improving the heating efficiency of small sized nanoparticles instead of larger ones. This approach might have important implications for cancer treatment and could help improving clinical efficacy. Electronic supplementary information (ESI) available: Unit cells per region calculation; core-shell Hamiltonian; magnetisation description functions; energy argument of Brillouin function; polydisperse models; details of experimental procedure; LRT versus core-shell model; model calculation software; and shell thickness study. See DOI: 10.1039/C5NR09093H

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry.

PubMed

Boguslawski, Katharina; Tecmer, Paweł

2017-12-12

Wave functions restricted to electron-pair states are promising models to describe static/nondynamic electron correlation effects encountered, for instance, in bond-dissociation processes and transition-metal and actinide chemistry. To reach spectroscopic accuracy, however, the missing dynamic electron correlation effects that cannot be described by electron-pair states need to be included a posteriori. In this Article, we extend the previously presented perturbation theory models with an Antisymmetric Product of 1-reference orbital Geminal (AP1roG) reference function that allows us to describe both static/nondynamic and dynamic electron correlation effects. Specifically, our perturbation theory models combine a diagonal and off-diagonal zero-order Hamiltonian, a single-reference and multireference dual state, and different excitation operators used to construct the projection manifold. We benchmark all proposed models as well as an a posteriori Linearized Coupled Cluster correction on top of AP1roG against CR-CC(2,3) reference data for reaction energies of several closed-shell molecules that are extrapolated to the basis set limit. Moreover, we test the performance of our new methods for multiple bond breaking processes in the homonuclear N 2 , C 2 , and F 2 dimers as well as the heteronuclear BN, CO, and CN + dimers against MRCI-SD, MRCI-SD+Q, and CR-CC(2,3) reference data. Our numerical results indicate that the best performance is obtained from a Linearized Coupled Cluster correction as well as second-order perturbation theory corrections employing a diagonal and off-diagonal zero-order Hamiltonian and a single-determinant dual state. These dynamic corrections on top of AP1roG provide substantial improvements for binding energies and spectroscopic properties obtained with the AP1roG approach, while allowing us to approach chemical accuracy for reaction energies involving closed-shell species.

Atypicality of Most Few-Body Observables

NASA Astrophysics Data System (ADS)

Hamazaki, Ryusuke; Ueda, Masahito

2018-02-01

The eigenstate thermalization hypothesis (ETH), which dictates that all diagonal matrix elements within a small energy shell be almost equal, is a major candidate to explain thermalization in isolated quantum systems. According to the typicality argument, the maximum variations of such matrix elements should decrease exponentially with increasing the size of the system, which implies the ETH. We show, however, that the typicality argument does not apply to most few-body observables for few-body Hamiltonians when the width of the energy shell decreases at most polynomially with increasing the size of the system.

Transition sum rules in the shell model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Yi; Johnson, Calvin W.

An important characterization of electromagnetic and weak transitions in atomic nuclei are sum rules. We focus on the non-energy-weighted sum rule (NEWSR), or total strength, and the energy- weighted sum rule (EWSR); the ratio of the EWSR to the NEWSR is the centroid or average energy of transition strengths from an nuclear initial state to all allowed final states. These sum rules can be expressed as expectation values of operators, in the case of the EWSR a double commutator. While most prior applications of the double-commutator have been to special cases, we derive general formulas for matrix elements of bothmore » operators in a shell model framework (occupation space), given the input matrix elements for the nuclear Hamiltonian and for the transition operator. With these new formulas, we easily evaluate centroids of transition strength functions, with no need to calculate daughter states. We then apply this simple tool to a number of nuclides, and demonstrate the sum rules follow smooth secular behavior as a function of initial energy, as well as compare the electric dipole (E1) sum rule against the famous Thomas-Reiche-Kuhn version. We also find surprising systematic behaviors for ground state electric quadrupole (E2) centroids in the $sd$-shell.« less

Transition sum rules in the shell model

DOE PAGES

Lu, Yi; Johnson, Calvin W.

2018-03-29

An important characterization of electromagnetic and weak transitions in atomic nuclei are sum rules. We focus on the non-energy-weighted sum rule (NEWSR), or total strength, and the energy- weighted sum rule (EWSR); the ratio of the EWSR to the NEWSR is the centroid or average energy of transition strengths from an nuclear initial state to all allowed final states. These sum rules can be expressed as expectation values of operators, in the case of the EWSR a double commutator. While most prior applications of the double-commutator have been to special cases, we derive general formulas for matrix elements of bothmore » operators in a shell model framework (occupation space), given the input matrix elements for the nuclear Hamiltonian and for the transition operator. With these new formulas, we easily evaluate centroids of transition strength functions, with no need to calculate daughter states. We then apply this simple tool to a number of nuclides, and demonstrate the sum rules follow smooth secular behavior as a function of initial energy, as well as compare the electric dipole (E1) sum rule against the famous Thomas-Reiche-Kuhn version. We also find surprising systematic behaviors for ground state electric quadrupole (E2) centroids in the $sd$-shell.« less

On equations of motion of a nonlinear hydroelastic structure

NASA Astrophysics Data System (ADS)

Plotnikov, P. I.; Kuznetsov, I. V.

2008-07-01

Formal derivation of equations of a nonlinear hydroelastic structure, which is a volume of an ideal incompressible fluid covered by a shell, is proposed. The study is based on two assumptions. The first assumption implies that the energy stored in the shell is completely determined by the mean curvature and by the elementary area. In a three-dimensional case, the energy stored in the shell is chosen in the form of the Willmore functional. In a two-dimensional case, a more generic form of the functional can be considered. The second assumption implies that the equations of motionhave a Hamiltonian structure and can be obtained from the Lagrangian variational principle. In a two-dimensional case, a condition for the hydroelastic structure is derived, which relates the external pressure and the curvature of the elastic shell.

Properties of infrared extrapolations in a harmonic oscillator basis

DOE PAGES

Coon, Sidney A.; Kruse, Michael K. G.

2016-02-22

Here, the success and utility of effective field theory (EFT) in explaining the structure and reactions of few-nucleon systems has prompted the initiation of EFT-inspired extrapolations to larger model spaces in ab initio methods such as the no-core shell model (NCSM). In this contribution, we review and continue our studies of infrared (ir) and ultraviolet (uv) regulators of NCSM calculations in which the input is phenomenological NN and NNN interactions fitted to data. We extend our previous findings that an extrapolation in the ir cutoff with the uv cutoff above the intrinsic uv scale of the interaction is quite successful,more » not only for the eigenstates of the Hamiltonian but also for expectation values of operators, such as r 2, considered long range. The latter results are obtained with Hamiltonians transformed by the similarity renormalization group (SRG) evolution. On the other hand, a possible extrapolation of ground state energies in the uv cutoff when the ir cutoff is below the intrinsic ir scale is not robust and does not agree with the ir extrapolation of the same data or with independent calculations using other methods.« less

Hamiltonian closures in fluid models for plasmas

NASA Astrophysics Data System (ADS)

Tassi, Emanuele

2017-11-01

This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and connections with previously discussed fluid models are pointed out.

Low-energy pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Gibbs, W. R.; Ai, Li; Kaufmann, W. B.

1998-02-01

An analysis of low-energy charged pion-nucleon data from recent π+/-p experiments is presented. From the scattering lengths and the Goldberger-Miyazawa-Oehme (GMO) sum rule we find a value of the pion-nucleon coupling constant of f2=0.0756+/-0.0007. We also find, contrary to most previous analyses, that the scattering volumes for the P31 and P13 partial waves are equal, within errors, corresponding to a symmetry found in the Hamiltonian of many theories. For the potential models used, the amplitudes are extrapolated into the subthreshold region to estimate the value of the Σ term. Off-shell amplitudes are also provided.

Ab initio calculation of one-nucleon halo states

NASA Astrophysics Data System (ADS)

Rodkin, D. M.; Tchuvil'sky, Yu M.

2018-02-01

We develop an approach to microscopic and ab initio description of clustered systems, states with halo nucleon and one-nucleon resonances. For these purposes a basis combining ordinary shell-model components and cluster-channel terms is built up. The transformation of clustered wave functions to the uniform Slater-determinant type is performed using the concept of cluster coefficients. The resulting basis of orthonormalized wave functions is used for calculating the eigenvalues and the eigenvectors of Hamiltonians built in the framework of ab initio approaches. Calculations of resonance and halo states of 5He, 9Be and 9B nuclei demonstrate that the approach is workable and labor-saving.

Quantum transport through single and multilayer icosahedral fullerenes

NASA Astrophysics Data System (ADS)

Lovey, Daniel A.; Romero, Rodolfo H.

2013-10-01

We use a tight-binding Hamiltonian and Green functions methods to calculate the quantum transmission through single-wall fullerenes and bilayered and trilayered onions of icosahedral symmetry attached to metallic leads. The electronic structure of the onion-like fullerenes takes into account the curvature and finite size of the fullerenes layers as well as the strength of the intershell interactions depending on to the number of interacting atom pairs belonging to adjacent shells. Misalignment of the symmetry axes of the concentric iscosahedral shells produces breaking of the level degeneracies of the individual shells, giving rise some narrow quasi-continuum bands instead of the localized discrete peaks of the individual fullerenes. As a result, the transmission function for non symmetrical onions is rapidly varying functions of the Fermi energy. Furthermore, we found that most of the features of the transmission through the onions are due to the electronic structure of the outer shell with additional Fano-like antiresonances arising from coupling with or between the inner shells.

Protons in non-ionic aqueous reverse micelles.

PubMed

Rodriguez, Javier; Martí, Jordi; Guàrdia, Elvira; Laria, Daniel

2007-05-03

Using molecular dynamics techniques, we investigate the solvation of an excess proton within an aqueous reverse micelle in vacuo, with the neutral surfactant diethylene glycol monodecyl ether [CH3(CH2)11(OC2H4)2OH]. The simulation experiments were performed using a multistate empirical valence bond Hamiltonian model. Our results show that the stable solvation environments for the excess proton are located in the water-surfactant interface and that its first solvation shell is composed exclusively by water molecules. The relative prevalence of Eigen- versus Zundel-like solvation structures is investigated; compared to bulk results, Zundel-like structures in micelles become somewhat more stable. Characteristic times for the proton translocation jumps have been computed using population relaxation time correlation functions. The micellar rate for proton transfer is approximately 40x smaller than that found in bulk water at ambient conditions. Differences in the computed rates are examined in terms of the hydrogen-bond connectivity involving the first solvation shell of the excess charge with the rest of the micellar environment. Simulation results would indicate that proton transfers are correlated with rare episodes during which the HB connectivity between the first and second solvation shells suffers profound modifications.

Relativistic top: An application of the BFV quantization procedure for systems with degenerate constraints

NASA Astrophysics Data System (ADS)

Nielsen, N. K.; Quaade, U. J.

1995-07-01

The physical phase space of the relativistic top, as defined by Hansson and Regge, is expressed in terms of canonical coordinates of the Poincaré group manifold. The system is described in the Hamiltonian formalism by the mass-shell condition and constraints that reduce the number of spin degrees of freedom. The constraints are second class and are modified into a set of first class constraints by adding combinations of gauge-fixing functions. The Batalin-Fradkin-Vilkovisky method is then applied to quantize the system in the path integral formalism in Hamiltonian form. It is finally shown that different gauge choices produce different equivalent forms of the constraints.

Factorization in large-scale many-body calculations

DOE PAGES

Johnson, Calvin W.; Ormand, W. Erich; Krastev, Plamen G.

2013-08-07

One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmetrized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm recreates the many-body matrix elementsmore » on the fly and can reduce the storage requirements by an order of magnitude or more. Here, we discuss factorization in general and introduce a novel, generalized factorization method, essentially a ‘double-factorization’ which speeds up basis generation and set-up of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.« less

Neutrino-nucleus reactions based on recent structure studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suzuki, Toshio; National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588

2015-05-15

Neutrino-nucleus reactions are studied with the use of new shell model Hamiltonians, which have proper tensor components in the interactions and prove to be successful in the description of Gamow-Teller (GT) strengths in nuclei. The new Hamiltonians are applied to obtain new neutrino-nucleus reaction cross sections in {sup 12}C, {sup 13}C, {sup 56}Fe and {sup 56}Ni induced by solar and supernova neutrinos. The element synthesis by neutrino processes in supernova explosions is discussed with the new cross sections. The enhancement of the production yields of {sup 7}Li, {sup 11}B and {sup 55}Mn is obtained while fragmented GT strength in {supmore » 56}Ni with two-peak structure is found to result in smaller e-capture rates at stellar environments. The monopole-based universal interaction with tensor force of π+ρ meson exchanges is used to evaluate GT strength in {sup 40}Ar and ν-induced reactions on {sup 40}Ar. It is found to reproduce well the experimental GT strength in {sup 40}Ar.« less

On the Stark effect in open shell complexes exhibiting partially quenched electronic angular momentum: Infrared laser Stark spectroscopy of OH–C 2H 2, OH–C 2H 4, and OH–H 2O

DOE PAGES

Moradi, Christopher P.; Douberly, Gary E.

2015-06-22

The Stark effect is considered for polyatomic open shell complexes that exhibit partially quenched electronic angular momentum. Matrix elements of the Stark Hamiltonian represented in a parity conserving Hund's case (a) basis are derived for the most general case, in which the permanent dipole moment has projections on all three inertial axes of the system. Transition intensities are derived, again for the most general case, in which the laser polarization has projections onto axes parallel and perpendicular to the Stark electric field, and the transition dipole moment vector is projected onto all three inertial axes in the molecular frame. Asmore » a result, simulations derived from this model are compared to experimental rovibrational Stark spectra of OH-C 2H 2, OH-C 2H 4, and OH-H 2O complexes formed in helium nanodroplets.« less

Nucleon correlations and the structure of Zn 41 30 71

DOE PAGES

Bottoni, Simone; Zhu, S.; Janssens, R. V. F.; ...

2017-11-06

Here, the structure of 71Zn was investigated by one-neutron transfer and heavy-ion induced complex (deep-inelastic) reactions using the GRETINA-CHICO2 and the Gammasphere setups, respectively. The observed inversion between the 9/2 + and 1/2 – states is explained in terms of the role of neutron pairing correlations. Non-collective sequences of levels were delineated above the 9/2 + isomeric state. These are interpreted as being associated with a modest oblate deformation in the framework of Monte-Carlo shell-model calculations carried out with the A3DA-m Hamiltonian in the pfg 9/2d 5/2 valence space. Similarities with the structure of 68 28Ni 40 were observed andmore » the shape-coexistence mechanism in the N = 40 region of neutron-rich nuclei is discussed in terms of the so-called Type-II shell evolution, with an emphasis on proton–neutron correlations between valence nucleons, especially those involving the shape-driving g 9/2 neutron orbital.« less

Nucleon correlations and the structure of 41 30 71Zn

NASA Astrophysics Data System (ADS)

Bottoni, S.; Zhu, S.; Janssens, R. V. F.; Carpenter, M. P.; Tsunoda, Y.; Otsuka, T.; Macchiavelli, A. O.; Cline, D.; Wu, C. Y.; Ayangeakaa, A. D.; Bucher, B.; Buckner, M. Q.; Campbell, C. M.; Chiara, C. J.; Crawford, H. L.; Cromaz, M.; David, H. M.; Fallon, P.; Gade, A.; Greene, J. P.; Harker, J.; Hayes, A. B.; Hoffman, C. R.; Kay, B. P.; Korichi, A.; Lauritsen, T.; Sethi, J.; Seweryniak, D.; Walters, W. B.; Weisshaar, D.; Wiens, A.

2017-12-01

The structure of 71Zn was investigated by one-neutron transfer and heavy-ion induced complex (deep-inelastic) reactions using the GRETINA-CHICO2 and the Gammasphere setups, respectively. The observed inversion between the 9/2+ and 1/2- states is explained in terms of the role of neutron pairing correlations. Non-collective sequences of levels were delineated above the 9/2+ isomeric state. These are interpreted as being associated with a modest oblate deformation in the framework of Monte-Carlo shell-model calculations carried out with the A3DA-m Hamiltonian in the pfg9/2d5/2 valence space. Similarities with the structure of 40,28,68Ni were observed and the shape-coexistence mechanism in the N = 40 region of neutron-rich nuclei is discussed in terms of the so-called Type-II shell evolution, with an emphasis on proton-neutron correlations between valence nucleons, especially those involving the shape-driving g9/2 neutron orbital.

Ab initio excited states from the in-medium similarity renormalization group

NASA Astrophysics Data System (ADS)

Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K.

2017-04-01

We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of 1 p 1 h excitations) becomes exact for a subset of eigenvalues. In the second approach, EOM techniques are applied to the IMSRG ground-state-decoupled Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two dimensions and the closed-shell nuclei 16O and 22O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but it is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster calculations. This work paves the way for more interesting applications of the EOM-IMSRG approach to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within one or two nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.

Ab initio calculation of the potential bubble nucleus 34Si

NASA Astrophysics Data System (ADS)

Duguet, T.; Somà, V.; Lecluse, S.; Barbieri, C.; Navrátil, P.

2017-03-01

Background: The possibility that an unconventional depletion (referred to as a "bubble") occurs in the center of the charge density distribution of certain nuclei due to a purely quantum mechanical effect has attracted theoretical and experimental attention in recent years. Based on a mean-field rationale, a correlation between the occurrence of such a semibubble and an anomalously weak splitting between low angular-momentum spin-orbit partners has been further conjectured. Energy density functional and valence-space shell model calculations have been performed to identify and characterize the best candidates, among which 34Si appears as a particularly interesting case. While the experimental determination of the charge density distribution of the unstable 34Si is currently out of reach, (d ,p ) experiments on this nucleus have been performed recently to test the correlation between the presence of a bubble and an anomalously weak 1 /2--3 /2- splitting in the spectrum of 35Si as compared to 37S. Purpose: We study the potential bubble structure of 34Si on the basis of the state-of-the-art ab initio self-consistent Green's function many-body method. Methods: We perform the first ab initio calculations of 34Si and 36S. In addition to binding energies, the first observables of interest are the charge density distribution and the charge root-mean-square radius for which experimental data exist in 36S. The next observable of interest is the low-lying spectroscopy of 35Si and 37S obtained from (d ,p ) experiments along with the spectroscopy of 33Al and 35P obtained from knock-out experiments. The interpretation in terms of the evolution of the underlying shell structure is also provided. The study is repeated using several chiral effective field theory Hamiltonians as a way to test the robustness of the results with respect to input internucleon interactions. The convergence of the results with respect to the truncation of the many-body expansion, i.e., with respect to the many-body correlations included in the calculation, is studied in detail. We eventually compare our predictions to state-of-the-art multireference energy density functional and shell model calculations. Results: The prediction regarding the (non)existence of the bubble structure in 34Si varies significantly with the nuclear Hamiltonian used. However, demanding that the experimental charge density distribution and the root-mean-square radius of 36S be well reproduced, along with 34Si and 36S binding energies, only leaves the NNLOsat Hamiltonian as a serious candidate to perform this prediction. In this context, a bubble structure, whose fingerprint should be visible in an electron scattering experiment of 34Si, is predicted. Furthermore, a clear correlation is established between the occurrence of the bubble structure and the weakening of the 1 /2--3 /2- splitting in the spectrum of 35Si as compared to 37S. Conclusions: The occurrence of a bubble structure in the charge distribution of 34Si is convincingly established on the basis of state-of-the-art ab initio calculations. This prediction will have to be reexamined in the future when improved chiral nuclear Hamiltonians are constructed. On the experimental side, present results act as a strong motivation to measure the charge density distribution of 34Si in future electron scattering experiments on unstable nuclei. In the meantime, it is of interest to perform one-neutron removal on 34Si and 36S in order to further test our theoretical spectral strength distributions over a wide energy range.

Integrable cosmological potentials

NASA Astrophysics Data System (ADS)

Sokolov, V. V.; Sorin, A. S.

2017-09-01

The problem of classification of the Einstein-Friedman cosmological Hamiltonians H with a single scalar inflaton field φ, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint H=0, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential V(φ). In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed.

Restricted Closed Shell Hartree Fock Roothaan Matrix Method Applied to Helium Atom Using Mathematica

ERIC Educational Resources Information Center

Acosta, César R.; Tapia, J. Alejandro; Cab, César

2014-01-01

Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix.…

Transition energy and potential energy curves for ionized inner-shell states of CO, O2 and N 2 calculated by several inner-shell multiconfigurational approaches.

PubMed

Moura, Carlos E V de; Oliveira, Ricardo R; Rocha, Alexandre B

2013-05-01

Potential energy curves and inner-shell ionization energies of carbon monoxide, oxygen and nitrogen molecules were calculated using several forms of the inner-shell multiconfigurational self-consistent field (IS-MCSCF) method-a recently proposed protocol to obtain specifically converged inner-shell states at this level. The particular forms of the IS-MCSCF method designated IS-GVB-PP, IS-FVBL and IS-CASSCF stand for perfect pairing generalized valence bond, full valence bond-like MCSCF and complete active space self consistent field, respectively. A comparison of these different versions of the IS-MCSCF method was carried out for the first time. The results indicate that inner-shell states are described accurately even for the simplest version of the method (IS-GVB-PP). Dynamic correlation was recovered by multireference configuration interaction or multireference perturbation theory. For molecules not having equivalent atoms, all methods led to comparable and accurate transition energies. For molecules with equivalent atoms, the most accurate results were obtained by multireference perturbation theory. Scalar relativistic effects were accounted for using the Douglas-Kroll-Hess Hamiltonian.

Quantum self-gravitating collapsing matter in a quantum geometry

NASA Astrophysics Data System (ADS)

Campiglia, Miguel; Gambini, Rodolfo; Olmedo, Javier; Pullin, Jorge

2016-09-01

The problem of how space-time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quantum level. We can write the metric as a parameterized Dirac observable at the quantum level and study the physics of the collapsing shell and black hole formation. We show how the singularity inside the black hole is eliminated by loop quantum gravity and how the shell can traverse it. The construction is compatible with a scenario in which the shell tunnels into a baby universe inside the black hole or one in which it could emerge through a white hole.

Excitons in Core-Shell Nanowires with Polygonal Cross Sections.

PubMed

Sitek, Anna; Urbaneja Torres, Miguel; Torfason, Kristinn; Gudmundsson, Vidar; Bertoni, Andrea; Manolescu, Andrei

2018-04-11

The distinctive prismatic geometry of semiconductor core-shell nanowires leads to complex localization patterns of carriers. Here, we describe the formation of optically active in-gap excitonic states induced by the interplay between localization of carriers in the corners and their mutual Coulomb interaction. To compute the energy spectra and configurations of excitons created in the conductive shell, we use a multielectron numerical approach based on the exact solution of the multiparticle Hamiltonian for electrons in the valence and conduction bands, which includes the Coulomb interaction in a nonperturbative manner. We expose the formation of well-separated quasidegenerate levels, and focus on the implications of the electron localization in the corners or on the sides of triangular, square, and hexagonal cross sections. We obtain excitonic in-gap states associated with symmetrically distributed electrons in the spin singlet configuration. They acquire large contributions due to Coulomb interaction, and thus are shifted to much higher energies than other states corresponding to the conduction electron and the vacancy localized in the same corner. We compare the results of the multielectron method with those of an electron-hole model, and we show that the latter does not reproduce the singlet excitonic states. We also obtain the exciton lifetime and explain selection rules which govern the recombination process.

A code for analysis of the fine structure in near-rigid weakly-bonded open-shell complexes that consist of a diatomic radical in a Σ3 state and a closed-shell molecule

NASA Astrophysics Data System (ADS)

Fawzy, Wafaa M.

2010-10-01

A FORTRAN code is developed for simulation and fitting the fine structure of a planar weakly-bonded open-shell complex that consists of a diatomic radical in a Σ3 electronic state and a diatomic or a polyatomic closed-shell molecule. The program sets up the proper total Hamiltonian matrix for a given J value and takes account of electron-spin-electron-spin, electron-spin rotation interactions, and the quartic and sextic centrifugal distortion terms within the complex. Also, R-dependence of electron-spin-electron-spin and electron-spin rotation couplings are considered. The code does not take account of effects of large-amplitude internal rotation of the diatomic radical within the complex. It is assumed that the complex has a well defined equilibrium geometry so that effects of large amplitude motion are negligible. Therefore, the computer code is suitable for a near-rigid rotor. Numerical diagonalization of the matrix provides the eigenvalues and the eigenfunctions that are necessary for calculating energy levels, frequencies, relative intensities of infrared or microwave transitions, and expectation values of the quantum numbers within the complex. Goodness of all the quantum numbers, with exception of J and parity, depends on relative sizes of the product of the rotational constants and quantum numbers (i.e. BJ, CJ, and AK), electron-spin-electron-spin, and electron-spin rotation couplings, as well as the geometry of the complex. Therefore, expectation values of the quantum numbers are calculated in the eigenfunctions basis of the complex. The computational time for the least squares fits has been significantly reduced by using the Hellman-Feynman theory for calculating the derivatives. The computer code is useful for analysis of high resolution infrared and microwave spectra of a planar near-rigid weakly-bonded open-shell complex that contains a diatomic fragment in a Σ3 electronic state and a closed-shell molecule. The computer program was successfully applied to analysis and fitting the observed high resolution infrared spectra of the O 2sbnd HF/O 2sbnd DF and O 2sbnd N 2O complexes. Test input file for simulation and fitting the high resolution infrared spectrum of the O 2sbnd DF complex is provided. Program summaryProgram title: TSIG_COMP Catalogue identifier: AEGM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 030 No. of bytes in distributed program, including test data, etc.: 51 663 Distribution format: tar.gz Programming language: Fortran 90, free format Computer: SGI Origin 3400, workstations and PCs Operating system: Linux, UNIX and Windows (see Restrictions below) RAM: Case dependent Classification: 16.2 Nature of problem: TSIG_COMP calculates frequencies, relative intensities, and expectation values of the various quantum numbers and parities of bound states involved in allowed ro-vibrational transitions in semi-rigid planar weakly-bonded open-shell complexes. The complexes of interest contain a free radical in a Σ3 state and a closed-shell partner, where the electron-spin-electron-spin interaction, electron-spin rotation interaction, and centrifugal forces significantly modify the spectral patterns. To date, ab initio methods are incapable of taking these effects into account to provide accurate predictions for the ro-vibrational energy levels of the complexes of interest. In the TSIG_COMP program, the problem is solved by using the proper effective Hamiltonian and molecular basis set. Solution method: The program uses a Hamiltonian operator that takes into account vibration, end-over-end rotation, electron-spin-electron-spin and electron-spin rotation interactions as well as the various centrifugal distortion terms. The Hamiltonian operator and the molecular basis set are used to set up the Hamiltonian matrix in the inertial axis system of the complex of interest. Diagonalization of the Hamiltonian matrix provides the eigenvalues and the eigenfunctions for the bound ro-vibrational states. These eigenvalues and eigenfunctions are used to calculate frequencies and relative intensities of the allowed infrared or microwave transitions as well as expectation values of all the quantum numbers and parities of states involved in the transitions. The program employs the method of least squares fits to fit the observed frequencies to the calculated frequencies to provide the molecular parameters that determine the geometry of the complex of interest. Restrictions: The number of transitions and parameters included in the fits is limited to 80 parameters and 200 transitions. However, these numbers can be increased by adjusting dimensions of the arrays (not recommended). Running the program under MS windows is recommended for simulations of any number of transitions and for fitting a relatively small number of parameters and transitions (maximum 15 parameters and 82 transitions), for fitting larger number of parameters run time error may occur. Because spectra of weakly bonded complexes are recorded at low temperatures, in most of cases fittings can be performed under MS windows. Running time: Problem-dependent. The provided test input for Linux fits 82 transitions and 21 parameters, the actual run time is 62 minutes. The provided test input file for MS windows fits 82 transitions and 15 parameters; the actual runtime is 5 minutes.

Approximate Theoretical Model for the Five Electronic States (Ω = 5/2, 3/2, 3/2, 1/2, 1/2) Arising from the Ground 3d9 Configuration in Nickel Halide Molecules and for Rotational Levels of the Two Ω = 1/2 States in that Manifold

NASA Astrophysics Data System (ADS)

Cheung, Allan S.-C.

2011-06-01

An effective Hamiltonian for a non-rotating diatomic molecule containing only crystal-field and spin-orbit operators has been set up to describe the energies of the five spin-orbit components that arise in the ground electronic configuration of the nickel monohalides. The model assumes that bonding in the nickel halides has the approximate form Ni+X-, with an electronic 3d9 configuration plus closed shells on the Ni+ moiety and a closed shell configuration on the X&- moiety. Least-squares fits of the observed five spin-orbit components of the three lowest electronic states in NiF and NiCl are then carried out in terms of the three crystal field parameters C0, C2, C4 and the spin-orbit coupling constant A. Following this, the usual effective Hamiltonian B(J-L-S)^2 for a rotating diatomic molecule is used to derive expressions for the unusually large Ω-type doubling parameter p in the two Ω = 1/2 states in the 3d9 manifold. These expressions show (for certain sign conventions) that the sum of the two p values should be -2B, but that their difference can vary between -10B and +10B. The theoretical magnitudes for p are in good agreement with the two observed p values for both NiF and NiCl, but the signs are not. The experimental signs can be brought into agreement with the theoretical signs by a fairly massive change in +/- parity assignments in the NiF and NiCl literature. The last part of the talk will focus on the theoretical and experimental implications of these parity changes.

A high-performance Fortran code to calculate spin- and parity-dependent nuclear level densities

NASA Astrophysics Data System (ADS)

Sen'kov, R. A.; Horoi, M.; Zelevinsky, V. G.

2013-01-01

A high-performance Fortran code is developed to calculate the spin- and parity-dependent shell model nuclear level densities. The algorithm is based on the extension of methods of statistical spectroscopy and implies exact calculation of the first and second Hamiltonian moments for different configurations at fixed spin and parity. The proton-neutron formalism is used. We have applied the method for calculating the level densities for a set of nuclei in the sd-, pf-, and pf+g- model spaces. Examples of the calculations for 28Si (in the sd-model space) and 64Ge (in the pf+g-model space) are presented. To illustrate the power of the method we estimate the ground state energy of 64Ge in the larger model space pf+g, which is not accessible to direct shell model diagonalization due to the prohibitively large dimension, by comparing with the nuclear level densities at low excitation energy calculated in the smaller model space pf. Program summaryProgram title: MM Catalogue identifier: AENM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 193181 No. of bytes in distributed program, including test data, etc.: 1298585 Distribution format: tar.gz Programming language: Fortran 90, MPI. Computer: Any architecture with a Fortran 90 compiler and MPI. Operating system: Linux. RAM: Proportional to the system size, in our examples, up to 75Mb Classification: 17.15. External routines: MPICH2 (http://www.mcs.anl.gov/research/projects/mpich2/) Nature of problem: Calculating of the spin- and parity-dependent nuclear level density. Solution method: The algorithm implies exact calculation of the first and second Hamiltonian moments for different configurations at fixed spin and parity. The code is parallelized using the Message Passing Interface and a master-slaves dynamical load-balancing approach. Restrictions: The program uses two-body interaction in a restricted single-level basis. For example, GXPF1A in the pf-valence space. Running time: Depends on the system size and the number of processors used (from 1 min to several hours).

Quantum gravitational collapse as a Dirac particle on the half line

NASA Astrophysics Data System (ADS)

Hassan, Syed Moeez; Husain, Viqar; Ziprick, Jonathan

2018-05-01

We show that the quantum dynamics of a thin spherical shell in general relativity is equivalent to the Coulomb-Dirac equation on the half line. The Hamiltonian has a one-parameter family of self-adjoint extensions with a discrete energy spectrum |E |m , where m is the rest mass of the shell and E is the Arnowitt-Deser-Misner mass. For sufficiently large m , the ground state energy level is negative. This suggests that classical positivity of energy does not survive quantization. The scattering states provide a realization of singularity avoidance. We speculate on the consequences of these results for black hole radiation.

Theoretical L-shell Coster-Kronig energies 11 or equal to z or equal to 103

NASA Technical Reports Server (NTRS)

Chen, M. H.; Crasemann, B.; Huang, K. N.; Aoyagi, M.; Mark, H.

1976-01-01

Relativistic relaxed-orbital calculations of L-shell Coster-Kronig transition energies have been performed for all possible transitions in atoms with atomic numbers. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order approximation to the local approximation was thus included. Quantum-electrodynamic corrections were made. Each transition energy was computed as the difference between results of separate self-consistent-field calculations for the initial, singly ionized state and the final two-hole state. The following quantities are listed: total transition energy, 'electric' (Dirac-Hartree-Fock-Slater) contribution, magnetic and retardation contributions, and contributions due to vacuum polarization and self energy.

Hamiltonian structure of the guiding center plasma model

NASA Astrophysics Data System (ADS)

Burby, J. W.; Sengupta, W.

2018-02-01

The guiding center plasma model (also known as kinetic MHD) is a rigorous sub-cyclotron-frequency closure of the Vlasov-Maxwell system. While the model has been known for decades and it plays a fundamental role in describing the physics of strongly magnetized collisionless plasmas, its Hamiltonian structure has never been found. We provide explicit expressions for the model's Poisson bracket and Hamiltonian and thereby prove that the model is an infinite-dimensional Hamiltonian system. The bracket is derived in a manner which ensures that it satisfies the Jacobi identity. We also report on several previously unknown circulation theorems satisfied by the guiding center plasma model. Without knowledge of the Hamiltonian structure, these circulation theorems would be difficult to guess.

Nuclear deformation in the laboratory frame

NASA Astrophysics Data System (ADS)

Gilbreth, C. N.; Alhassid, Y.; Bertsch, G. F.

2018-01-01

We develop a formalism for calculating the distribution of the axial quadrupole operator in the laboratory frame within the rotationally invariant framework of the configuration-interaction shell model. The calculation is carried out using a finite-temperature auxiliary-field quantum Monte Carlo method. We apply this formalism to isotope chains of even-mass samarium and neodymium nuclei and show that the quadrupole distribution provides a model-independent signature of nuclear deformation. Two technical advances are described that greatly facilitate the calculations. The first is to exploit the rotational invariance of the underlying Hamiltonian to reduce the statistical fluctuations in the Monte Carlo calculations. The second is to determine quadruple invariants from the distribution of the axial quadrupole operator in the laboratory frame. This allows us to extract effective values of the intrinsic quadrupole shape parameters without invoking an intrinsic frame or a mean-field approximation.

A partial Hamiltonian approach for current value Hamiltonian systems

NASA Astrophysics Data System (ADS)

Naz, R.; Mahomed, F. M.; Chaudhry, Azam

2014-10-01

We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.

Isoscalar neutron-proton pairing and SU(4)-symmetry breaking in Gamow-Teller transitions

NASA Astrophysics Data System (ADS)

Kaneko, K.; Sun, Y.; Mizusaki, T.

2018-05-01

The isoscalar neutron-proton pairing is thought to be important for nuclei with equal number of protons and neutrons but its manifestation in structure properties remains to be understood. We investigate the Gamow-Teller (GT) transitions for the f7 /2-shell nuclei in large-scale shell-model calculations with the realistic Hamiltonian. We show that the isoscalar T =0 ,Jπ=1+ neutron-proton pairing interaction plays a decisive role for the concentration of GT strengths at the first-excited 11+ state in 42Sc, and that the suppression of these strengths in 46V, 50Mn, and 54Co is mainly caused by the spin-orbit force supplemented by the quadrupole-quadrupole interaction. Based on the good reproduction of the charge-exchange reaction data, we further analyze the interplay between the isoscalar and isovector pairing correlations. We conclude that even for the most promising A =42 nuclei where the SU(4) isoscalar-isovector-pairing symmetry is less broken, the probability of forming an isoscalar neutron-proton pairing condensation is less than 60% as compared to the expectation at the SU(4)-symmetry limit.

Hamiltonian thermostats fail to promote heat flow

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.

2013-12-01

Hamiltonian mechanics can be used to constrain temperature simultaneously with energy. We illustrate the interesting situations that develop when two different temperatures are imposed within a composite Hamiltonian system. The model systems we treat are ϕ4 chains, with quartic tethers and quadratic nearest-neighbor Hooke's-law interactions. This model is known to satisfy Fourier's law. Our prototypical problem sandwiches a Newtonian subsystem between hot and cold Hamiltonian reservoir regions. We have characterized four different Hamiltonian reservoir types. There is no tendency for any of these two-temperature Hamiltonian simulations to transfer heat from the hot to the cold degrees of freedom. Evidently steady heat flow simulations require energy sources and sinks, and are therefore incompatible with Hamiltonian mechanics.

Low-energy pion-nucleon scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gibbs, W.R.; Ai, L.; Kaufmann, W.B.

An analysis of low-energy charged pion-nucleon data from recent {pi}{sup {plus_minus}}p experiments is presented. From the scattering lengths and the Goldberger-Miyazawa-Oehme (GMO) sum rule we find a value of the pion-nucleon coupling constant of f{sup 2}=0.0756{plus_minus}0.0007. We also find, contrary to most previous analyses, that the scattering volumes for the P{sub 31} and P{sub 13} partial waves are equal, within errors, corresponding to a symmetry found in the Hamiltonian of many theories. For the potential models used, the amplitudes are extrapolated into the subthreshold region to estimate the value of the {Sigma} term. Off-shell amplitudes are also provided. {copyright} {italmore » 1998} {ital The American Physical Society}« less

Can model Hamiltonians describe the electron-electron interaction in π-conjugated systems?: PAH and graphene

NASA Astrophysics Data System (ADS)

Chiappe, G.; Louis, E.; San-Fabián, E.; Vergés, J. A.

2015-11-01

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser-Parr-Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree-Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree-Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an ‘effective’ Hamiltonian including only on-site interactions (Hubbard)? The performance of CI will be checked on small molecules. The electronic structure of azulene and fused azulene will be used to illustrate several aspects of the method. As regards graphene, several questions will be considered: (i) paramagnetic versus antiferromagnetic solutions, (ii) forbidden gap versus dot size, (iii) graphene nano-ribbons, and (iv) optical properties.

Bi-Hamiltonian structure of the Kermack-McKendrick model for epidemics

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-11-01

The dynamical system proposed by Kermack and McKendrick (1933) to model the spread of epidemics is shown to admit bi-Hamiltonian structure without any restrictions on the rate constants. These two inequivalent Hamiltonian structures are compatible.

Dynamical Typicality Approach to Eigenstate Thermalization

NASA Astrophysics Data System (ADS)

Reimann, Peter

2018-06-01

We consider the set of all initial states within a microcanonical energy shell of an isolated many-body quantum system, which exhibit an arbitrary but fixed nonequilibrium expectation value for some given observable A . On the condition that this set is not too small, it is shown by means of a dynamical typicality approach that most such initial states exhibit thermalization if and only if A satisfies the so-called weak eigenstate thermalization hypothesis (wETH). Here, thermalization means that the expectation value of A spends most of its time close to the microcanonical value after initial transients have died out. The wETH means that, within the energy shell, most eigenstates of the pertinent system Hamiltonian exhibit very similar expectation values of A .

Symmetry energies for A =24 and 48 and the USD and KB3 shell model Hamiltonians

NASA Astrophysics Data System (ADS)

Kingan, A.; Neergârd, K.; Zamick, L.

2017-12-01

Calculations in the sd and pf shells reported some time ago by Satuła et al. [Phys. Lett. B 407, 103 (1997), 10.1016/S0370-2693(97)00711-9] are redone for an extended analysis of the results. As in the original work, we do calculations for one mass number in each shell and consider in each case the sequence of lowest energies for isospins 0, 2, and 4, briefly the symmetry spectrum. Following further the original work, we study how this spectrum changes when parts of the two-nucleon interaction are turned off. The variation of its width is explored in detail. A differential combination ɛW of the three energies was taken in the original work as a measure of the so-called Wigner term in semiempirical mass formulas, and it was found to decrease drastically when the two-nucleon interaction in the channel of zero isospin is turned off. Our analysis shows that the width of the symmetry spectrum experiences an equally drastic decrease, which can be explained qualitatively in terms of schematic approximations. We therefore suggest that the decrease of ɛW be seen mainly as a side effect of a narrowing of the symmetry spectrum rather than an independent manifestation of the two-nucleon interaction in the channel of zero isospin.

Neutron knockout from 68,70Ni ground and isomeric states.

NASA Astrophysics Data System (ADS)

Recchia, F.; Weisshaar, D.; Gade, A.; Tostevin, J. A.; Janssens, R. V. F.; Albers, M.; Bader, V. M.; Baugher, T.; Bazin, D.; Berryman, J. S.; Brown, B. A.; Campbell, C. M.; Carpenter, M. P.; Chen, J.; Chiara, C. J.; Crawford, H. L.; Hoffman, C. R.; Kondev, F. G.; Korichi, A.; Langer, C.; Lauritsen, T.; Liddick, S. N.; Lunderberg, E.; Noji, S.; Prokop, C.; Stroberg, S. R.; Suchyta, S.; Wimmer, K.; Zhu, S.

2018-02-01

Neutron-rich isotopes are an important source of new information on nuclear physics. Specifically, the spin-isospin components in the nucleon-nucleon (NN) interaction, e.g., the proton-neutron tensor force, are expected to modify shell structure in exotic nuclei. These potential changes in the intrinsic shell structure are of fundamental interest. The study of the excitation energy of states corresponding to specific configurations in even-even isotopes, together with the single-particle character of the first excited states of odd-A, neutron-rich Ni isotopes, probes the evolution of the neutron orbitals around the Fermi surface as a function of the neutron number a step forward in the understanding of the region and the nature of the NN interaction at large N/Z ratios. In an experiment carried out at the National Superconducting Cyclotron Laboratory [1], new spectroscopic information was obtained for 68Ni and the distribution of single-particle strengths in 67,69Ni was characterized by means of single-neutron knockout from 68,70Ni secondary beams. The spectroscopic strengths, deduced from the measured partial cross sections to the individual states tagged by their de-exciting gamma rays, is used to identify and quantify configurations that involve neutron excitations across the N = 40 harmonic oscillator shell closure. The de-excitation γ rays were measured with the GRETINA tracking array [2]. The results challenge the validity of the most current shell-model Hamiltonians and effective interactions, highlighting shortcomings that cannot yet be explained. These results suggest that our understanding of the low-energy states in such nuclei is not complete and requires further investigation.

Nonlinear saturation of wave packets excited by low-energy electron horseshoe distributions.

PubMed

Krafft, C; Volokitin, A

2013-05-01

Horseshoe distributions are shell-like particle distributions that can arise in space and laboratory plasmas when particle beams propagate into increasing magnetic fields. The present paper studies the stability and the dynamics of wave packets interacting resonantly with electrons presenting low-energy horseshoe or shell-type velocity distributions in a magnetized plasma. The linear instability growth rates are determined as a function of the ratio of the plasma to the cyclotron frequencies, of the velocity and the opening angle of the horseshoe, and of the relative thickness of the shell. The nonlinear stage of the instability is investigated numerically using a symplectic code based on a three-dimensional Hamiltonian model. Simulation results show that the dynamics of the system is mainly governed by wave-particle interactions at Landau and normal cyclotron resonances and that the high-order normal cyclotron resonances play an essential role. Specific features of the dynamics of particles interacting simultaneously with two or more waves at resonances of different natures and orders are discussed, showing that such complex processes determine the main characteristics of the wave spectrum's evolution. Simulations with wave packets presenting quasicontinuous spectra provide a full picture of the relaxation of the horseshoe distribution, revealing two main phases of the evolution: an initial stage of wave energy growth, characterized by a fast filling of the shell, and a second phase of slow damping of the wave energy, accompanied by final adjustments of the electron distribution. The influence of the density inhomogeneity along the horseshoe on the wave-particle dynamics is also discussed.

Hamiltonian dynamics of thermostated systems: two-temperature heat-conducting phi4 chains.

PubMed

Hoover, Wm G; Hoover, Carol G

2007-04-28

We consider and compare four Hamiltonian formulations of thermostated mechanics, three of them kinetic, and the other one configurational. Though all four approaches "work" at equilibrium, their application to many-body nonequilibrium simulations can fail to provide a proper flow of heat. All the Hamiltonian formulations considered here are applied to the same prototypical two-temperature "phi4" model of a heat-conducting chain. This model incorporates nearest-neighbor Hooke's-Law interactions plus a quartic tethering potential. Physically correct results, obtained with the isokinetic Gaussian and Nose-Hoover thermostats, are compared with two other Hamiltonian results. The latter results, based on constrained Hamiltonian thermostats, fail to model correctly the flow of heat.

On the paradoxical evolution of the number of photons in a new model of interpolating Hamiltonians

NASA Astrophysics Data System (ADS)

Valverde, Clodoaldo; Baseia, Basílio

2018-01-01

We introduce a new Hamiltonian model which interpolates between the Jaynes-Cummings model (JCM) and other types of such Hamiltonians. It works with two interpolating parameters, rather than one as traditional. Taking advantage of this greater degree of freedom, we can perform continuous interpolation between the various types of these Hamiltonians. As applications, we discuss a paradox raised in literature and compare the time evolution of the photon statistics obtained in the various interpolating models. The role played by the average excitation in these comparisons is also highlighted.

Hamiltonian vs Lagrangian Embedding of a Massive Spin-One Theory Involving Two-Form Field

NASA Astrophysics Data System (ADS)

Harikumar, E.; Sivakumar, M.

We consider the Hamiltonian and Lagrangian embedding of a first-order, massive spin-one, gauge noninvariant theory involving antisymmetric tensor field. We apply the BFV-BRST generalized canonical approach to convert the model to a first class system and construct nilpotent BFV-BRST charge and a unitarizing Hamiltonian. The canonical analysis of the Stückelberg formulation of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the Lagrangian embedded model. We show that to obtain manifestly covariant Stückelberg Lagrangian from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.

R matrices of three-state Hamiltonians solvable by coordinate Bethe ansatz

NASA Astrophysics Data System (ADS)

Fonseca, T.; Frappat, L.; Ragoucy, E.

2015-01-01

We review some of the strategies that can be implemented to infer an R-matrix from the knowledge of its Hamiltonian. We apply them to the classification achieved in Crampé, Frappat, and Ragoucy, J. Phys. A 46, 405001 (2013), on three state U(1)-invariant Hamiltonians solvable by coordinate Bethe ansatz, focusing on models for which the S-matrix is not trivial. For the 19-vertex solutions, we recover the R-matrices of the well-known Zamolodchikov-Fateev and Izergin-Korepin models. We point out that the generalized Bariev Hamiltonian is related to both main and special branches studied by Martins in Nucl. Phys. B 874, 243 (2013), that we prove to generate the same Hamiltonian. The 19-vertex SpR model still resists to the analysis, although we are able to state some no-go theorems on its R-matrix. For 17-vertex Hamiltonians, we produce a new R-matrix.

Microscopic study of spin cut-off factors of nuclear level densities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gholami, M.; Kildir, M.; Behkami, A. N.

Level densities and spin cut-off factors have been investigated within the microscopic approach based on the BCS Hamiltonian. In particular, the spin cut-off parameters have been calculated at neutron binding energies over a large range of nuclear mass using the BCS theory. The spin cut-off parameters {sigma}{sup 2}(E) have also been obtained from the Gilbert and Cameron expression and from rigid body calculations. The results were compared with their corresponding macroscopic values. It was found that the values of {sigma}{sup 2}(E) did not increase smoothly with A as expected based on macroscopic theory. Instead, the values of {sigma}{sup 2}(E) showmore » structure reflecting the angular momentum of the shell model orbitals near the Fermi energy.« less

A Synthetical Two-Component Model with Peakon Solutions: One More Bi-Hamiltonian Case

NASA Astrophysics Data System (ADS)

Mengxia, Zhang; Xiaomin, Yang

2018-05-01

Compatible pairs of Hamiltonian operators for the synthetical two-component model of Xia, Qiao, and Zhou are derived systematically by means of the spectral gradient method. A new two-component system, which is bi-Hamiltonian, is presented. For this new system, the construction of its peakon solutions is considered.

Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag

NASA Astrophysics Data System (ADS)

Xu, Beibei; Chen, Diyi; Zhang, Hao; Wang, Feifei; Zhang, Xinguang; Wu, Yonghong

2017-06-01

This paper focus on a Hamiltonian mathematical modeling for a hydro-turbine governing system including fractional item and time-lag. With regards to hydraulic pressure servo system, a universal dynamical model is proposed, taking into account the viscoelastic properties and low-temperature impact toughness of constitutive materials as well as the occurrence of time-lag in the signal transmissions. The Hamiltonian model of the hydro-turbine governing system is presented using the method of orthogonal decomposition. Furthermore, a novel Hamiltonian function that provides more detailed energy information is presented, since the choice of the Hamiltonian function is the key issue by putting the whole dynamical system to the theory framework of the generalized Hamiltonian system. From the numerical experiments based on a real large hydropower station, we prove that the Hamiltonian function can describe the energy variation of the hydro-turbine suitably during operation. Moreover, the effect of the fractional α and the time-lag τ on the dynamic variables of the hydro-turbine governing system are explored and their change laws identified, respectively. The physical meaning between fractional calculus and time-lag are also discussed in nature. All of the above theories and numerical results are expected to provide a robust background for the safe operation and control of large hydropower stations.

Combining the spin-separated exact two-component relativistic Hamiltonian with the equation-of-motion coupled-cluster method for the treatment of spin-orbit splittings of light and heavy elements.

PubMed

Cao, Zhanli; Li, Zhendong; Wang, Fan; Liu, Wenjian

2017-02-01

The spin-separated exact two-component (X2C) relativistic Hamiltonian [sf-X2C+so-DKHn, J. Chem. Phys., 2012, 137, 154114] is combined with the equation-of-motion coupled-cluster method with singles and doubles (EOM-CCSD) for the treatment of spin-orbit splittings of open-shell molecular systems. Scalar relativistic effects are treated to infinite order from the outset via the spin-free part of the X2C Hamiltonian (sf-X2C), whereas the spin-orbit couplings (SOC) are handled at the CC level via the first-order Douglas-Kroll-Hess (DKH) type of spin-orbit operator (so-DKH1). Since the exponential of single excitations, i.e., exp(T 1 ), introduces sufficient spin orbital relaxations, the inclusion of SOC at the CC level is essentially the same in accuracy as the inclusion of SOC from the outset in terms of the two-component spinors determined variationally by the sf-X2C+so-DKH1 Hamiltonian, but is computationally more efficient. Therefore, such an approach (denoted as sf-X2C-EOM-CCSD(SOC)) can achieve uniform accuracy for the spin-orbit splittings of both light and heavy elements. For light elements, the treatment of SOC can even be postponed until the EOM step (denoted as sf-X2C-EOM(SOC)-CCSD), so as to further reduce the computational cost. To reveal the efficacy of sf-X2C-EOM-CCSD(SOC) and sf-X2C-EOM(SOC)-CCSD, the spin-orbit splittings of the 2 Π states of monohydrides up to the sixth row of the periodic table are investigated. The results show that sf-X2C-EOM-CCSD(SOC) predicts very accurate results (within 5%) for elements up to the fifth row, whereas sf-X2C-EOM(SOC)-CCSD is useful only for light elements (up to the third row but with some exceptions). For comparison, the sf-X2C-S-TD-DFT-SOC approach [spin-adapted open-shell time-dependent density functional theory, Mol. Phys., 2013, 111, 3741] is applied to the same systems. The overall accuracy (1-10%) is satisfactory.

ELECTRON-CAPTURE AND β-DECAY RATES FOR sd-SHELL NUCLEI IN STELLAR ENVIRONMENTS RELEVANT TO HIGH-DENSITY O–NE–MG CORES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suzuki, Toshio; Toki, Hiroshi; Nomoto, Ken’ichi, E-mail: suzuki@phys.chs.nihon-u.ac.jp

Electron-capture and β-decay rates for nuclear pairs in the sd-shell are evaluated at high densities and high temperatures relevant to the final evolution of electron-degenerate O–Ne–Mg cores of stars with initial masses of 8–10 M{sub ⊙}. Electron capture induces a rapid contraction of the electron-degenerate O–Ne–Mg core. The outcome of rapid contraction depends on the evolutionary changes in the central density and temperature, which are determined by the competing processes of contraction, cooling, and heating. The fate of the stars is determined by these competitions, whether they end up with electron-capture supernovae or Fe core-collapse supernovae. Since the competing processes aremore » induced by electron capture and β-decay, the accurate weak rates are crucially important. The rates are obtained for pairs with A = 20, 23, 24, 25, and 27 by shell-model calculations in the sd-shell with the USDB Hamiltonian. Effects of Coulomb corrections on the rates are evaluated. The rates for pairs with A = 23 and 25 are important for nuclear Urca processes that determine the cooling rate of the O–Ne–Mg core, while those for pairs with A = 20 and 24 are important for the core contraction and heat generation rates in the core. We provide these nuclear rates at stellar environments in tables with fine enough meshes at various densities and temperatures for studies of astrophysical processes sensitive to the rates. In particular, the accurate rate tables are crucially important for the final fates of not only O–Ne–Mg cores but also a wider range of stars, such as C–O cores of lower-mass stars.« less

The Artificial Hamiltonian, First Integrals, and Closed-Form Solutions of Dynamical Systems for Epidemics

NASA Astrophysics Data System (ADS)

Naz, Rehana; Naeem, Imran

2018-03-01

The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.

Hamiltonian models for topological phases of matter in three spatial dimensions

NASA Astrophysics Data System (ADS)

Williamson, Dominic J.; Wang, Zhenghan

2017-02-01

We present commuting projector Hamiltonian realizations of a large class of (3 + 1)D topological models based on mathematical objects called unitary G-crossed braided fusion categories. This construction comes with a wealth of examples from the literature of symmetry-enriched topological phases. The spacetime counterparts to our Hamiltonians are unitary state sum topological quantum fields theories (TQFTs) that appear to capture all known constructions in the literature, including the Crane-Yetter-Walker-Wang and 2-Group gauge theory models. We also present Hamiltonian realizations of a state sum TQFT recently constructed by Kashaev whose relation to existing models was previously unknown. We argue that this TQFT is captured as a special case of the Crane-Yetter-Walker-Wang model, with a premodular input category in some instances.

Exploring corrections to the Optomechanical Hamiltonian.

PubMed

Sala, Kamila; Tufarelli, Tommaso

2018-06-14

We compare two approaches for deriving corrections to the "linear model" of cavity optomechanics, in order to describe effects that are beyond first order in the radiation pressure coupling. In the regime where the mechanical frequency is much lower than the cavity one, we compare: (I) a widely used phenomenological Hamiltonian conserving the photon number; (II) a two-mode truncation of C. K. Law's microscopic model, which we take as the "true" system Hamiltonian. While these approaches agree at first order, the latter model does not conserve the photon number, resulting in challenging computations. We find that approach (I) allows for several analytical predictions, and significantly outperforms the linear model in our numerical examples. Yet, we also find that the phenomenological Hamiltonian cannot fully capture all high-order corrections arising from the C. K. Law model.

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar

2016-06-15

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators aremore » useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.« less

Potentials of Mean Force With Ab Initio Mixed Hamiltonian Models of Solvation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dupuis, Michel; Schenter, Gregory K.; Garrett, Bruce C.

2003-08-01

We give an account of a computationally tractable and efficient procedure for the calculation of potentials of mean force using mixed Hamiltonian models of electronic structure where quantum subsystems are described with computationally intensive ab initio wavefunctions. The mixed Hamiltonian is mapped into an all-classical Hamiltonian that is amenable to a thermodynamic perturbation treatment for the calculation of free energies. A small number of statistically uncorrelated (solute-solvent) configurations are selected from the Monte Carlo random walk generated with the all-classical Hamiltonian approximation. Those are used in the averaging of the free energy using the mixed quantum/classical Hamiltonian. The methodology ismore » illustrated for the micro-solvated SN2 substitution reaction of methyl chloride by hydroxide. We also compare the potential of mean force calculated with the above protocol with an approximate formalism, one in which the potential of mean force calculated with the all-classical Hamiltonian is simply added to the energy of the isolated (non-solvated) solute along the reaction path. Interestingly the latter approach is found to be in semi-quantitative agreement with the full mixed Hamiltonian approximation.« less

Benchmarking Inverse Statistical Approaches for Protein Structure and Design with Exactly Solvable Models.

PubMed

Jacquin, Hugo; Gilson, Amy; Shakhnovich, Eugene; Cocco, Simona; Monasson, Rémi

2016-05-01

Inverse statistical approaches to determine protein structure and function from Multiple Sequence Alignments (MSA) are emerging as powerful tools in computational biology. However the underlying assumptions of the relationship between the inferred effective Potts Hamiltonian and real protein structure and energetics remain untested so far. Here we use lattice protein model (LP) to benchmark those inverse statistical approaches. We build MSA of highly stable sequences in target LP structures, and infer the effective pairwise Potts Hamiltonians from those MSA. We find that inferred Potts Hamiltonians reproduce many important aspects of 'true' LP structures and energetics. Careful analysis reveals that effective pairwise couplings in inferred Potts Hamiltonians depend not only on the energetics of the native structure but also on competing folds; in particular, the coupling values reflect both positive design (stabilization of native conformation) and negative design (destabilization of competing folds). In addition to providing detailed structural information, the inferred Potts models used as protein Hamiltonian for design of new sequences are able to generate with high probability completely new sequences with the desired folds, which is not possible using independent-site models. Those are remarkable results as the effective LP Hamiltonians used to generate MSA are not simple pairwise models due to the competition between the folds. Our findings elucidate the reasons for the success of inverse approaches to the modelling of proteins from sequence data, and their limitations.

Random crystal field effect on the magnetic and hysteresis behaviors of a spin-1 cylindrical nanowire

NASA Astrophysics Data System (ADS)

Zaim, N.; Zaim, A.; Kerouad, M.

2017-02-01

In this work, the magnetic behavior of the cylindrical nanowire, consisting of a ferromagnetic core of spin-1 atoms surrounded by a ferromagnetic shell of spin-1 atoms is studied in the presence of a random crystal field interaction. Based on Metropolis algorithm, the Monte Carlo simulation has been used to investigate the effects of the concentration of the random crystal field p, the crystal field D and the shell exchange interaction Js on the phase diagrams and the hysteresis behavior of the system. Some characteristic behaviors have been found, such as the first and second-order phase transitions joined by tricritical point for appropriate values of the system parameters, triple and isolated critical points can be also found. Depending on the Hamiltonian parameters, single, double and para hysteresis regions are explicitly determined.

Approximate theoretical model for the five electronic states ( Ω = 5/2, 3/2, 3/2, 1/2, 1/2) arising from the ground 3d 9 configuration in nickel halide molecules and for rotational levels of the two Ω = 1/2 states in that manifold

NASA Astrophysics Data System (ADS)

Hougen, Jon T.

2011-05-01

In the first part of this paper an effective Hamiltonian for a non-rotating diatomic molecule containing only crystal-field and spin-orbit operators is set up to describe the energies of the five spin-orbit components that arise in the ground electronic configuration of the nickel monohalides. The model assumes that bonding in the nickel halides has the approximate form Ni +X -, with an electronic 3d 9 configuration plus closed shells on the Ni + moiety and a closed shell configuration on the X - moiety. From a crystal-field point of view, interactions of the positive d-hole with the cylindrically symmetrical electric charge distribution of the hypothetical NiX - closed-shell core can then be parameterized by three terms in a traditional expansion in spherical harmonics: C0 + C2Y20( θ, ϕ) + C4Y40( θ, ϕ). Interaction of the hole with the magnetic field generated by its own orbital motion can be parameterized by a traditional spin-orbit interaction operator A L · S. The Hamiltonian matrix is set up in a basis set consisting of the 10 Hund's case (a) basis functions | L, Λ; S , Σ> that arise when L = 2 and S = 1/2. Least-squares fits of the observed five spin-orbit components of the three lowest electronic states in NiF and NiCl are then carried out in terms of the four parameters C0, C2, C4, and A which lead to good agreement, except for the two | Ω| = 1/2 states. The large equal and opposite residuals of the | Ω| = 1/2 states can be reduced to values comparable with those for the | Ω| = 3/2 and | Ω| = 5/2 states by fixing A to its value in Ni + and then introducing an empirical correction factor for one off-diagonal orbital matrix element. In the second part of this paper the usual effective Hamiltonian B( J- L- S) 2 for a rotating diatomic molecule is used to derive expressions for the Ω-type doubling parameter p in the two | Ω| = 1/2 states. These expressions show (for certain sign conventions) that the sum of the two p values should be -2 B, but that their difference can vary between -10 B and +10 B. These theoretical results are in good agreement with the two observed p values for both NiF and NiCl. The present formalism should in principle be applicable to NiBr and NiI, and to the halides of palladium, since Pd + has a well isolated 4d 9 electronic ground configuration. Extension to metal halides having d n configurations with n < 9, or to platinum halides may present difficulties, since manifolds from the d n and d n-1s configurations may be heavily mixed, thus requiring "too many" parameters in the electronic part of the problem. Application to linear triatomic molecules may also present problems because of the large number of vibronic perturbations made possible by their four vibrational degrees of freedom.

The emergence of collective phenomena in systems with random interactions

NASA Astrophysics Data System (ADS)

Abramkina, Volha

Emergent phenomena are one of the most profound topics in modern science, addressing the ways that collectivities and complex patterns appear due to multiplicity of components and simple interactions. Ensembles of random Hamiltonians allow one to explore emergent phenomena in a statistical way. In this work we adopt a shell model approach with a two-body interaction Hamiltonian. The sets of the two-body interaction strengths are selected at random, resulting in the two-body random ensemble (TBRE). Symmetries such as angular momentum, isospin, and parity entangled with complex many-body dynamics result in surprising order discovered in the spectrum of low-lying excitations. The statistical patterns exhibited in the TBRE are remarkably similar to those observed in real nuclei. Signs of almost every collective feature seen in nuclei, namely, pairing superconductivity, deformation, and vibration, have been observed in random ensembles [3, 4, 5, 6]. In what follows a systematic investigation of nuclear shape collectivities in random ensembles is conducted. The development of the mean field, its geometry, multipole collectivities and their dependence on the underlying two-body interaction are explored. Apart from the role of static symmetries such as SU(2) angular momentum and isospin groups, the emergence of dynamical symmetries including the seniority SU(2), rotational symmetry, as well as the Elliot SU(3) is shown to be an important precursor for the existence of geometric collectivities.

Some preliminary calculations of whole atom Compton scattering of unpolarized photons

NASA Astrophysics Data System (ADS)

Bergstrom, P. M.; Surić, T.; Pisk, K.; Pratt, R. H.

1992-07-01

This paper represents a preliminary attempt to develop a practical prescription for calculating whole atom cross sections for the Compton scattering of unpolarized photons from the bound electrons of an atom for the entire spectrum of scattered photon energies. We initially study the scattering of 2.94 keV photons from carbon. We make use of our new second order S-matrix computer code in this case to verify that, when our recently developed criterion for the validity of the relativistic impulse approximation (which concerns the average momentum contributing to the photon spectrum ( pav)) is satisfied, the spectrum is adequately described by the impulse approximation. This criterion is generally satisfied in the peak intensity region for scattering by the outer shells, which dominate at these scattered photon energies. For soft scattered photons, however, the spectrum, dominated by K shell contributions, is given by terms corresponding to the contribution of the " p· A" term in the nonrelativistic interaction Hamiltonian, not included in the impulse approximation. Here, the spectrum is adequately reproduced by the K shell contribution. We then consider scattering of 17.4 keV photons from aluminum and 279.1 keV photons from lead. In these cases we use the S-matrix for the K shell and the impulse approximation for the outer shells, and find good agreement with experiment.

Scaling Limit for a Generalization of the Nelson Model and its Application to Nuclear Physics

NASA Astrophysics Data System (ADS)

Suzuki, Akito

We study a mathematically rigorous derivation of a quantum mechanical Hamiltonian in a general framework. We derive such a Hamiltonian by taking a scaling limit for a generalization of the Nelson model, which is an abstract interaction model between particles and a Bose field with some internal degrees of freedom. Applying it to a model for the field of the nuclear force with isospins, we obtain a Schrödinger Hamiltonian with a matrix-valued potential, the one pion exchange potential, describing an effective interaction between nucleons.

Operator evolution for ab initio electric dipole transitions of 4He

DOE PAGES

Schuster, Micah D.; Quaglioni, Sofia; Johnson, Calvin W.; ...

2015-07-24

A goal of nuclear theory is to make quantitative predictions of low-energy nuclear observables starting from accurate microscopic internucleon forces. A major element of such an effort is applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence of ab initio calculations as a function of the model space size. The consistent simultaneous transformation of external operators, however, has been overlooked in applications of the theory, particularly for nonscalar transitions. We study the evolution of the electric dipole operator in the framework of the similarity renormalization group method and apply the renormalized matrix elements to the calculationmore » of the 4He total photoabsorption cross section and electric dipole polarizability. All observables are calculated within the ab initio no-core shell model. Furthermore, we find that, although seemingly small, the effects of evolved operators on the photoabsorption cross section are comparable in magnitude to the correction produced by including the chiral three-nucleon force and cannot be neglected.« less

Modified n-level, n - 1-mode Tavis-Cummings model and algebraic Bethe ansatz

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2018-01-01

Using the quantum group technique we construct a one-parametric family of integrable modifications of the n-level, n-1 mode Tavis-Cummings Hamiltonian possessing an additional Stark-type term. We show that in the ‘quasiclassical’ limit the constructed Hamiltonian transforms into the integrable Hamiltonian of the quantum n-level, n-1 mode Tavis-Cummings model with the equal interaction strengths considered in Skrypnyk (2008 J. Phys. A: Math. Theor. 41 475202, 2009 J. Math. Phys. 50 103523). We diagonalize the constructed ‘modified’ Tavis-Cummings Hamiltonian and its second order integrals of motion using the nested Bethe ansatz.

Magnetic anisotropy in binuclear complexes in the weak-exchange limit: From the multispin to the giant-spin Hamiltonian

NASA Astrophysics Data System (ADS)

Maurice, Rémi; de Graaf, Coen; Guihéry, Nathalie

2010-06-01

This paper studies the physical basis of the giant-spin Hamiltonian, which is usually used to describe the anisotropy of single-molecule magnets. A rigorous extraction of the model has been performed in the weak-exchange limit of a binuclear centrosymmetric Ni(II) complex, using correlated ab initio calculations and effective Hamiltonian theory. It is shown that the giant-spin Hamiltonian is not appropriate to describe polynuclear complexes as soon as spin mixing becomes non-negligible. A relevant model is proposed involving fourth-order operators, different from the traditionally used Stevens operators. The new giant-spin Hamiltonian correctly reproduces the effects of the spin mixing in the weak-exchange limit. A procedure to switch on and off the spin mixing in the extraction has been implemented in order to separate this effect from other anisotropic effects and to numerically evaluate both contributions to the tunnel splitting. Furthermore, the new giant-spin Hamiltonian has been derived analytically from the multispin Hamiltonian at the second order of perturbation and the theoretical link between the two models is studied to gain understanding concerning the microscopic origin of the fourth-order interaction in terms of axial, rhombic, or mixed (axial-rhombic) character. Finally, an adequate method is proposed to extract the proper magnetic axes frame for polynuclear anisotropic systems.

Canonical formulation and conserved charges of double field theory

DOE PAGES

Naseer, Usman

2015-10-26

We provide the canonical formulation of double field theory. It is shown that this dynamics is subject to primary and secondary constraints. The Poisson bracket algebra of secondary constraints is shown to close on-shell according to the C-bracket. We also give a systematic way of writing boundary integrals in doubled geometry. Finally, by including appropriate boundary terms in the double field theory Hamiltonian, expressions for conserved energy and momentum of an asymptotically flat doubled space-time are obtained and applied to a number of solutions.

Universal Adiabatic Quantum Computing using Double Quantum Dot Charge Qubits

NASA Astrophysics Data System (ADS)

Ryan-Anderson, Ciaran; Jacobson, N. Tobias; Landahl, Andrew

Adiabatic quantum computation (AQC) provides one path to achieving universal quantum computing in experiment. Computation in the AQC model occurs by starting with an easy to prepare groundstate of some simple Hamiltonian and then adiabatically evolving the Hamiltonian to obtain the groundstate of a final, more complex Hamiltonian. It has been shown that the circuit model can be mapped to AQC Hamiltonians and, thus, AQC can be made universal. Further, these Hamiltonians can be made planar and two-local. We propose using double quantum dot charge qubits (DQDs) to implement such universal AQC Hamiltonians. However, the geometry and restricted set of interactions of DQDs make the application of even these 2-local planar Hamiltonians non-trivial. We present a construction tailored to DQDs to overcome the geometric and interaction contraints and allow for universal AQC. These constraints are dealt with in this construction by making use of perturbation gadgets, which introduce ancillary qubits to mediate interactions. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

A unified theoretical framework for mapping models for the multi-state Hamiltonian.

PubMed

Liu, Jian

2016-11-28

We propose a new unified theoretical framework to construct equivalent representations of the multi-state Hamiltonian operator and present several approaches for the mapping onto the Cartesian phase space. After mapping an F-dimensional Hamiltonian onto an F+1 dimensional space, creation and annihilation operators are defined such that the F+1 dimensional space is complete for any combined excitation. Commutation and anti-commutation relations are then naturally derived, which show that the underlying degrees of freedom are neither bosons nor fermions. This sets the scene for developing equivalent expressions of the Hamiltonian operator in quantum mechanics and their classical/semiclassical counterparts. Six mapping models are presented as examples. The framework also offers a novel way to derive such as the well-known Meyer-Miller model.

Low- and high-spin iron (II) complexes studied by effective crystal field method combined with molecular mechanics.

PubMed

Darkhovskii, M B; Pletnev, I V; Tchougréeff, A L

2003-11-15

A computational method targeted to Werner-type complexes is developed on the basis of quantum mechanical effective Hamiltonian crystal field (EHCF) methodology (previously proposed for describing electronic structure of transition metal complexes) combined with the Gillespie-Kepert version of molecular mechanics (MM). It is a special version of the hybrid quantum/MM approach. The MM part is responsible for representing the whole molecule, including ligand atoms and metal ion coordination sphere, but leaving out the effects of the d-shell. The quantum mechanical EHCF part is limited to the metal ion d-shell. The method reproduces with reasonable accuracy geometry and spin states of the Fe(II) complexes with monodentate and polydentate aromatic ligands with nitrogen donor atoms. In this setting a single set of MM parameters set is shown to be sufficient for handling all spin states of the complexes under consideration. Copyright 2003 Wiley Periodicals, Inc.

Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perin, M.; Chandre, C.; Tassi, E.

2015-09-15

Moment closures of the Vlasov-Ampère system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two, and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary numbermore » of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed.« less

Twisted quantum double model of topological order with boundaries

NASA Astrophysics Data System (ADS)

Bullivant, Alex; Hu, Yuting; Wan, Yidun

2017-10-01

We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group G and a 3-cocycle in the third cohomology group of G over U (1 ) , a boundary Hamiltonian can be defined by a subgroup K of G and a 2-cochain in the second cochain group of K over U (1 ) . The consistency between the bulk and boundary Hamiltonians is dictated by what we call the Frobenius condition that constrains the 2-cochain given the 3-cocyle. We offer a closed-form formula computing the ground-state degeneracy of the model on a cylinder in terms of the input data only, which can be naturally generalized to surfaces with more boundaries. We also explicitly write down the ground-state wave function of the model on a disk also in terms of the input data only.

Construction of Hamiltonians by supervised learning of energy and entanglement spectra

NASA Astrophysics Data System (ADS)

Fujita, Hiroyuki; Nakagawa, Yuya O.; Sugiura, Sho; Oshikawa, Masaki

2018-02-01

Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter, nuclear, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is generically impossible to treat these problems from first principles. Thus the construction of a proper model, namely, effective Hamiltonian, is essential. Here, we propose a simple supervised learning algorithm for constructing Hamiltonians from given energy or entanglement spectra. We apply the proposed scheme to the Hubbard model at the half-filling, and compare the obtained effective low-energy spin model with several analytic results based on the high-order perturbation theory, which have been inconsistent with each other. We also show that our approach can be used to construct the entanglement Hamiltonian of a quantum many-body state from its entanglement spectrum as well. We exemplify this using the ground states of the S =1 /2 two-leg Heisenberg ladders. We observe a qualitative difference between the entanglement Hamiltonians of the two phases (the Haldane and the rung singlet phase) of the model due to the different origin of the entanglement. In the Haldane phase, we find that the entanglement Hamiltonian is nonlocal by nature, and the locality can be restored by introducing the anisotropy and turning the ground state into the large-D phase. Possible applications to the model construction from experimental data and to various problems of strongly correlated systems are discussed.

Hamiltonian identifiability assisted by single-probe measurement

NASA Astrophysics Data System (ADS)

Sone, Akira; Cappellaro, Paola; Quantum Engineering Group Team

2017-04-01

We study the Hamiltonian identifiability of a many-body spin- 1 / 2 system assisted by the measurement on a single quantum probe based on the eigensystem realization algorithm (ERA) approach employed in. We demonstrate a potential application of Gröbner basis to the identifiability test of the Hamiltonian, and provide the necessary experimental resources, such as the lower bound in the number of the required sampling points, the upper bound in total required evolution time, and thus the total measurement time. Focusing on the examples of the identifiability in the spin chain model with nearest-neighbor interaction, we classify the spin-chain Hamiltonian based on its identifiability, and provide the control protocols to engineer the non-identifiable Hamiltonian to be an identifiable Hamiltonian.

Branched Hamiltonians and supersymmetry

DOE PAGES

Curtright, Thomas L.; Zachos, Cosmas K.

2014-03-21

Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback potentials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian chaotic dynamical systems in a classical setting, and as encountered in analogous renormalization group flows for quantum theories which exhibit RG cycles. In conclusion, a basic two-worlds model, with a pair of Hamiltonian branches related by supersymmetry, is considered in detail.

The quantization of the chiral Schwinger model based on the BFT - BFV formalism

NASA Astrophysics Data System (ADS)

Kim, Won T.; Kim, Yong-Wan; Park, Mu-In; Park, Young-Jai; Yoon, Sean J.

1997-03-01

We apply the newly improved Batalin - Fradkin - Tyutin (BFT) Hamiltonian method to the chiral Schwinger model in the case of the regularization ambiguity a>1. We show that one can systematically construct the first class constraints by the BFT Hamiltonian method, and also show that the well-known Dirac brackets of the original phase space variables are exactly the Poisson brackets of the corresponding modified fields in the extended phase space. Furthermore, we show that the first class Hamiltonian is simply obtained by replacing the original fields in the canonical Hamiltonian by these modified fields. Performing the momentum integrations, we obtain the corresponding first class Lagrangian in the configuration space.

Shell-model-like approach based on cranking covariant density functional theory: Band crossing and shape evolution in 60Fe

NASA Astrophysics Data System (ADS)

Shi, Z.; Zhang, Z. H.; Chen, Q. B.; Zhang, S. Q.; Meng, J.

2018-03-01

The shell-model-like approach is implemented to treat the cranking many-body Hamiltonian based on the covariant density functional theory including pairing correlations with exact particle number conservation. The self-consistency is achieved by iterating the single-particle occupation probabilities back to the densities and currents. As an example, the rotational structures observed in the neutron-rich nucleus 60Fe are investigated and analyzed. Without introducing any ad hoc parameters, the bandheads, the rotational spectra, and the relations between the angular momentum and rotational frequency for the positive-parity band A and negative-parity bands B and C are well reproduced. The essential role of the pairing correlations is revealed. It is found that for band A, the band crossing is due to the change of the last two occupied neutrons from the 1 f5 /2 signature partners to the 1 g9 /2 signature partners. For the two negative-parity signature partner bands B and C, the band crossings are due to the pseudocrossing between the 1 f7 /2 ,5 /2 and the 1 f5 /2 ,1 /2 orbitals. Generally speaking, the deformation parameters β for bands A, B, and C decrease with rotational frequency. For band A, the deformation jumps from β ≈0.19 to β ≈0.29 around the band crossing. In comparison with its signature partner band C, band B exhibits appreciable triaxial deformation.

Nonholonomic Hamiltonian Method for Meso-macroscale Simulations of Reacting Shocks

NASA Astrophysics Data System (ADS)

Fahrenthold, Eric; Lee, Sangyup

2015-06-01

The seamless integration of macroscale, mesoscale, and molecular scale models of reacting shock physics has been hindered by dramatic differences in the model formulation techniques normally used at different scales. In recent research the authors have developed the first unified discrete Hamiltonian approach to multiscale simulation of reacting shock physics. Unlike previous work, the formulation employs reacting themomechanical Hamiltonian formulations at all scales, including the continuum. Unlike previous work, the formulation employs a nonholonomic modeling approach to systematically couple the models developed at all scales. Example applications of the method show meso-macroscale shock to detonation simulations in nitromethane and RDX. Research supported by the Defense Threat Reduction Agency.

Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics

PubMed Central

2017-01-01

We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics. PMID:28932256

Hamiltonian Effective Field Theory Study of the N^{*}(1535) Resonance in Lattice QCD.

PubMed

Liu, Zhan-Wei; Kamleh, Waseem; Leinweber, Derek B; Stokes, Finn M; Thomas, Anthony W; Wu, Jia-Jun

2016-02-26

Drawing on experimental data for baryon resonances, Hamiltonian effective field theory (HEFT) is used to predict the positions of the finite-volume energy levels to be observed in lattice QCD simulations of the lowest-lying J^{P}=1/2^{-} nucleon excitation. In the initial analysis, the phenomenological parameters of the Hamiltonian model are constrained by experiment and the finite-volume eigenstate energies are a prediction of the model. The agreement between HEFT predictions and lattice QCD results obtained on volumes with spatial lengths of 2 and 3 fm is excellent. These lattice results also admit a more conventional analysis where the low-energy coefficients are constrained by lattice QCD results, enabling a determination of resonance properties from lattice QCD itself. Finally, the role and importance of various components of the Hamiltonian model are examined.

Hamiltonian modelling of relative motion.

PubMed

Kasdin, N Jeremy; Gurfil, Pini

2004-05-01

This paper presents a Hamiltonian approach to modelling relative spacecraft motion based on derivation of canonical coordinates for the relative state-space dynamics. The Hamiltonian formulation facilitates the modelling of high-order terms and orbital perturbations while allowing us to obtain closed-form solutions to the relative motion problem. First, the Hamiltonian is partitioned into a linear term and a high-order term. The Hamilton-Jacobi equations are solved for the linear part by separation, and new constants for the relative motions are obtained, they are called epicyclic elements. The influence of higher order terms and perturbations, such as the oblateness of the Earth, are incorporated into the analysis by a variation of parameters procedure. Closed-form solutions for J(2-) and J(4-)invariant orbits and for periodic high-order unperturbed relative motion, in terms of the relative motion elements only, are obtained.

Finite Group Invariance and Solution of Jaynes-Cummings Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haydargil, Derya; Koc, Ramazan

2004-10-04

The finite group invariance of the E x {beta} and Jaynes-Cummings models are studied. A method is presented to obtain finite group invariance of the E x {beta} system.A suitable transformation of a Jaynes-Cummings Hamiltonian leads to equivalence of E x {beta} system. Then a general method is applied to obtain the solution of Jaynes-Cummings Hamiltonian with Kerr nonlinearity. Number operator for this structure and the generators of su(2) algebra are used to find the eigenvalues of the Jaynes-Cummings Hamiltonian for different states. By using the invariance of number operator the solution of modified Jaynes-Cummings Hamiltonian is also discussed.

The Schwinger Model on S 1: Hamiltonian Formulation, Vacuum and Anomaly

NASA Astrophysics Data System (ADS)

Stuart, David

2014-12-01

We present a Hamiltonian formulation of the Schwinger model with spatial domain taken to be the circle. It is shown that, in Coulomb gauge, the Hamiltonian is a semi-bounded, self-adjoint operator which is invariant under the group of large gauge transformations. There is a nontrivial action of on fermionic Fock space and its vacuum. This action plays a role analogous to that played by the spectral flow in the infinite Dirac sea formalism. The formulation allows (1) a description of the anomaly and its relation to the group action, and (2) an explicit identification of the vacuum. The anomaly in the chiral conservation law appears as a consequence of insisting upon semi-boundedness and gauge invariance of the quantized Hamiltonian.

Bounded Hamiltonian in the Fourth-Order Extension of the Chern-Simons Theory

NASA Astrophysics Data System (ADS)

Abakumova, V. A.; Kaparulin, D. S.; Lyakhovich, S. L.

2018-04-01

The problem of constructing alternative Hamiltonian formulations in the extended Chern-Simons theory with higher derivatives is considered. It is shown that the fourth-order extended theory admits a four-parameter series of alternative Hamiltonians which can be bounded from below, even if the canonical energy of the model is unbounded from below.

A study of the linear free energy model for DNA structures using the generalized Hamiltonian formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yavari, M., E-mail: yavari@iaukashan.ac.ir

2016-06-15

We generalize the results of Nesterenko [13, 14] and Gogilidze and Surovtsev [15] for DNA structures. Using the generalized Hamiltonian formalism, we investigate solutions of the equilibrium shape equations for the linear free energy model.

Deuteron-induced nucleon transfer reactions within an ab initio framework: First application to p -shell nuclei

DOE PAGES

Raimondi, Francesco; Hupin, Guillaume; Navratil, Petr; ...

2016-05-10

Low-energy transfer reactions in which a proton is stripped from a deuteron projectile and dropped into a target play a crucial role in the formation of nuclei in both primordial and stellar nucleosynthesis, as well as in the study of exotic nuclei using radioactive beam facilities and inverse kinematics. Here, ab initio approaches have been successfully applied to describe the 3H(d,n) 4He and 3He(d,p) 4He fusion processes. An ab initio treatment of transfer reactions would also be desirable for heavier targets. In this work, we extend the ab initio description of (d,p) reactions to processes with light p-shell nuclei. Asmore » a first application, we study the elastic scattering of deuterium on 7Li and the 7Li(d,p) 8Li transfer reaction based on a two-body Hamiltonian. We use the no-core shell model to compute the wave functions of the nuclei involved in the reaction, and describe the dynamics between targets and projectiles with the help of microscopic-cluster states in the spirit of the resonating group method. The shapes of the excitation functions for deuterons impinging on 7Li are qualitatively reproduced up to the deuteron breakup energy. The interplay between d– 7Li and p– 8Li particle-decay channels determines some features of the 9Be spectrum above the d+ 7Li threshold. Our prediction for the parity of the 17.298 MeV resonance is at odds with the experimental assignment. Deuteron stripping reactions with p-shell targets can now be computed ab initio, but calculations are very demanding. Finally, a quantitative description of the 7Li(d,p) 8Li reaction will require further work to include the effect of three-nucleon forces and additional decay channels and to improve the convergence rate of our calculations.« less

Deuteron-induced nucleon transfer reactions within an ab initio framework: First application to p -shell nuclei

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raimondi, Francesco; Hupin, Guillaume; Navratil, Petr

Low-energy transfer reactions in which a proton is stripped from a deuteron projectile and dropped into a target play a crucial role in the formation of nuclei in both primordial and stellar nucleosynthesis, as well as in the study of exotic nuclei using radioactive beam facilities and inverse kinematics. Here, ab initio approaches have been successfully applied to describe the 3H(d,n) 4He and 3He(d,p) 4He fusion processes. An ab initio treatment of transfer reactions would also be desirable for heavier targets. In this work, we extend the ab initio description of (d,p) reactions to processes with light p-shell nuclei. Asmore » a first application, we study the elastic scattering of deuterium on 7Li and the 7Li(d,p) 8Li transfer reaction based on a two-body Hamiltonian. We use the no-core shell model to compute the wave functions of the nuclei involved in the reaction, and describe the dynamics between targets and projectiles with the help of microscopic-cluster states in the spirit of the resonating group method. The shapes of the excitation functions for deuterons impinging on 7Li are qualitatively reproduced up to the deuteron breakup energy. The interplay between d– 7Li and p– 8Li particle-decay channels determines some features of the 9Be spectrum above the d+ 7Li threshold. Our prediction for the parity of the 17.298 MeV resonance is at odds with the experimental assignment. Deuteron stripping reactions with p-shell targets can now be computed ab initio, but calculations are very demanding. Finally, a quantitative description of the 7Li(d,p) 8Li reaction will require further work to include the effect of three-nucleon forces and additional decay channels and to improve the convergence rate of our calculations.« less

Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.

PubMed

Ben Zion, Yossi; Horwitz, Lawrence

2010-04-01

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.

Hamiltonian identifiability assisted by a single-probe measurement

NASA Astrophysics Data System (ADS)

Sone, Akira; Cappellaro, Paola

2017-02-01

We study the Hamiltonian identifiability of a many-body spin-1 /2 system assisted by the measurement on a single quantum probe based on the eigensystem realization algorithm approach employed in Zhang and Sarovar, Phys. Rev. Lett. 113, 080401 (2014), 10.1103/PhysRevLett.113.080401. We demonstrate a potential application of Gröbner basis to the identifiability test of the Hamiltonian, and provide the necessary experimental resources, such as the lower bound in the number of the required sampling points, the upper bound in total required evolution time, and thus the total measurement time. Focusing on the examples of the identifiability in the spin-chain model with nearest-neighbor interaction, we classify the spin-chain Hamiltonian based on its identifiability, and provide the control protocols to engineer the nonidentifiable Hamiltonian to be an identifiable Hamiltonian.

Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models

NASA Astrophysics Data System (ADS)

Ghosh, Pijush K.; Sinha, Debdeep

2018-01-01

A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occurs in a pairwise fashion. It is also shown that with the choice of a suitable co-ordinate, the Hamiltonian can always be reformulated in the background of a pseudo-Euclidean metric. If the equations of motion of some of the well-known many-body systems like Calogero models are generalized to include balanced loss and gain, it appears that the same may not be amenable to a Hamiltonian formulation. A few exactly solvable systems with balanced loss and gain, along with a set of integrals of motion are constructed. The examples include a coupled chain of nonlinear oscillators and a many-particle Calogero-type model with four-body inverse square plus two-body pair-wise harmonic interactions. For the case of nonlinear oscillators, stable solution exists even if the loss and gain parameter has unbounded upper range. Further, the range of the parameter for which the stable solutions are obtained is independent of the total number of the oscillators. The set of coupled nonlinear equations are solved exactly for the case when the values of all the constants of motions except the Hamiltonian are equal to zero. Exact, analytical classical solutions are presented for all the examples considered.

Spin-based quantum computation in multielectron quantum dots

NASA Astrophysics Data System (ADS)

Hu, Xuedong; Das Sarma, S.

2001-10-01

In a quantum computer the hardware and software are intrinsically connected because the quantum Hamiltonian (or more precisely its time development) is the code that runs the computer. We demonstrate this subtle and crucial relationship by considering the example of electron-spin-based solid-state quantum computer in semiconductor quantum dots. We show that multielectron quantum dots with one valence electron in the outermost shell do not behave simply as an effective single-spin system unless special conditions are satisfied. Our work compellingly demonstrates that a delicate synergy between theory and experiment (between software and hardware) is essential for constructing a quantum computer.

Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

NASA Astrophysics Data System (ADS)

Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.

2018-03-01

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

Collectivity of light Ge and As isotopes

NASA Astrophysics Data System (ADS)

Corsi, A.; Delaroche, J.-P.; Obertelli, A.; Baugher, T.; Bazin, D.; Boissinot, S.; Flavigny, F.; Gade, A.; Girod, M.; Glasmacher, T.; Grinyer, G. F.; Korten, W.; Libert, J.; Ljungvall, J.; McDaniel, S.; Ratkiewicz, A.; Signoracci, A.; Stroberg, R.; Sulignano, B.; Weisshaar, D.

2013-10-01

Background: The self-conjugate nuclei of the A˜70 mass region display rapid shape evolution over isotopic or isotonic chains. Shape coexistence has been observed in Se and Kr isotopes reflecting the existence of deformed subshell gaps corresponding to different shell configurations. As and Ge isotopes are located halfway between such deformed nuclei and the Z=28 shell closure.Purpose: The present work aims at clarifying the low-lying spectroscopy of 66Ge and 67As, and providing a better insight into the evolution of collectivity in light even-even Ge and even-odd As isotopes.Methods: We investigate the low-lying levels and collectivity of the neutron deficient 67As and 66Ge through intermediate-energy Coulomb excitation, inelastic scattering, and proton knockout measurements. The experiment was performed using a cocktail beam of 68Se, 67As, and 66Ge nuclei at an energy of 70-80 MeV/nucleon. Spectroscopic properties of the low-lying states are compared to those calculated via shell model with the JUN45 interaction and beyond-mean-field calculations with the five-dimensional collective Hamiltonian method implemented using the Gogny D1S interaction. The structure evolution of the lower-mass Ge and As isotopes is discussed.Results: Reduced electric quadrupole transition probabilities B(E2) have been extracted from the Coulomb-excitation cross sections measured in 66Ge and 67As. The value obtained for the B(E2;01+→21+) in 66Ge is in agreement with a recent measurement, ruling out the existence of a minimum at N=34 in the B(E2) systematics as previously observed. New transitions have been found in 67As and were assigned to the decay of low-lying negative-parity states.

Emergent properties of nuclei from ab initio coupled-cluster calculations

NASA Astrophysics Data System (ADS)

Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R.; Papenbrock, T.

2016-06-01

Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. This endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. This paper reviews some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLO{}{{sat}} is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to 56Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon-nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. The coupling to the continuum impacts the energies of the {J}π =1/{2}-,3/{2}-,7/{2}-,3/{2}+ states in {}{17,23,25}O, and—contrary to naive shell-model expectations—the level ordering of the {J}π =3/{2}+,5/{2}+,9/{2}+ states in {}{53,55,61}Ca. ).

A Hamiltonian electromagnetic gyrofluid model

NASA Astrophysics Data System (ADS)

Waelbroeck, F. L.; Hazeltine, R. D.; Morrison, P. J.

2009-03-01

An isothermal truncation of the electromagnetic gyrofluid model of Snyder and Hammett [Phys. Plasmas 8, 3199 (2001)] is shown to be Hamiltonian. The corresponding noncanonical Lie-Poisson bracket and its Casimir invariants are presented. The invariants are used to obtain a set of coupled Grad-Shafranov equations describing equilibria and propagating coherent structures.

Superradiant phase transition in a model of three-level-Λ systems interacting with two bosonic modes

NASA Astrophysics Data System (ADS)

Hayn, Mathias; Emary, Clive; Brandes, Tobias

2012-12-01

We consider an ensemble of three-level particles in Lambda configuration interacting with two bosonic modes. The Hamiltonian has the form of a generalized Dicke model. We show that in the thermodynamic limit this model supports a superradiant quantum phase transition. Remarkably, this can be both a first- and a second-order phase transition. A connection of the phase diagram to the symmetries of the Hamiltonian is also given. In addition, we show that this model can describe atoms interacting with an electromagnetic field in which the microscopic Hamiltonian includes a diamagnetic contribution. Even though the parameters of the atomic system respect the Thomas-Reiche-Kuhn sum rule, the system still shows a superradiant phase transition.

Tight-binding model for borophene and borophane

NASA Astrophysics Data System (ADS)

Nakhaee, M.; Ketabi, S. A.; Peeters, F. M.

2018-03-01

Starting from the simplified linear combination of atomic orbitals method in combination with first-principles calculations, we construct a tight-binding (TB) model in the two-centre approximation for borophene and hydrogenated borophene (borophane). The Slater and Koster approach is applied to calculate the TB Hamiltonian of these systems. We obtain expressions for the Hamiltonian and overlap matrix elements between different orbitals for the different atoms and present the SK coefficients in a nonorthogonal basis set. An anisotropic Dirac cone is found in the band structure of borophane. We derive a Dirac low-energy Hamiltonian and compare the Fermi velocities with that of graphene.

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Changlani, Hitesh J.; Zheng, Huihuo; Wagner, Lucas K.

2015-09-14

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t tomore » be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.« less

Model many-body Stoner Hamiltonian for binary FeCr alloys

NASA Astrophysics Data System (ADS)

Nguyen-Manh, D.; Dudarev, S. L.

2009-09-01

We derive a model tight-binding many-body d -electron Stoner Hamiltonian for FeCr binary alloys and investigate the sensitivity of its mean-field solutions to the choice of hopping integrals and the Stoner exchange parameters. By applying the local charge-neutrality condition within a self-consistent treatment we show that the negative enthalpy-of-mixing anomaly characterizing the alloy in the low chromium concentration limit is due entirely to the presence of the on-site exchange Stoner terms and that the occurrence of this anomaly is not specifically related to the choice of hopping integrals describing conventional chemical bonding between atoms in the alloy. The Bain transformation pathway computed, using the proposed model Hamiltonian, for the Fe15Cr alloy configuration is in excellent agreement with ab initio total-energy calculations. Our investigation also shows how the parameters of a tight-binding many-body model Hamiltonian for a magnetic alloy can be derived from the comparison of its mean-field solutions with other, more accurate, mean-field approximations (e.g., density-functional calculations), hence stimulating the development of large-scale computational algorithms for modeling radiation damage effects in magnetic alloys and steels.

Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems

NASA Astrophysics Data System (ADS)

Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2011-09-01

The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.

Riemannian geometry of Hamiltonian chaos: hints for a general theory.

PubMed

Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco

2008-10-01

We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.

Study of the 190Hg Nucleus: Testing the Existence of U(5) Symmetry

NASA Astrophysics Data System (ADS)

Jahangiri Tazekand, Z.; Mohseni, M.; Mohammadi, M. A.; Sabri, H.

2018-06-01

In this paper, we have considered the energy spectra, quadrupole transition probabilities, energy surface, charge radii, and quadrupole moment of the190Hg nucleus to describe the interplay between phase transitions and configuration mixing of intruder excitations. To this aim, we have used four different formalisms: (i) interacting boson model including configuration mixing, (ii) Z(5) critical symmetry, (iii) U(6)-based transitional Hamiltonian, and (iv) a transitional interacting boson model Hamiltonian in both interacting boson model (IBM)-1 and IBM-2 versions which are based on affine \\widehat{SU(1,1)} Lie algebra. Results show the advantages of configuration mixing and transitional Hamiltonians, in particular IBM-2 formalism, to reproduce the experimental counterparts when the weight of spherical symmetry increased.

Implementation of the SU(2) Hamiltonian Symmetry for the DMRG Algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alvarez, Gonzalo

2012-01-01

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992, 1993) and Hamiltonian symmetries play an important role. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This paper explains how the the DMRG++ code (Alvarez, 2009) has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries are discussed for the one-orbital Hubbard model, and for a two-orbital Hubbard model for iron-based superconductors. The computational bottleneck of the algorithm and themore » use of shared memory parallelization are also addressed.« less

Effective Hamiltonians for correlated narrow energy band systems and magnetic insulators: Role of spin-orbit interactions in metal-insulator transitions and magnetic phase transitions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakraborty, Subrata; Vijay, Amrendra, E-mail: avijay@iitm.ac.in

Using a second-quantized many-electron Hamiltonian, we obtain (a) an effective Hamiltonian suitable for materials whose electronic properties are governed by a set of strongly correlated bands in a narrow energy range and (b) an effective spin-only Hamiltonian for magnetic materials. The present Hamiltonians faithfully include phonon and spin-related interactions as well as the external fields to study the electromagnetic response properties of complex materials and they, in appropriate limits, reduce to the model Hamiltonians due to Hubbard and Heisenberg. With the Hamiltonian for narrow-band strongly correlated materials, we show that the spin-orbit interaction provides a mechanism for metal-insulator transition, whichmore » is distinct from the Mott-Hubbard (driven by the electron correlation) and the Anderson mechanism (driven by the disorder). Next, with the spin-only Hamiltonian, we demonstrate the spin-orbit interaction to be a reason for the existence of antiferromagnetic phase in materials which are characterized by a positive isotropic spin-exchange energy. This is distinct from the Néel-VanVleck-Anderson paradigm which posits a negative spin-exchange for the existence of antiferromagnetism. We also find that the Néel temperature increases as the absolute value of the spin-orbit coupling increases.« less

A computer program for two-particle intrinsic coefficients of fractional parentage

NASA Astrophysics Data System (ADS)

Deveikis, A.

2012-06-01

A Fortran 90 program CESOS for the calculation of the two-particle intrinsic coefficients of fractional parentage for several j-shells with isospin and an arbitrary number of oscillator quanta (CESOs) is presented. The implemented procedure for CESOs calculation consistently follows the principles of antisymmetry and translational invariance. The approach is based on a simple enumeration scheme for antisymmetric many-particle states, efficient algorithms for calculation of the coefficients of fractional parentage for j-shells with isospin, and construction of the subspace of the center-of-mass Hamiltonian eigenvectors corresponding to the minimal eigenvalue equal to 3/2 (in ℏω). The program provides fast calculation of CESOs for a given particle number and produces results possessing small numerical uncertainties. The introduced CESOs may be used for calculation of expectation values of two-particle nuclear shell-model operators within the isospin formalism. Program summaryProgram title: CESOS Catalogue identifier: AELT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELT_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 932 No. of bytes in distributed program, including test data, etc.: 61 023 Distribution format: tar.gz Programming language: Fortran 90 Computer: Any computer with a Fortran 90 compiler Operating system: Windows XP, Linux RAM: The memory demand depends on the number of particles A and the excitation energy of the system E. Computation of the A=6 particle system with the total angular momentum J=0 and the total isospin T=1 requires around 4 kB of RAM at E=0,˜3 MB at E=3, and ˜172 MB at E=5. Classification: 17.18 Nature of problem: The code CESOS generates a list of two-particle intrinsic coefficients of fractional parentage for several j-shells with isospin. Solution method: The method is based on the observation that CESOs may be obtained by diagonalizing the center-of-mass Hamiltonian in the basis set of antisymmetric A-particle oscillator functions with singled out dependence on Jacobi coordinates of two last particles and choosing the subspace of its eigenvectors corresponding to the minimal eigenvalue equal to 3/2. Restrictions: One run of the code CESOS generates CESOs for one specified set of (A,E,J,T) values only. The restrictions on the (A,E,J,T) values are completely determined by the restrictions on the computation of the single-shell CFPs and two-particle multishell CFPs (GCFPs) [1]. The full sets of single-shell CFPs may be calculated up to the j=9/2 shell (for any particular shell of the configuration); the shell with j⩾11/2 cannot get full (it is the implementation constraint). The calculation of GCFPs is limited by A<86 when E=0 (due to the memory constraints); small numbers of particles allow significantly higher excitations. Any allowed values of J and T may be chosen for the specified values of A and E. The complete list of allowed values of J and T for the chosen values of A and E may be generated by the GCFP program - CPC Program Library, Catalogue Id. AEBI_v1_0. The actual scale of the CESOs computation problem depends strongly on the magnitude of the A and E values. Though there are no limitations on A and E values (within the limits of single-shell CFPs and multishell CFPs calculation), however the generation of corresponding list of CESOs is the subject of available computing resources. For example, the computing time of CESOs for A=6, JT=10 at E=5 took around 14 hours. The system with A=11, JT=1/23/2 at E=2 requires around 15 hours. These computations were performed on Pentium 3 GHz PC with 1 GB RAM [2]. Unusual features: It is possible to test the computed CESOs without saving them to a file. This allows the user to learn their number and approximate computation time and to evaluate the accuracy of calculations. Additional comments: The program CESOS uses the code from GCFP program for calculation of the two-particle multishell coefficients of fractional parentage. Running time: It depends on the size of the problem. The A=6 particle system with the JT=01 took around 31 seconds on Pentium 3 GHz PC with 1 GB RAM at E=3 and about 2.6 hours at E=5.

Quantum Finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2007-09-01

Foreword; Preface; Acknowledgements; 1. Synopsis; Part I. Fundamental Concepts of Finance: 2. Introduction to finance; 3. Derivative securities; Part II. Systems with Finite Number of Degrees of Freedom: 4. Hamiltonians and stock options; 5. Path integrals and stock options; 6. Stochastic interest rates' Hamiltonians and path integrals; Part III. Quantum Field Theory of Interest Rates Models: 7. Quantum field theory of forward interest rates; 8. Empirical forward interest rates and field theory models; 9. Field theory of Treasury Bonds' derivatives and hedging; 10. Field theory Hamiltonian of forward interest rates; 11. Conclusions; Appendix A: mathematical background; Brief glossary of financial terms; Brief glossary of physics terms; List of main symbols; References; Index.

Low-energy nuclear spectroscopy in a microscopic multiphonon approach

NASA Astrophysics Data System (ADS)

Lo Iudice, N.; Ponomarev, V. Yu; Stoyanov, Ch; Sushkov, A. V.; Voronov, V. V.

2012-04-01

The low-lying spectra of heavy nuclei are investigated within the quasiparticle-phonon model. This microscopic approach goes beyond the quasiparticle random-phase approximation by treating a Hamiltonian of separable form in a microscopic multiphonon basis. It is therefore able to describe the anharmonic features of collective modes as well as the multiphonon states, whose experimental evidence is continuously growing. The method can be put in close correspondence with the proton-neutron interacting boson model. By associating the microscopic isoscalar and isovector quadrupole phonons with proton-neutron symmetric and mixed-symmetry quadrupole bosons, respectively, the microscopic states can be classified, just as in the algebraic model, according to their phonon content and their symmetry. In addition, these states disclose the nuclear properties which are to be ascribed to genuine shell effects, not included in the algebraic approach. Due to its flexibility, the method can be implemented numerically for systematic studies of spectroscopic properties throughout entire regions of vibrational nuclei. The spectra and multipole transition strengths so computed are in overall good agreement with the experimental data. By exploiting the correspondence of the method with the interacting boson model, it is possible to embed the microscopic states into this algebraic frame and, therefore, face the study of nuclei far from shell closures, not directly accessible to merely microscopic approaches. Here, it is shown how this task is accomplished through systematic investigations of magnetic dipole and, especially, electric dipole modes along paths moving from the vibrational to the transitional regions. The method is very well suited to the study of well-deformed nuclei. It provides reliable descriptions of low-lying magnetic as well as electric multipole modes of nuclei throughout the rare-earth and actinide regions. Attention is focused here on the low-lying 0+ states produced in large abundance in recent experiments. The analysis shows that the quasiparticle-phonon model accounts for the occurrence of so many 0+ levels and discloses their nature.

Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

NASA Astrophysics Data System (ADS)

Risser, Steven Michael

This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb interactions in the Huckel Hamiltonian results in calculated hyperpolarizabilities that are much larger than the experimentally determined values. Comparison of hyperpolarizabilities calculated for small benzene derivatives using both the Huckel and PPP Hamiltonians shows that inclusion of explicit Coulomb interactions is not as significant for aromatic molecules. This assertion is supported by comparison of the calculated results to the experimentally determined values. This allows for predictions of the hyperpolarizability of various liquid crystal molecules to be made.

Symmetries of SU(2) Skyrmion in Hamiltonian and Lagrangian Approaches

NASA Astrophysics Data System (ADS)

Hong, Soon-Tae; Kim, Yong-Wan; Park, Young-Jai

We apply the Batalin-Fradkin-Tyutin (BFT) method to the SU(2) Skyrmion to study the full symmetry structure of the model at the first-class Hamiltonian level. On the other hand, we also analyze the symmetry structure of the action having the WZ term, which corresponds to this Hamiltonian, in the framework of the Lagrangian approach. Furthermore, following the BFV formalism we derive the BRST invariant gauge fixed Lagrangian from the above extended action.

Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

NASA Astrophysics Data System (ADS)

Yuzbashyan, Emil A.

2018-05-01

We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

Constraints and stability in vector theories with spontaneous Lorentz violation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bluhm, Robert; Gagne, Nolan L.; Potting, Robertus

2008-06-15

Vector theories with spontaneous Lorentz violation, known as bumblebee models, are examined in flat spacetime using a Hamiltonian constraint analysis. In some of these models, Nambu-Goldstone modes appear with properties similar to photons in electromagnetism. However, depending on the form of the theory, additional modes and constraints can appear that have no counterparts in electromagnetism. An examination of these constraints and additional degrees of freedom, including their nonlinear effects, is made for a variety of models with different kinetic and potential terms, and the results are compared with electromagnetism. The Hamiltonian constraint analysis also permits an investigation of the stabilitymore » of these models. For certain bumblebee theories with a timelike vector, suitable restrictions of the initial-value solutions are identified that yield ghost-free models with a positive Hamiltonian. In each case, the restricted phase space is found to match that of electromagnetism in a nonlinear gauge.« less

Modeling a 400 Hz Signal Transmission Through the South China Sea Basin

DTIC Science & Technology

2009-03-01

TRACING ..........................8 1. General Ray Theory and the Eikonal Approximation .....................8 2. Hamiltonian Ray Tracing...HAMILTONIAN RAY TRACING 1. General Ray Theory and the Eikonal Approximation In general, modeling acoustic propagation through the ocean necessitates... eikonal and represents the phase component of the solution. Since solutions of constant phase represent wave fronts, and rays travel in a direction

Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, Diego

We study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and N-> infty kinetic limit (where N is the number of particles). The linear stability of equilibria in the kinetic model is studied as well as the initial value problem including Landau damping . Numerical simulations show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles and show that the N=2 limit has a family of rotating integrable solutions that provide an accurate description of the dynamics. We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.

Self-consistent chaos in a mean-field Hamiltonian model of fluids and plasmas

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, D.; Firpo, Marie-Christine

2002-11-01

We present a mean-field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas. In plasmas, the model describes the self-consistent evolution of electron holes and clumps in phase space. In fluids, the model describes the dynamics of vortices with negative and positive circulation in shear flows. The mean-field nature of the system makes it a tractable model to study the dynamics of large degrees-of-freedom, coupled Hamiltonian systems. Here we focus in the role of self-consistent chaos in the formation and destruction of phase space coherent structures. Numerical simulations in the finite N and in the Narrow kinetic limit (where N is the number of particles) show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles, and show that the N = 2 limit has a family of rotating integrable solutions described by a one degree-of-freedom nontwist Hamiltonian. The coherence of the dipole is explained in terms of a parametric resonance between the rotation frequency of the macroparticles and the oscillation frequency of the self-consistent mean field. For a class of initial conditions, the mean field exhibits a self-consistent, elliptic-hyperbolic bifurcation that leads to the destruction of the dipole and violent mixing of the phase space.

Stability of Inhomogeneous Equilibria of Hamiltonian Continuous Media Field Theories

NASA Astrophysics Data System (ADS)

Hagstrom, George

2013-10-01

There are a wide variety of 1 + 1 Hamiltonian continuous media field theories that exhibit phase space pattern formation. In plasma physics, the most famous of these is the Vlasov-Poisson equation, but other examples include the incompressible Euler equation in two-dimensions and the Hamiltonian Mean Field (or XY) model. One of the characteristic phenomenon that occurs in systems described by these equations is the formation of cat's eye patterns in phase space as a result of the nonlinear saturation of instabilities. Corresponding to each of these cat's eyes is a spatially inhomogeneous equilibrium solution of the underlying model, in plasma physics these are called BGK modes, but analogous solutions exist in all of the above systems. Here we analyze the stability of inhomogeneous equilibria in the Hamiltonian Mean Field model and in the Single Wave model, which is an equation that was derived to provide a model of the formation of electron holes in plasmas. We use action angle variables and the properties of elliptic functions to analyze the resulting dispersion relation construct linearly stable inhomogeneous equilibria for in the limit of small numbers of particles and study the behavior of solutions near these equilibria. Work supported by USDOE grant no. DE-FG02-ER53223.

Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians

DOE Office of Scientific and Technical Information (OSTI.GOV)

Longhi, Stefano, E-mail: stefano.longhi@fisi.polimi.it

Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H{sup -hat} (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H{sup -hat} (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for themore » Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization.« less

Emergent properties of nuclei from ab initio coupled-cluster calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R.

Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. Our endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. We review some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLOmore » $${}_{{\\rm{sat}}}$$ is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to 56Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon–nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. Finally, the coupling to the continuum impacts the energies of the $${J}^{\\pi }=1/{2}^{-},3/{2}^{-},7/{2}^{-},3/{2}^{+}$$ states in $${}^{\\mathrm{17,23,25}}$$O, and—contrary to naive shell-model expectations—the level ordering of the $${J}^{\\pi }=3/{2}^{+},5/{2}^{+},9/{2}^{+}$$ states in $${}^{\\mathrm{53,55,61}}$$Ca.« less

Emergent properties of nuclei from ab initio coupled-cluster calculations

DOE PAGES

Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R.; ...

2016-05-17

Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. Our endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. We review some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLOmore » $${}_{{\\rm{sat}}}$$ is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to 56Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon–nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. Finally, the coupling to the continuum impacts the energies of the $${J}^{\\pi }=1/{2}^{-},3/{2}^{-},7/{2}^{-},3/{2}^{+}$$ states in $${}^{\\mathrm{17,23,25}}$$O, and—contrary to naive shell-model expectations—the level ordering of the $${J}^{\\pi }=3/{2}^{+},5/{2}^{+},9/{2}^{+}$$ states in $${}^{\\mathrm{53,55,61}}$$Ca.« less

Spinons and holons for the one-dimensional three-band Hubbard models of high-temperature superconductors.

PubMed Central

Tahir-Kheli, J; Goddard, W A

1993-01-01

The one-dimensional three-band Hubbard Hamiltonian is shown to be equivalent to an effective Hamiltonian that has independent spinon and holon quasiparticle excitations plus a weak coupling of the two. The spinon description includes both copper sites and oxygen hole sites leading to a one-dimensional antiferromagnet incommensurate with the copper lattice. The holons are spinless noninteracting fermions in a simple cosine band. Because the oxygen sites are in the Hamiltonian, the quasiparticles are much simpler than in the exact solution of the t-J model for 2t = +/- J. If a similar description is correct for two dimensions, then the holons will attract in a p-wave potential. PMID:11607436

Magnetic and superconducting competition within the Hubbard dimer. Exact solution

NASA Astrophysics Data System (ADS)

Matlak, M.; Somska, T.; Grabiec, B.

2005-02-01

We express the Hubbard dimer Hamiltonian in the second quantization with theuse of the Hubbard and spin operators. We consider the case of positive and negative U. We decompose the resulting Hamiltonian into several parts collecting all the terms belonging to the same energy level. Such a decomposition visualizes explicitely all intrinsic interactions competing together and deeply hidden in the original form of the dimer Hamiltonian. Among them are competitive ferromagnetic and antiferromagnetic interactions. There are also hopping terms present which describe Cooper pairs hopping between sites 1 and 2 with positive and negative coupling constants (similar as in Kulik-Pedan, Penson-Kolb models). We show that the competition between intrinsic interactions strongly depends on the model parametrs and the averaged occupation number of electrons n [0, 4] resulting in different regimes of the model (as e.g. t-J model regime, etc.).

Local density approximation in site-occupation embedding theory

NASA Astrophysics Data System (ADS)

Senjean, Bruno; Tsuchiizu, Masahisa; Robert, Vincent; Fromager, Emmanuel

2017-01-01

Site-occupation embedding theory (SOET) is a density functional theory (DFT)-based method which aims at modelling strongly correlated electrons. It is in principle exact and applicable to model and quantum chemical Hamiltonians. The theory is presented here for the Hubbard Hamiltonian. In contrast to conventional DFT approaches, the site (or orbital) occupations are deduced in SOET from a partially interacting system consisting of one (or more) impurity site(s) and non-interacting bath sites. The correlation energy of the bath is then treated implicitly by means of a site-occupation functional. In this work, we propose a simple impurity-occupation functional approximation based on the two-level (2L) Hubbard model which is referred to as two-level impurity local density approximation (2L-ILDA). Results obtained on a prototypical uniform eight-site Hubbard ring are promising. The extension of the method to larger systems and more sophisticated model Hamiltonians is currently in progress.

Hamiltonian methods of modeling and control of AC microgrids with spinning machines and inverters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matthews, Ronald C.; Weaver, Wayne W.; Robinett, Rush D.

This study presents a novel approach to the modeling and control of AC microgrids that contain spinning machines, power electronic inverters and energy storage devices. The inverters in the system can adjust their frequencies and power angles very quickly, so the modeling focuses on establishing a common reference frequency and angle in the microgrid based on the spinning machines. From this dynamic model, nonlinear Hamiltonian surface shaping and power flow control method is applied and shown to stabilize. From this approach the energy flow in the system is used to show the energy storage device requirements and limitations for themore » system. This paper first describes the model for a single bus AC microgrid with a Hamiltonian control, then extends this model and control to a more general class of multiple bus AC microgrids. Finally, simulation results demonstrate the efficacy of the approach in stabilizing and optimization of the microgrid.« less

Hamiltonian methods of modeling and control of AC microgrids with spinning machines and inverters

DOE PAGES

Matthews, Ronald C.; Weaver, Wayne W.; Robinett, Rush D.; ...

2017-12-22

This study presents a novel approach to the modeling and control of AC microgrids that contain spinning machines, power electronic inverters and energy storage devices. The inverters in the system can adjust their frequencies and power angles very quickly, so the modeling focuses on establishing a common reference frequency and angle in the microgrid based on the spinning machines. From this dynamic model, nonlinear Hamiltonian surface shaping and power flow control method is applied and shown to stabilize. From this approach the energy flow in the system is used to show the energy storage device requirements and limitations for themore » system. This paper first describes the model for a single bus AC microgrid with a Hamiltonian control, then extends this model and control to a more general class of multiple bus AC microgrids. Finally, simulation results demonstrate the efficacy of the approach in stabilizing and optimization of the microgrid.« less

Using Stan for Item Response Theory Models

ERIC Educational Resources Information Center

Ames, Allison J.; Au, Chi Hang

2018-01-01

Stan is a flexible probabilistic programming language providing full Bayesian inference through Hamiltonian Monte Carlo algorithms. The benefits of Hamiltonian Monte Carlo include improved efficiency and faster inference, when compared to other MCMC software implementations. Users can interface with Stan through a variety of computing…

Excitation spectrum and staggering transformations in lattice quantum models.

PubMed

Faria da Veiga, Paulo A; O'Carroll, Michael; Schor, Ricardo

2002-08-01

We consider the energy-momentum excitation spectrum of diverse lattice Hamiltonian operators: the generator of the Markov semigroup of Ginzburg-Landau models with Langevin stochastic dynamics, the Hamiltonian of a scalar quantum field theory, and the Hamiltonian associated with the transfer matrix of a classical ferromagnetic spin system at high temperature. The low-lying spectrum consists of a one-particle state and a two-particle band. The two-particle spectrum is determined using a lattice version of the Bethe-Salpeter equation. In addition to the two-particle band, depending on the lattice dimension and on the attractive or repulsive character of the interaction between the particles of the system, there is, respectively, a bound state below or above the two-particle band. We show how the existence or nonexistence of these bound states can be understood in terms of a nonrelativistic single-particle lattice Schrödinger Hamiltonian with a delta potential. A staggering transformation relates the spectra of the attractive and the repulsive cases.

Entanglement spectrum and boundary theories with projected entangled-pair states

NASA Astrophysics Data System (ADS)

Cirac, J. Ignacio; Poilblanc, Didier; Schuch, Norbert; Verstraete, Frank

2011-06-01

In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated with their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using projected entangled-pair states. This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models: a deformed AKLT model [I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.59.799 59, 799 (1987)], an Ising-type model [F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.96.220601 96, 220601 (2006)], and Kitaev’s toric code [A. Kitaev, Ann. Phys.APNYA60003-491610.1016/S0003-4916(02)00018-0 303, 2 (2003)], both in finite ladders and in infinite square lattices. In the second case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield nonlocal Hamiltonians. Because our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.

Dynamical decoupling of unbounded Hamiltonians

NASA Astrophysics Data System (ADS)

Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin

2018-03-01

We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

Physical implementation of protected qubits

NASA Astrophysics Data System (ADS)

Douçot, B.; Ioffe, L. B.

2012-07-01

We review the general notion of topological protection of quantum states in spin models and its relation with the ideas of quantum error correction. We show that topological protection can be viewed as a Hamiltonian realization of error correction: for a quantum code for which the minimal number of errors that remain undetected is N, the corresponding Hamiltonian model of the effects of the environment noise appears only in the Nth order of the perturbation theory. We discuss the simplest model Hamiltonians that realize topological protection and their implementation in superconducting arrays. We focus on two dual realizations: in one the protected state is stored in the parity of the Cooper pair number, in the other, in the parity of the flux number. In both cases the superconducting arrays allow a number of fault-tolerant operations that should make the universal quantum computation possible.

Relativistic equation-of-motion coupled-cluster method using open-shell reference wavefunction: Application to ionization potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pathak, Himadri, E-mail: hmdrpthk@gmail.com; Sasmal, Sudip, E-mail: sudipsasmal.chem@gmail.com; Vaval, Nayana

2016-08-21

The open-shell reference relativistic equation-of-motion coupled-cluster method within its four-component description is successfully implemented with the consideration of single- and double- excitation approximations using the Dirac-Coulomb Hamiltonian. At the first attempt, the implemented method is employed to calculate ionization potential value of heavy atomic (Ag, Cs, Au, Fr, and Lr) and molecular (HgH and PbF) systems, where the effect of relativity does really matter to obtain highly accurate results. Not only the relativistic effect but also the effect of electron correlation is crucial in these heavy atomic and molecular systems. To justify the fact, we have taken two further approximationsmore » in the four-component relativistic equation-of-motion framework to quantify how the effect of electron correlation plays a role in the calculated values at different levels of theory. All these calculated results are compared with the available experimental data as well as with other theoretically calculated values to judge the extent of accuracy obtained in our calculations.« less

Nonunitary quantum computation in the ground space of local Hamiltonians

NASA Astrophysics Data System (ADS)

Usher, Naïri; Hoban, Matty J.; Browne, Dan E.

2017-09-01

A central result in the study of quantum Hamiltonian complexity is that the k -local Hamiltonian problem is quantum-Merlin-Arthur-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above another, promised one of these is true. Given the ground state of the Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the ground space of a Hamiltonian. However, we now have quantum computing models based on measurement instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational tool. In this work, we generalize Kitaev's construction to allow for nonunitary evolution including postselection. Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame postselection. We consider the computational complexity consequences of this construction and then consider how the probability of an event upon which we are postselecting affects the gap between the ground-state energy and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the two are not immediately related by giving a family of circuits where the probability of an event upon which we postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial.

Local Hamiltonian Monte Carlo study of the massive schwinger model, the decoupling of heavy flavours

NASA Astrophysics Data System (ADS)

Ranft, J.

1983-12-01

The massive Schwinger model with two flavours is studied using the local hamiltonian lattice Monte Carlo method. Chiral symmetry breaking is studied using the fermion condensate as order parameter. For a small ratio of the two fermion masses, degeneracy of the two flavours is found. For a large ratio of the masses, the heavy flavour decouples and the light fermion behaves like in the one flavour Schwinger model. On leave from Sektion Physik, Karl-Marx-Universität, Leipzig, GDR.

Relativistic quantum optics: The relativistic invariance of the light-matter interaction models

NASA Astrophysics Data System (ADS)

Martín-Martínez, Eduardo; Rodriguez-Lopez, Pablo

2018-05-01

In this article we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model atoms interacting with light. We find explicitly how the light-matter interaction Hamiltonians change under general coordinate transformations, and analyze the subtleties of the Hamiltonians commonly used to describe the light-matter interaction when relativistic motion is taken into account.

Integrable Time-Dependent Quantum Hamiltonians

NASA Astrophysics Data System (ADS)

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

2018-05-01

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes

NASA Astrophysics Data System (ADS)

Kowalski, A. M.; Rossignoli, R.

2018-04-01

We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian, and possesses stable and unstable regimes. The dynamics of the whole system is shown to be strongly influenced by the quantum subsystem. In particular, chaos is seen to arise in the vicinity of a quantum critical case, which separates the stable and unstable regimes of the bosonic system.

Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

NASA Astrophysics Data System (ADS)

Balajany, Hamideh; Mehrafarin, Mohammad

2018-06-01

In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis-Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et al. (2013) [21] for these Berry phases, which is resolved to yield agreement with our results.

Deep neural networks for direct, featureless learning through observation: The case of two-dimensional spin models

NASA Astrophysics Data System (ADS)

Mills, Kyle; Tamblyn, Isaac

2018-03-01

We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4 ×4 Ising model. Using its success at this task, we motivate the study of the larger 8 ×8 Ising model, showing that the deep neural network can learn the nearest-neighbor Ising Hamiltonian after only seeing a vanishingly small fraction of configuration space. Additionally, we show that the neural network has learned both the energy and magnetization operators with sufficient accuracy to replicate the low-temperature Ising phase transition. We then demonstrate the ability of the neural network to learn other spin models, teaching the convolutional deep neural network to accurately predict the long-range interaction of a screened Coulomb Hamiltonian, a sinusoidally attenuated screened Coulomb Hamiltonian, and a modified Potts model Hamiltonian. In the case of the long-range interaction, we demonstrate the ability of the neural network to recover the phase transition with equivalent accuracy to the numerically exact method. Furthermore, in the case of the long-range interaction, the benefits of the neural network become apparent; it is able to make predictions with a high degree of accuracy, and do so 1600 times faster than a CUDA-optimized exact calculation. Additionally, we demonstrate how the neural network succeeds at these tasks by looking at the weights learned in a simplified demonstration.

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

NASA Astrophysics Data System (ADS)

Abanin, Dmitry; De Roeck, Wojciech; Ho, Wen Wei; Huveneers, François

2017-09-01

Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency {ν}. We prove that up to a quasi-exponential time {τ_* ˜ e^{c ν/log^3 ν}}, the system barely absorbs energy. Instead, there is an effective local Hamiltonian {\\widehat D} that governs the time evolution up to {τ_*}, and hence this effective Hamiltonian is a conserved quantity up to {τ_*}. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi-Hubbard model where the interaction U is much larger than the hopping J. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time {τ_*} that is (almost) exponential in {U/J}.

FAST TRACK COMMUNICATION: Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd k

NASA Astrophysics Data System (ADS)

Quesne, C.

2010-02-01

In a recent communication paper by Tremblay et al (2009 J. Phys. A: Math. Theor. 42 205206), it has been conjectured that for any integer value of k, some novel exactly solvable and integrable quantum Hamiltonian Hk on a plane is superintegrable and that the additional integral of motion is a 2kth-order differential operator Y2k. Here we demonstrate the conjecture for the infinite family of Hamiltonians Hk with odd k >= 3, whose first member corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination of the centre-of-mass motion. Our approach is based on the construction of some D2k-extended and invariant Hamiltonian {\\cal H}_k, which can be interpreted as a modified boson oscillator Hamiltonian. The latter is then shown to possess a D2k-invariant integral of motion {\\cal Y}_{2k}, from which Y2k can be obtained by projection in the D2k identity representation space.

On the exactness of effective Floquet Hamiltonians employed in solid-state NMR spectroscopy

NASA Astrophysics Data System (ADS)

Garg, Rajat; Ramachandran, Ramesh

2017-05-01

Development of theoretical models based on analytic theory has remained an active pursuit in molecular spectroscopy for its utility both in the design of experiments as well as in the interpretation of spectroscopic data. In particular, the role of "Effective Hamiltonians" in the evolution of theoretical frameworks is well known across all forms of spectroscopy. Nevertheless, a constant revalidation of the approximations employed in the theoretical frameworks is necessitated by the constant improvements on the experimental front in addition to the complexity posed by the systems under study. Here in this article, we confine our discussion to the derivation of effective Floquet Hamiltonians based on the contact transformation procedure. While the importance of the effective Floquet Hamiltonians in the qualitative description of NMR experiments has been realized in simpler cases, its extension in quantifying spectral data deserves a cautious approach. With this objective, the validity of the approximations employed in the derivation of the effective Floquet Hamiltonians is re-examined through a comparison with exact numerical methods under differing experimental conditions. The limitations arising from the existing analytic methods are outlined along with remedial measures for improving the accuracy of the derived effective Floquet Hamiltonians.

Effective Hamiltonian for travelling discrete breathers

NASA Astrophysics Data System (ADS)

MacKay, Robert S.; Sepulchre, Jacques-Alexandre

2002-05-01

Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.

Ladder operators and coherent states for the Jaynes-Cummings model in the rotating-wave approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hussin, V.; Nieto, L.M.

2005-12-15

Using algebraic techniques, we realize a systematic search of different types of ladder operators for the Jaynes-Cummings model in the rotating-wave approximation. The link between our results and previous studies on the diagonalization of the associated Hamiltonian is established. Using some of the ladder operators obtained before, examples are given on the possibility of constructing a variety of interesting coherent states for this Hamiltonian.

Cluster state generation in one-dimensional Kitaev honeycomb model via shortcut to adiabaticity

NASA Astrophysics Data System (ADS)

Kyaw, Thi Ha; Kwek, Leong-Chuan

2018-04-01

We propose a mean to obtain computationally useful resource states also known as cluster states, for measurement-based quantum computation, via transitionless quantum driving algorithm. The idea is to cool the system to its unique ground state and tune some control parameters to arrive at computationally useful resource state, which is in one of the degenerate ground states. Even though there is set of conserved quantities already present in the model Hamiltonian, which prevents the instantaneous state to go to any other eigenstate subspaces, one cannot quench the control parameters to get the desired state. In that case, the state will not evolve. With involvement of the shortcut Hamiltonian, we obtain cluster states in fast-forward manner. We elaborate our proposal in the one-dimensional Kitaev honeycomb model, and show that the auxiliary Hamiltonian needed for the counterdiabatic driving is of M-body interaction.

Floquet prethermalization in the resonantly driven Hubbard model

NASA Astrophysics Data System (ADS)

Herrmann, Andreas; Murakami, Yuta; Eckstein, Martin; Werner, Philipp

2017-12-01

We demonstrate the existence of long-lived prethermalized states in the Mott insulating Hubbard model driven by periodic electric fields. These states, which also exist in the resonantly driven case with a large density of photo-induced doublons and holons, are characterized by a nonzero current and an effective temperature of the doublons and holons which depends sensitively on the driving condition. Focusing on the specific case of resonantly driven models whose effective time-independent Hamiltonian in the high-frequency driving limit corresponds to noninteracting fermions, we show that the time evolution of the double occupation can be reproduced by the effective Hamiltonian, and that the prethermalization plateaus at finite driving frequency are controlled by the next-to-leading-order correction in the high-frequency expansion of the effective Hamiltonian. We propose a numerical procedure to determine an effective Hubbard interaction that mimics the correlation effects induced by these higher-order terms.

Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem

NASA Astrophysics Data System (ADS)

Farrés, Ariadna; Jorba, Àngel; Mondelo, Josep-Maria

2017-09-01

The Augmented Hill Three-Body problem is an extension of the classical Hill problem that, among other applications, has been used to model the motion of a solar sail around an asteroid. This model is a 3 degrees of freedom (3DoF) Hamiltonian system that depends on four parameters. This paper describes the bounded motions (periodic orbits and invariant tori) in an extended neighbourhood of some of the equilibrium points of the model. An interesting feature is the existence of equilibrium points with a 1:1 resonance, whose neighbourhood we also describe. The main tools used are the computation of periodic orbits (including their stability and bifurcations), the reduction of the Hamiltonian to centre manifolds at equilibria, and the numerical approximation of invariant tori. It is remarkable how the combination of these techniques allows the description of the dynamics of a 3DoF Hamiltonian system.

Applications of the trilinear Hamiltonian with three trapped ions

NASA Astrophysics Data System (ADS)

Hablutzel Marrero, Roland Esteban; Ding, Shiqian; Maslennikov, Gleb; Gan, Jaren; Nimmrichter, Stefan; Roulet, Alexandre; Dai, Jibo; Scarani, Valerio; Matsukevich, Dzmitry

2017-04-01

The trilinear Hamiltonian a† bc + ab†c† , which describes a nonlinear interaction between harmonic oscillators, can be implemented to study different phenomena ranging from simple quantum models to quantum thermodynamics. We engineer this coupling between three modes of motion of three trapped 171Yb+ ions, where the interaction arises naturally from their mutual (anharmonic) Coulomb repulsion. By tuning our trapping parameters we are able to turn on / off resonant exchange of energy between the modes on demand. We present applications of this Hamiltonian for simulations of the parametric down conversion process in the regime of depleted pump, a simple model of Hawking radiation, and the Tavis-Cummings model. We also discuss the implementation of the quantum absorption refrigerator in such system and experimentally study effects of quantum coherence on its performance. This research is supported by the National Research Foundation, Prime Minister's Office, Singapore and the Ministry of Education, Singapore under the Research Centres of Excellence programme.

Two-color Fermi-liquid theory for transport through a multilevel Kondo impurity

NASA Astrophysics Data System (ADS)

Karki, D. B.; Mora, Christophe; von Delft, Jan; Kiselev, Mikhail N.

2018-05-01

We consider a quantum dot with K ≥2 orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multilevel Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel S =1 Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fermi liquid. Using nonequilibrium (Keldysh) perturbation theory around the strong-coupling fixed point we analyze the transport properties of the model at finite temperature, Zeeman magnetic field, and source-drain voltage applied across the quantum dot. We compute the Fermi-liquid transport constants and discuss different universality classes associated with emergent symmetries.

Relational time in anyonic systems

NASA Astrophysics Data System (ADS)

Nikolova, A.; Brennen, G. K.; Osborne, T. J.; Milburn, G. J.; Stace, T. M.

2018-03-01

In a seminal paper [Phys. Rev. D 27, 2885 (1983), 10.1103/PhysRevD.27.2885], Page and Wootters suggest that time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing with the "problem of time" stemming from vanishing Hamiltonian dynamics in many theories of quantum gravity. Their approach seeks to identify relational dynamics given a Hamiltonian constraint on the physical states. Here we present a "state-centric" reformulation of the Page and Wootters model better suited to cases where the Hamiltonian constraint is satisfied, such as anyons emerging in Chern-Simons theories. We describe relational time by encoding logical "clock" qubits into topologically protected anyonic degrees of freedom. The minimum temporal increment of such anyonic clocks is determined by the universality of the anyonic braid group, with nonuniversal models naturally exhibiting discrete time. We exemplify this approach by using SU (2) 2 anyons and discuss generalizations to other states and models.

Energy spectrum and electrical conductivity of graphene with a nitrogen impurity

NASA Astrophysics Data System (ADS)

Repetskii, S. P.; Vyshivanaya, I. G.; Skotnikov, V. A.; Yatsenyuk, A. A.

2015-04-01

The electronic structure of graphene with a nitrogen impurity has been studied based on the model of tight binding using exchange-correlation potentials in the density-functional theory. Wave functions of 2 s and 2 p states of neutral noninteracting carbon atoms have been chosen as the basis. When studying the matrix elements of the Hamiltonian, the first three coordination shells have been taken into account. It has been established that the hybridization of electron-energy bands leads to the splitting of the electron energy spectrum near the Fermi level. Due to the overlap of the energy bands, the arising gap behaves as a quasi-gap, in which the density of the electron levels is much lower than in the rest of the spectrum. It has been established that the conductivity of graphene decreases with increasing nitrogen concentration. Since the increase in the nitrogen concentration leads to an increase in the density of states at the Fermi level, the decrease in the conductivity is due to a sharper decrease in the time of relaxation of the electron sates.

Measurement of key resonance states for the P 30 ( p , γ ) S 31 reaction rate, and the production of intermediate-mass elements in nova explosions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kankainen, A.; Woods, P. J.; Schatz, H.

2017-06-01

We report the first experimental constraints on spectroscopic factors and strengths of key resonances in the P-30(p, gamma)S-31 reaction critical for determining the production of intermediate-mass elements up to Ca in nova ejecta. The P-30(d,n)S-31 reaction was studied in inverse kinematics using the GRETINA gamma-ray array to measure the angle-integrated cross-sections of states above the proton threshold. In general, negative parity states are found to be most strongly produced but the absolute values of spectroscopic factors are typically an order of magnitude lower than predicted by the shell-model calculations employing WBP Hamiltonian for the negative-parity states. The results clearly indicatemore » the dominance of a single 3/2(-) resonance state at 196 keV in the region of nova burning T approximate to 0.10-0.17 GM, well within the region of interest for nova nucleosynthesis. Hydrodynamic simulations of nova explosions have been performed to demonstrate the effect on the composition of nova ejecta.« less

Multi-orbital non-crossing approximation from maximally localized Wannier functions: the Kondo signature of copper phthalocyanine on Ag(100).

PubMed

Korytár, Richard; Lorente, Nicolás

2011-09-07

We have developed a multi-orbital approach to compute the electronic structure of a quantum impurity using the non-crossing approximation. The calculation starts with a mean-field evaluation of the system's electronic structure using a standard quantum chemistry code; here we use density functional theory (DFT). We transformed the one-electron structure into an impurity Hamiltonian by using maximally localized Wannier functions. Hence, we have developed a method to study the Kondo effect in systems based on an initial one-electron calculation. We have applied our methodology to a copper phthalocyanine molecule chemisorbed on Ag(100), and we have described its spectral function for three different cases where the molecule presents a single spin or two spins with ferro- and anti-ferromagnetic exchange couplings. We find that the use of broken-symmetry mean-field theories such as Kohn-Sham DFT cannot deal with the complexity of the spin of open-shell molecules on metal surfaces and extra modeling is needed. © 2011 IOP Publishing Ltd

Measurement of key resonance states for the 30P (p , γ)31S reaction rate, and the production of intermediate-mass elements in nova explosions

NASA Astrophysics Data System (ADS)

Kankainen, A.; Woods, P. J.; Schatz, H.; Poxon-Pearson, T.; Doherty, D. T.; Bader, V.; Baugher, T.; Bazin, D.; Brown, B. A.; Browne, J.; Estrade, A.; Gade, A.; José, J.; Kontos, A.; Langer, C.; Lotay, G.; Meisel, Z.; Montes, F.; Noji, S.; Nunes, F.; Perdikakis, G.; Pereira, J.; Recchia, F.; Redpath, T.; Stroberg, R.; Scott, M.; Seweryniak, D.; Stevens, J.; Weisshaar, D.; Wimmer, K.; Zegers, R.

2017-06-01

We report the first experimental constraints on spectroscopic factors and strengths of key resonances in the 30P (p , γ)31S reaction critical for determining the production of intermediate-mass elements up to Ca in nova ejecta. The 30P (d , n)31S reaction was studied in inverse kinematics using the GRETINA γ-ray array to measure the angle-integrated cross-sections of states above the proton threshold. In general, negative-parity states are found to be most strongly produced but the absolute values of spectroscopic factors are typically an order of magnitude lower than predicted by the shell-model calculations employing WBP Hamiltonian for the negative-parity states. The results clearly indicate the dominance of a single 3 /2- resonance state at 196 keV in the region of nova burning T ≈ 0.10- 0.17 GK, well within the region of interest for nova nucleosynthesis. Hydrodynamic simulations of nova explosions have been performed to demonstrate the effect on the composition of nova ejecta.

Modeling the Conformation-Specific Infrared Spectra of N-Alkylbenzenes

NASA Astrophysics Data System (ADS)

Tabor, Daniel P.; Sibert, Edwin; Hewett, Daniel M.; Korn, Joseph A.; Zwier, Timothy S.

2016-06-01

Conformation-specific UV-IR double resonance spectra are presented for n-alkylbenzenes. With the aid of a local mode Hamiltonian that includes the effects of stretch-bend Fermi coupling, the spectra of ethyl, n-propyl, and n-butylbenzene are assigned to individual conformers. These molecules allow for further development of the work on a first principles method for calculating alkyl stretch spectra. Due to the consistency of the anharmonic couplings from conformer to conformer, construction of the model Hamiltonian for a given conformer only requires a harmonic frequency calculation at the conformer's minimum geometry as an input. The model Hamiltonian can be parameterized with either density functional theory or MP2 electronic structure calculations. The relative strengths and weaknesses of these methods are evaluated, including their predictions of the relative energetics of the conformers. Finally, the IR spectra for conformers that have the alkyl chain bend back and interact with the π cloud of the benzene ring are modeled.

Modeling Optical Spectra of Large Organic Systems Using Real-Time Propagation of Semiempirical Effective Hamiltonians.

PubMed

Ghosh, Soumen; Andersen, Amity; Gagliardi, Laura; Cramer, Christopher J; Govind, Niranjan

2017-09-12

We present an implementation of a time-dependent semiempirical method (INDO/S) in NWChem using real-time (RT) propagation to address, in principle, the entire spectrum of valence electronic excitations. Adopting this model, we study the UV/vis spectra of medium-sized systems such as P3B2 and f-coronene, and in addition much larger systems such as ubiquitin in the gas phase and the betanin chromophore in the presence of two explicit solvents (water and methanol). RT-INDO/S provides qualitatively and often quantitatively accurate results when compared with RT- TDDFT or experimental spectra. Even though we only consider the INDO/S Hamiltonian in this work, our implementation provides a framework for performing electron dynamics in large systems using semiempirical Hartree-Fock Hamiltonians in general.

Polymeric quantum mechanics and the zeros of the Riemann zeta function

NASA Astrophysics Data System (ADS)

Berra-Montiel, Jasel; Molgado, Alberto

We analyze the Berry-Keating model and the Sierra and Rodríguez-Laguna Hamiltonian within the polymeric quantization formalism. By using the polymer representation, we obtain for both models, the associated polymeric quantum Hamiltonians and the corresponding stationary wave functions. The self-adjointness condition provides a proper domain for the Hamiltonian operator and the energy spectrum, which turned out to be dependent on an introduced scale parameter. By performing a counting of semiclassical states, we prove that the polymer representation reproduces the smooth part of the Riemann-von Mangoldt formula, and also introduces a correction depending on the energy and the scale parameter. This may shed some light on the understanding of the fluctuation behavior of the zeros of the Riemann function from a purely quantum point of view.

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagarello, F., E-mail: fabio.bagarello@unipa.it

In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we willmore » find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.« less

Lineshape analysis of coherent multidimensional optical spectroscopy using incoherent light

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ulness, Darin J.; Turner, Daniel B., E-mail: dturner@nyu.edu

2015-06-07

Coherent two-dimensional electronic spectroscopy using incoherent (noisy) light, I{sup (4)} 2D ES, holds intriguing challenges and opportunities. One challenge is to determine how I{sup (4)} 2D ES compares to femtosecond 2D ES. Here, we merge the sophisticated energy-gap Hamiltonian formalism that is often used to model femtosecond 2D ES with the factorized time-correlation formalism that is needed to describe I{sup (4)} 2D ES. The analysis reveals that in certain cases the energy-gap Hamiltonian is insufficient to model the spectroscopic technique correctly. The results using a modified energy-gap Hamiltonian show that I{sup (4)} 2D ES can reveal detailed lineshape information, but,more » contrary to prior reports, does not reveal dynamics during the waiting time.« less

A new approach in the design of an interactive environment for teaching Hamiltonian digraphs

NASA Astrophysics Data System (ADS)

Iordan, A. E.; Panoiu, M.

2014-03-01

In this article the authors present the necessary steps in object orientated design of an interactive environment that is dedicated to the process of acquaintances assimilation in Hamiltonian graphs theory domain, especially for the simulation of algorithms which determine the Hamiltonian trails and circuits. The modelling of the interactive environment is achieved through specific UML diagrams representing the steps of analysis, design and implementation. This interactive environment is very useful for both students and professors, because computer programming domain, especially digraphs theory domain is comprehended and assimilated with difficulty by students.

Continuation of periodic orbits in symmetric Hamiltonian and conservative systems

NASA Astrophysics Data System (ADS)

Galan-Vioque, J.; Almaraz, F. J. M.; Macías, E. F.

2014-12-01

We present and review results on the continuation and bifurcation of periodic solutions in conservative, reversible and Hamiltonian systems in the presence of symmetries. In particular we show how two-point boundary value problem continuation software can be used to compute families of periodic solutions of symmetric Hamiltonian systems. The technique is introduced with a very simple model example (the mathematical pendulum), justified with a theoretical continuation result and then applied to two non trivial examples: the non integrable spring pendulum and the continuation of the figure eight solution of the three body problem.

Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kagan, Mikhail

2005-11-15

In this paper we review a model based on loop quantum cosmology that arises from a symmetry reduction of the self-dual Plebanski action. In this formulation the symmetry reduction leads to a very simple Hamiltonian constraint that can be quantized explicitly in the framework of loop quantum cosmology. We investigate the phenomenological implications of this model in the semiclassical regime and compare those with the known results of the standard Loop Quantum Cosmology.

Heavy element effects in the diagonal Born–Oppenheimer correction within a relativistic spin-free Hamiltonian

DOE PAGES

Imafuku, Yuji; Abe, Minori; Schmidt, Michael W.; ...

2016-03-22

Methodologies beyond the Born–Oppenheimer (BO) approximation are nowadays important to explain high precision spectroscopic measurements. Most previous evaluations of the BO correction are, however, focused on light-element molecules and based on a nonrelativistic Hamiltonian, so no information about the BO approximation (BOA) breakdown in heavy-element molecules is available. The present work is the first to investigate the BOA breakdown for the entire periodic table, by considering scalar relativistic effects in the Diagonal BO correction (DBOC). In closed shell atoms, the relativistic EDBOC scales as Z 1.25 and the nonrelativistic EDBOC scales as Z 1.17, where Z is the atomic number.more » Hence, we found that EDBOC becomes larger in heavy element atoms and molecules, and the relativistic EDBOC increases faster than nonrelativistic EDBOC. We have further investigated the DBOC effects on properties such as potential energy curves, spectroscopic parameters, and various energetic properties. The DBOC effects for these properties are mostly affected by the lightest atom in the molecule. Furthermore, in X 2 or XAt molecule (X = H, Li, Na, K, Rb, and Cs) the effect of DBOC systematically decreases when X becomes heavier but in HX molecules, the effect of DBOC seems relatively similar among all the molecules.« less

Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.

PubMed

Gosset, David; Terhal, Barbara M; Vershynina, Anna

2015-04-10

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

Universal Adiabatic Quantum Computation via the Space-Time Circuit-to-Hamiltonian Construction

NASA Astrophysics Data System (ADS)

Gosset, David; Terhal, Barbara M.; Vershynina, Anna

2015-04-01

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic X X Z chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q -deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

A Hamiltonian driven quantum-like model for overdistribution in episodic memory recollection.

NASA Astrophysics Data System (ADS)

Broekaert, Jan B.; Busemeyer, Jerome R.

2017-06-01

While people famously forget genuine memories over time, they also tend to mistakenly over-recall equivalent memories concerning a given event. The memory phenomenon is known by the name of episodic overdistribution and occurs both in memories of disjunctions and partitions of mutually exclusive events and has been tested, modeled and documented in the literature. The total classical probability of recalling exclusive sub-events most often exceeds the probability of recalling the composed event, i.e. a subadditive total. We present a Hamiltonian driven propagation for the Quantum Episodic Memory model developed by Brainerd (et al., 2015) for the episodic memory overdistribution in the experimental immediate item false memory paradigm (Brainerd and Reyna, 2008, 2010, 2015). Following the Hamiltonian method of Busemeyer and Bruza (2012) our model adds time-evolution of the perceived memory state through the stages of the experimental process based on psychologically interpretable parameters - γ_c for recollection capability of cues, κ_p for bias or description-dependence by probes and β for the average gist component in the memory state at start. With seven parameters the Hamiltonian model shows good accuracy of predictions both in the EOD-disjunction and in the EOD-subadditivity paradigm. We noticed either an outspoken preponderance of the gist over verbatim trace, or the opposite, in the initial memory state when β is real. Only for complex β a mix of both traces is present in the initial state for the EOD-subadditivity paradigm.

Mobile spin impurity in an optical lattice

NASA Astrophysics Data System (ADS)

Duncan, C. W.; Bellotti, F. F.; Öhberg, P.; Zinner, N. T.; Valiente, M.

2017-07-01

We investigate the Fermi polaron problem in a spin-1/2 Fermi gas in an optical lattice for the limit of both strong repulsive contact interactions and one dimension. In this limit, a polaronic-like behaviour is not expected, and the physics is that of a magnon or impurity. While the charge degrees of freedom of the system are frozen, the resulting tight-binding Hamiltonian for the impurity’s spin exhibits an intriguing structure that strongly depends on the filling factor of the lattice potential. This filling dependency also transfers to the nature of the interactions for the case of two magnons and the important spin balanced case. At low filling, and up until near unit filling, the single impurity Hamiltonian faithfully reproduces a single-band, quasi-homogeneous tight-binding problem. As the filling is increased and the second band of the single particle spectrum of the periodic potential is progressively filled, the impurity Hamiltonian, at low energies, describes a single particle trapped in a multi-well potential. Interestingly, once the first two bands are fully filled, the impurity Hamiltonian is a near-perfect realisation of the Su-Schrieffer-Heeger model. Our studies, which go well beyond the single-band approximation, that is, the Hubbard model, pave the way for the realisation of interacting one-dimensional models of condensed matter physics.

Trojan dynamics well approximated by a new Hamiltonian normal form

NASA Astrophysics Data System (ADS)

Páez, Rocío Isabel; Locatelli, Ugo

2015-10-01

We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the planar circular restricted three-body problem, by introducing a number of key new ideas in the formulation. In some sense, we adapt the approach of Garfinkel to the context of the normal form theory and its modern techniques. First, we make use of Delaunay variables for a physically accurate representation of the system. Therefore, we introduce a novel manipulation of the variables so as to respect the natural behaviour of the model. We develop a normalization procedure over the fast angle which exploits the fact that singularities in this model are essentially related to the slow angle. Thus, we produce a new normal form, i.e. an integrable approximation to the Hamiltonian. We emphasize some practical examples of the applicability of our normalizing scheme, e.g. the estimation of the stable libration region. Finally, we compare the level curves produced by our normal form with surfaces of section provided by the integration of the non-normalized Hamiltonian, with very good agreement. Further precision tests are also provided. In addition, we give a step-by-step description of the algorithm, allowing for extensions to more complicated models.

Hamiltonian derivation of the nonhydrostatic pressure-coordinate model

NASA Astrophysics Data System (ADS)

Salmon, Rick; Smith, Leslie M.

1994-07-01

In 1989, the Miller-Pearce (MP) model for nonhydrostatic fluid motion governed by equations written in pressure coordinates was extended by removing the prescribed reference temperature, T(sub s)(p), while retaining the conservation laws and other desirable properties. It was speculated that this extension of the MP model had a Hamiltonian structure and that a slick derivation of the Ertel property could be constructed if the relevant Hamiltonian were known. In this note, the extended equations are derived using Hamilton's principle. The potential vorticity law arises from the usual particle-relabeling symmetry of the Lagrangian, and even the absence of sound waves is anticipated from the fact that the pressure inside the free energy G(p, theta) in the derived equation is hydrostatic and thus G is insensitive to local pressure fluctuations. The model extension is analogous to the semigeostrophic equations for nearly geostrophic flow, which do not incorporate a prescribed reference state, while the earlier MP model is analogous to the quasigeostrophic equations, which become highly inaccurate when the flow wanders from a prescribed state with nearly flat isothermal surfaces.

Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene.

PubMed

Morrison, Adrian F; Herbert, John M

2017-06-14

Recently, we introduced an ab initio version of the Frenkel-Davydov exciton model for computing excited-state properties of molecular crystals and aggregates. Within this model, supersystem excited states are approximated as linear combinations of excitations localized on molecular sites, and the electronic Hamiltonian is constructed and diagonalized in a direct-product basis of non-orthogonal configuration state functions computed for isolated fragments. Here, we derive and implement analytic derivative couplings for this model, including nuclear derivatives of the natural transition orbital and symmetric orthogonalization transformations that are part of the approximation. Nuclear derivatives of the exciton Hamiltonian's matrix elements, required in order to compute the nonadiabatic couplings, are equivalent to the "Holstein" and "Peierls" exciton/phonon couplings that are widely discussed in the context of model Hamiltonians for energy and charge transport in organic photovoltaics. As an example, we compute the couplings that modulate triplet exciton transport in crystalline tetracene, which is relevant in the context of carrier diffusion following singlet exciton fission.

Local magnetizations in impure two-dimensional antiferromagnets

NASA Astrophysics Data System (ADS)

van Luijk, J. A.; Arts, A. F. M.; de Wijn, H. W.

1980-03-01

The local magnetizations near dilute substitutional impurities in the quadratic-layer antiferromagnet K2MnF4 are studied both experimentally and theoretically. The impurities considered are the nonmagnetic Zn and Mg, as well as Ni. The magnetizations are probed through the positions of the impurity-associated satellites in the nuclear magnetic resonance of the out-of-layer and in-layer 19F nuclei adjacent to the magnetic ions. It is discussed in which way the effects of lattice deformations can be eliminated in order to obtain the variations of the local magnetizations with temperature. The theoretical treatment is based on Green's-function techniques. The decoupling employed is within the local spin-deviation operators and accounts for correlation between nearest neighbors. It reduces the renormalized spin-wave Hamiltonian to an effective quadratic form, rendering decoupling of Green's functions unnecessary. The spectral distributions of the excitations are calculated including local modes. The theory is subsequently applied to the 13-site cluster consisting of the impurity and the first three shells of Mn around it. Good agreement is found. The magnetization is significantly modified in the first shell. The further shells are only weakly affected, however somewhat stronger than in comparable three-dimensional systems. For nonmagnetic impurities the thermal spin deviation in the first shell is about 13 larger than that of the host; in the Ni-doped system the additional deviations are within 1%. The zero-point deviation of the Ni is 0.11 units of spin, as compared to 0.17 in the host. A further experimental result is a uniform shift, increasing with concentration, of the sublattice magnetization at large distance from the impurity. It must be related to the finite density of states near the zone center in two-dimensional systems. Finally, some data are presented on the local susceptibilities.

Quantum error suppression with commuting Hamiltonians: two local is too local.

PubMed

Marvian, Iman; Lidar, Daniel A

2014-12-31

We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped, they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the two-local case. By making the favorable assumption that the gap is infinite, we show that single-site perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonian which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the no-hiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems. The main reason that two-local commuting Hamiltonians cannot be used for quantum error suppression is that their ground subspaces have only short-range (two-body) entanglement.

Effective time-independent analysis for quantum kicked systems.

PubMed

Bandyopadhyay, Jayendra N; Guha Sarkar, Tapomoy

2015-03-01

We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent approximate effective time-independent scenario, whereby the system is rendered integrable. The time evolution is factorized into an initial kick, followed by an evolution dictated by a time-independent Hamiltonian and a final kick. This method is applied to the kicked top model. The effective time-independent Hamiltonian thus obtained does not suffer from spurious divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is used. The quasienergy spectrum of the Floquet operator is found to be in excellent agreement with the energy levels of the effective Hamiltonian for a wide range of system parameters. The density of states for the effective system exhibits sharp peaklike features, pointing towards quantum criticality. The dynamics in the classical limit of the integrable effective Hamiltonian shows remarkable agreement with the nonintegrable map corresponding to the actual time-dependent system in the nonchaotic regime. This suggests that the effective Hamiltonian serves as a substitute for the actual system in the nonchaotic regime at both the quantum and classical level.

Effective time-independent analysis for quantum kicked systems

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Jayendra N.; Guha Sarkar, Tapomoy

2015-03-01

We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent approximate effective time-independent scenario, whereby the system is rendered integrable. The time evolution is factorized into an initial kick, followed by an evolution dictated by a time-independent Hamiltonian and a final kick. This method is applied to the kicked top model. The effective time-independent Hamiltonian thus obtained does not suffer from spurious divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is used. The quasienergy spectrum of the Floquet operator is found to be in excellent agreement with the energy levels of the effective Hamiltonian for a wide range of system parameters. The density of states for the effective system exhibits sharp peaklike features, pointing towards quantum criticality. The dynamics in the classical limit of the integrable effective Hamiltonian shows remarkable agreement with the nonintegrable map corresponding to the actual time-dependent system in the nonchaotic regime. This suggests that the effective Hamiltonian serves as a substitute for the actual system in the nonchaotic regime at both the quantum and classical level.

A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree.

PubMed

Nagoor Gani, A; Latha, S R

2016-01-01

A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. As the number of vertices and edges grow, it becomes very difficult to keep track of all the different ways through which the vertices are connected. Hence, analysis of large graphs can be efficiently done with the assistance of a computer system that interprets graphs as matrices. And, of course, a good and well written algorithm will expedite the analysis even faster. The most convenient way to quickly test whether there is an edge between two vertices is to represent graphs using adjacent matrices. In this paper, a new algorithm is proposed to find fuzzy Hamiltonian cycle using adjacency matrix and the degree of the vertices of a fuzzy graph. A fuzzy graph structure is also modeled to illustrate the proposed algorithms with the selected air network of Indigo airlines.

Quantum finance Hamiltonian for coupon bond European and barrier options.

PubMed

Baaquie, Belal E

2008-03-01

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

Cranking Calculation in the sdg Interacting Boson Model

NASA Astrophysics Data System (ADS)

Wang, Baolin

1998-10-01

A self-consistent cranking calculation of the intrinsic states of the sdg interacting boson model is performed. The formulae of the moment of inertia are given in a general sdg IBM multipole Hamiltonian with one- and two-body terms. In the quadrupole interaction, the intrinsic states, the quadrupole and hexadecapole deformation and the moment of inertia are investigated in the large N limit. Using a simple Hamiltonian, the results of numerical calculations for 152, 154Sm and 154-160 Gd satisfactorily reproduce the experimental data.

Correspondence between a shaken honeycomb lattice and the Haldane model

NASA Astrophysics Data System (ADS)

Modugno, Michele; Pettini, Giulio

2017-11-01

We investigate the correspondence between the tight-binding Floquet Hamiltonian of a periodically modulated honeycomb lattice and the Haldane model. We show that—though the two systems share the same topological phase diagram, as reported in a breakthrough experiment with ultracold atoms in a stretched honeycomb lattice [G. Jotzu et al., Nature (London) 515, 237 (2014), 10.1038/nature13915]—the corresponding Hamiltonians are not equivalent, the one of the shaken lattice presenting a much richer structure.

Hamiltonian and potentials in derivative pricing models: exact results and lattice simulations

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.; Corianò, Claudio; Srikant, Marakani

2004-03-01

The pricing of options, warrants and other derivative securities is one of the great success of financial economics. These financial products can be modeled and simulated using quantum mechanical instruments based on a Hamiltonian formulation. We show here some applications of these methods for various potentials, which we have simulated via lattice Langevin and Monte Carlo algorithms, to the pricing of options. We focus on barrier or path dependent options, showing in some detail the computational strategies involved.

Connections between ’t Hooft’s beables and canonical descriptions of dissipative systems

NASA Astrophysics Data System (ADS)

Schuch, Dieter; Blasone, Massimo

2017-08-01

According to a proposal by ’t Hooft, information loss introduced by constraints in certain classical dissipative systems may lead to quantization. This scheme can be realized within the Bateman model of two coupled oscillators, one damped and one accelerated. In this paper we analyze the links of this approach to effective Hamiltonians where the environmental degrees of freedom do not appear explicitly but their effect leads to the same friction force appearing in the Bateman model. In particular, it is shown that by imposing constraints, the Bateman Hamiltonian can be transformed into an effective one expressed in expanding coordinates. This one can be transformed via a canonical transformation into Caldirola and Kanai’s effective Hamiltonian that can be linked to the conventional system-plus-reservoir approach, for example, in a form used by Caldeira and Leggett.

Generalized shortcuts to adiabaticity and enhanced robustness against decoherence

NASA Astrophysics Data System (ADS)

Santos, Alan C.; Sarandy, Marcelo S.

2018-01-01

Shortcuts to adiabaticity provide a general approach to mimic adiabatic quantum processes via arbitrarily fast evolutions in Hilbert space. For these counter-diabatic evolutions, higher speed comes at higher energy cost. Here, the counter-diabatic theory is employed as a minimal energy demanding scheme for speeding up adiabatic tasks. As a by-product, we show that this approach can be used to obtain infinite classes of transitionless models, including time-independent Hamiltonians under certain conditions over the eigenstates of the original Hamiltonian. We apply these results to investigate shortcuts to adiabaticity in decohering environments by introducing the requirement of a fixed energy resource. In this scenario, we show that generalized transitionless evolutions can be more robust against decoherence than their adiabatic counterparts. We illustrate this enhanced robustness both for the Landau-Zener model and for quantum gate Hamiltonians.

Stability of equilibrium solutions of Hamiltonian systems with n-degrees of freedom and single resonance in the critical case

NASA Astrophysics Data System (ADS)

dos Santos, Fabio; Vidal, Claudio

2018-04-01

In this paper we give new results for the stability of one equilibrium solution of an autonomous analytic Hamiltonian system in a neighborhood of the equilibrium point with n-degrees of freedom. Our Main Theorem generalizes several results existing in the literature and mainly we give information in the critical cases (i.e., the condition of stability and instability is not fulfilled). In particular, our Main Theorem provides necessary and sufficient conditions for stability of the equilibrium solutions under the existence of a single resonance. Using analogous tools used in the Main Theorem for the critical case, we study the stability or instability of degenerate equilibrium points in Hamiltonian systems with one degree of freedom. We apply our results to the stability of Hamiltonians of the type of cosmological models as in planar as in the spatial case.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

PubMed

Deng, Mao-Lin; Zhu, Wei-Qiu

2016-08-01

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Hamiltonian structure of three-dimensional gravity in Vielbein formalism

NASA Astrophysics Data System (ADS)

Hajihashemi, Mahdi; Shirzad, Ahmad

2018-01-01

Considering Chern-Simons like gravity theories in three dimensions as first order systems, we analyze the Hamiltonian structure of three theories Topological massive gravity, New massive gravity, and Zwei-Dreibein Gravity. We show that these systems demonstrate a new feature of the constrained systems in which a new kind of constraints emerge due to factorization of determinant of the matrix of Poisson brackets of constraints. We find the desired number of degrees of freedom as well as the generating functional of local Lorentz transformations and diffeomorphism through canonical structure of the system. We also compare the Hamiltonian structure of linearized version of the considered models with the original ones.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn

2016-08-15

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

NASA Astrophysics Data System (ADS)

Keck, Maximilian; Montangero, Simone; Santoro, Giuseppe E.; Fazio, Rosario; Rossini, Davide

2017-11-01

We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between nonadiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (the average value of the Hamiltonian) as a measure of the deviation from reaching the final target ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the nonadiabatic effects and the dissipative processes. We compare these results with the matrix-product-operator simulations of an Ising system and show that the phenomenology we found also applies for this more realistic case.

High-spin level structure and Ground-state phase transition in the odd-mass 103-109Rh isotopes in the framework of exactly solvable sdg interacting boson-fermion model

NASA Astrophysics Data System (ADS)

Ghapanvari, M.; Ghorashi, A. H.; Ranjbar, Z.; Jafarizadeh, M. A.

2018-03-01

In this article, the negative-parity states in the odd-mass 103 - 109Rh isotopes in terms of the sd and sdg interacting-boson fermion models were studied. The transitional interacting boson-fermion model Hamiltonians in sd and sdg-IBFM versions based on affine SU (1 , 1) Lie Algebra were employed to describe the evolution from the spherical to deformed gamma unstable shapes along with the chain of Rh isotopes. In this method, sdg-IBFM Hamiltonian, which is a three level pairing Hamiltonian was determined easily via the exactly solvable method. Some observables of the shape phase transitions such as energy levels, the two neutron separation energies, signature splitting of the γ-vibrational band, the α-decay and double β--decay energies were calculated and examined for these isotopes. The present calculation correctly reproduces the spherical to gamma-soft phase transition in the Rh isotopes. Some comparisons were made with sd-IBFM.

Dissipative N-point-vortex Models in the Plane

NASA Astrophysics Data System (ADS)

Shashikanth, Banavara N.

2010-02-01

A method is presented for constructing point vortex models in the plane that dissipate the Hamiltonian function at any prescribed rate and yet conserve the level sets of the invariants of the Hamiltonian model arising from the SE (2) symmetries. The method is purely geometric in that it uses the level sets of the Hamiltonian and the invariants to construct the dissipative field and is based on elementary classical geometry in ℝ3. Extension to higher-dimensional spaces, such as the point vortex phase space, is done using exterior algebra. The method is in fact general enough to apply to any smooth finite-dimensional system with conserved quantities, and, for certain special cases, the dissipative vector field constructed can be associated with an appropriately defined double Nambu-Poisson bracket. The most interesting feature of this method is that it allows for an infinite sequence of such dissipative vector fields to be constructed by repeated application of a symmetric linear operator (matrix) at each point of the intersection of the level sets.

Canonical formalism for modelling and control of rigid body dynamics.

PubMed

Gurfil, P

2005-12-01

This paper develops a new paradigm for stabilization of rigid-body dynamics. The state-space model is formulated using canonical elements, known as the Serret-Andoyer (SA) variables, thus far scarcely used for engineering applications. The main feature of the SA formalism is the reduction of the dynamics via the underlying symmetry stemming from conservation of angular momentum and rotational kinetic energy. The controllability of the system model is examined using the notion of accessibility, and is shown to be accessible from all points. Based on the accessibility proof, two nonlinear asymptotic feedback stabilizers are developed: a damping feedback is designed based on the Jurdjevic-Quinn method, and a Hamiltonian controller is derived by using the Hamiltonian as a natural Lyapunov function for the closed-loop dynamics. It is shown that the Hamiltonian control is both passive and inverse optimal with respect to a meaningful performance index. The performance of the new controllers is examined and compared using simulations of realistic scenarios from the satellite attitude dynamics field.

Replica Approach for Minimal Investment Risk with Cost

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-06-01

In the present work, the optimal portfolio minimizing the investment risk with cost is discussed analytically, where an objective function is constructed in terms of two negative aspects of investment, the risk and cost. We note the mathematical similarity between the Hamiltonian in the mean-variance model and the Hamiltonians in the Hopfield model and the Sherrington-Kirkpatrick model, show that we can analyze this portfolio optimization problem by using replica analysis, and derive the minimal investment risk with cost and the investment concentration of the optimal portfolio. Furthermore, we validate our proposed method through numerical simulations.

First-order symmetry-adapted perturbation theory for multiplet splittings.

PubMed

Patkowski, Konrad; Żuchowski, Piotr S; Smith, Daniel G A

2018-04-28

We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S 2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S 2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

First-order symmetry-adapted perturbation theory for multiplet splittings

NASA Astrophysics Data System (ADS)

Patkowski, Konrad; Żuchowski, Piotr S.; Smith, Daniel G. A.

2018-04-01

We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

Efficient geometry optimization by Hellmann-Feynman forces with the anti-Hermitian contracted Schrödinger equation

NASA Astrophysics Data System (ADS)

Foley, Jonathan J.; Mazziotti, David A.

2010-10-01

An efficient method for geometry optimization based on solving the anti-Hermitian contracted Schrödinger equation (ACSE) is presented. We formulate a reduced version of the Hellmann-Feynman theorem (HFT) in terms of the two-electron reduced Hamiltonian operator and the two-electron reduced density matrix (2-RDM). The HFT offers a considerable reduction in computational cost over methods which rely on numerical derivatives. While previous geometry optimizations with numerical gradients required 2M evaluations of the ACSE where M is the number of nuclear degrees of freedom, the HFT requires only a single ACSE calculation of the 2-RDM per gradient. Synthesizing geometry optimization techniques with recent extensions of the ACSE theory to arbitrary electronic and spin states provides an important suite of tools for accurately determining equilibrium and transition-state structures of ground- and excited-state molecules in closed- and open-shell configurations. The ability of the ACSE to balance single- and multi-reference correlation is particularly advantageous in the determination of excited-state geometries where the electronic configurations differ greatly from the ground-state reference. Applications are made to closed-shell molecules N2, CO, H2O, the open-shell molecules B2 and CH, and the excited state molecules N2, B2, and BH. We also study the HCN ↔ HNC isomerization and the geometry optimization of hydroxyurea, a molecule which has a significant role in the treatment of sickle-cell anaemia.

Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano

NASA Astrophysics Data System (ADS)

Falaize, Antoine; Hélie, Thomas

2017-03-01

This paper deals with the time-domain simulation of an electro-mechanical piano: the Fender Rhodes. A simplified description of this multi-physical system is considered. It is composed of a hammer (nonlinear mechanical component), a cantilever beam (linear damped vibrating component) and a pickup (nonlinear magneto-electronic transducer). The approach is to propose a power-balanced formulation of the complete system, from which a guaranteed-passive simulation is derived to generate physically-based realistic sound synthesis. Theses issues are addressed in four steps. First, a class of Port-Hamiltonian Systems is introduced: these input-to-output systems fulfill a power balance that can be decomposed into conservative, dissipative and source parts. Second, physical models are proposed for each component and are recast in the port-Hamiltonian formulation. In particular, a finite-dimensional model of the cantilever beam is derived, based on a standard modal decomposition applied to the Euler-Bernoulli model. Third, these systems are interconnected, providing a nonlinear finite-dimensional Port-Hamiltonian System of the piano. Fourth, a passive-guaranteed numerical method is proposed. This method is built to preserve the power balance in the discrete-time domain, and more precisely, its decomposition structured into conservative, dissipative and source parts. Finally, simulations are performed for a set of physical parameters, based on empirical but realistic values. They provide a variety of audio signals which are perceptively relevant and qualitatively similar to some signals measured on a real instrument.

A Few Integrable Dynamical Systems, Recurrence Operators, Expanding Integrable Models and Hamiltonian Structures by the r-Matrix Method

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Muhammad, Iqbal; Yue, Chao

2017-10-01

We extend two known dynamical systems obtained by Blaszak, et al. via choosing Casimir functions and utilizing Novikov-Lax equation so that a series of novel dynamical systems including generalized Burgers dynamical system, heat equation, and so on, are followed to be generated. Then we expand some differential operators presented in the paper to deduce two types of expanding dynamical models. By taking the generalized Burgers dynamical system as an example, we deform its expanding model to get a half-expanding system, whose recurrence operator is derived from Lax representation, and its Hamiltonian structure is also obtained by adopting a new way. Finally, we expand the generalized Burgers dynamical system to the (2+1)-dimensional case whose Hamiltonian structure is derived by Poisson tensor and gradient of the Casimir function. Besides, a kind of (2+1)-dimensional expanding dynamical model of the (2+1)-dimensional dynamical system is generated as well. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

On quantum integrability of the Landau-Lifshitz model

NASA Astrophysics Data System (ADS)

Melikyan, A.; Pinzul, A.

2009-10-01

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Atomic structure calculations and identification of EUV and SXR spectral lines in Sr XXX

NASA Astrophysics Data System (ADS)

Goyal, Arun; Khatri, Indu; Aggarwal, Sunny; Singh, A. K.; Mohan, Man

2015-08-01

We report an extensive theoretical study of atomic data for Sr XXX in a wide range with L-shell electron excitations to the M-shell. We have calculated energy levels, wave-function compositions and lifetimes for lowest 113 fine structure levels and wavelengths of an extreme Ultraviolet (EUV) and soft X-ray (SXR) transitions. We have employed multi-configuration Dirac Fock method (MCDF) approach within the framework of Dirac-Coulomb Hamiltonian including quantum electrodynamics (QED) and Breit corrections. We have also presented the radiative data for electric and magnetic dipole (E1, M1) and quadrupole (E2, M2) transitions from the ground state. We have made comparisons with available energy levels compiled by NIST and achieve good agreement. But due to inadequate data in the literature, analogous relativistic distorted wave calculations have also been performed using flexible atomic code (FAC) to assess the reliability and accuracy of our results. Additionally, we have provided new atomic data for Sr XXX which is not published elsewhere in the literature and we believe that our results may be beneficial in fusion plasma research and astrophysical investigations and applications.

Kirchhoff's rule for quantum wires

NASA Astrophysics Data System (ADS)

Kostrykin, V.; Schrader, R.

1999-01-01

We formulate and discuss one-particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with n channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy E>0 is given explicitly in terms of the boundary conditions and the lengths of the internal lines. It is shown to be unitary, which may be viewed as the quantum version of Kirchhoff's law. We exhibit covariance and symmetry properties. It is symmetric if the boundary conditions are real. Also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low-energy behaviour of one theory gives the high-energy behaviour of the transformed theory. Finally, we provide a composition rule by which the on-shell S-matrix of a graph is factorizable in terms of the S-matrices of its subgraphs. All proofs use only known facts from the theory of self-adjoint extensions, standard linear algebra, complex function theory and elementary arguments from the theory of Hermitian symplectic forms.

Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians.

PubMed

Ghassemi Tabrizi, Shadan; Arbuznikov, Alexei V; Kaupp, Martin

2018-03-26

Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl] 4 ('Ni 4 ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp - is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni 4 , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Next generation of the self-consistent and environment-dependent Hamiltonian: Applications to various boron allotropes from zero- to three-dimensional structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tandy, P.; Yu, Ming; Leahy, C.

2015-03-28

An upgrade of the previous self-consistent and environment-dependent linear combination of atomic orbitals Hamiltonian (referred as SCED-LCAO) has been developed. This improved version of the semi-empirical SCED-LCAO Hamiltonian, in addition to the inclusion of self-consistent determination of charge redistribution, multi-center interactions, and modeling of electron-electron correlation, has taken into account the effect excited on the orbitals due to the atomic aggregation. This important upgrade has been subjected to a stringent test, the construction of the SCED-LCAO Hamiltonian for boron. It was shown that the Hamiltonian for boron has successfully characterized the electron deficiency of boron and captured the complex chemicalmore » bonding in various boron allotropes, including the planar and quasi-planar, the convex, the ring, the icosahedral, and the fullerene-like clusters, the two-dimensional monolayer sheets, and the bulk alpha boron, demonstrating its transferability, robustness, reliability, and predictive power. The molecular dynamics simulation scheme based on the Hamiltonian has been applied to explore the existence and the energetics of ∼230 compact boron clusters B{sub N} with N in the range from ∼100 to 768, including the random, the rhombohedral, and the spherical icosahedral structures. It was found that, energetically, clusters containing whole icosahedral B{sub 12} units are more stable for boron clusters of larger size (N > 200). The ease with which the simulations both at 0 K and finite temperatures were completed is a demonstration of the efficiency of the SCED-LCAO Hamiltonian.« less

Next generation of the self-consistent and environment-dependent Hamiltonian: Applications to various boron allotropes from zero- to three-dimensional structures

NASA Astrophysics Data System (ADS)

Tandy, P.; Yu, Ming; Leahy, C.; Jayanthi, C. S.; Wu, S. Y.

2015-03-01

An upgrade of the previous self-consistent and environment-dependent linear combination of atomic orbitals Hamiltonian (referred as SCED-LCAO) has been developed. This improved version of the semi-empirical SCED-LCAO Hamiltonian, in addition to the inclusion of self-consistent determination of charge redistribution, multi-center interactions, and modeling of electron-electron correlation, has taken into account the effect excited on the orbitals due to the atomic aggregation. This important upgrade has been subjected to a stringent test, the construction of the SCED-LCAO Hamiltonian for boron. It was shown that the Hamiltonian for boron has successfully characterized the electron deficiency of boron and captured the complex chemical bonding in various boron allotropes, including the planar and quasi-planar, the convex, the ring, the icosahedral, and the fullerene-like clusters, the two-dimensional monolayer sheets, and the bulk alpha boron, demonstrating its transferability, robustness, reliability, and predictive power. The molecular dynamics simulation scheme based on the Hamiltonian has been applied to explore the existence and the energetics of ˜230 compact boron clusters BN with N in the range from ˜100 to 768, including the random, the rhombohedral, and the spherical icosahedral structures. It was found that, energetically, clusters containing whole icosahedral B12 units are more stable for boron clusters of larger size (N > 200). The ease with which the simulations both at 0 K and finite temperatures were completed is a demonstration of the efficiency of the SCED-LCAO Hamiltonian.

Robustness against non-magnetic impurities in topological superconductors

NASA Astrophysics Data System (ADS)

Nagai, Y.; Ota, Y.; Machida, M.

2014-12-01

We study the robustness against non-magnetic impurities in a three-dimensional topological superconductor, focusing on an effective model (massive Dirac Bogoliubov-de Gennes (BdG) Hamiltonian with s-wave on-site pairing) of CuxBi2Se3 with the parameter set determined by the first-principles calculation. With the use of the self-consistent T- matrix approximation for impurity scattering, we discuss the impurity-concentration dependence of the zero-energy density of states. We show that a single material variable, measuring relativistic effects in the Dirac-BdG Hamiltonian, well characterizes the numerical results. In the nonrelativistic limit, the odd-parity fully-gapped topological superconductivity is fragile against non-magnetic impurities, since this superconductivity can be mapped onto the p-wave superconductivity. On the other hand, in the ultrarelativistic limit, the superconductivity is robust against the non-magnetic impurities, since the effective model has the s-wave superconductivity. We derive the effective Hamiltonian in the both limit.

General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skrypnyk, T., E-mail: taras.skrypnyk@unimib.it, E-mail: tskrypnyk@imath.kiev.ua

Using the technique of classical r-matrices and quantum Lax operators, we construct the most general form of the quantum integrable “n-level, many-mode” spin-boson Jaynes-Cummings-Dicke-type hamiltonians describing an interaction of a molecule of N n-level atoms with many modes of electromagnetic field and containing, in general, additional non-linear interaction terms. We explicitly obtain the corresponding quantum Lax operators and spin-boson analogs of the generalized Gaudin hamiltonians and prove their quantum commutativity. We investigate symmetries of the obtained models that are associated with the geometric symmetries of the classical r-matrices and construct the corresponding algebra of quantum integrals. We consider in detailmore » three classes of non-skew-symmetric classical r-matrices with spectral parameters and explicitly obtain the corresponding quantum Lax operators and Jaynes-Cummings-Dicke-type hamiltonians depending on the considered r-matrix.« less

Investigation of triaxiality in 54122-128Xe isotopes in the framework of sdg-IBM

NASA Astrophysics Data System (ADS)

Jafarizadeh, M. A.; Ranjbar, Z.; Fouladi, N.; Ghapanvari, M.

In this paper, a transitional interacting boson model (IBM) Hamiltonian in both sd-(IBM) and sdg-IBM versions based on affine SU(1, 1) Lie algebra is employed to describe deviations from the gamma-unstable nature of Hamiltonian along the chain of Xe isotopes. sdg-IBM Hamiltonian proposed a better interpretation of this deviation which cannot be explained in the sd-boson models. The nuclei studied have well-known γ bands close to the γ-unstable limit. The energy levels, B(E2) transition rates and signature splitting of the γ -vibrational band are calculated via the affine SU(1,1) Lie algebra. An acceptable degree of agreement was achieved based on this procedure. It is shown that in these isotopes the signature splitting is better reproduced by the inclusion of sdg-IBM. In none of them, any evidence for a stable, triaxial ground state shape is found.

R-matrix-valued Lax pairs and long-range spin chains

NASA Astrophysics Data System (ADS)

Sechin, I.; Zotov, A.

2018-06-01

In this paper we discuss R-matrix-valued Lax pairs for slN Calogero-Moser model and their relation to integrable quantum long-range spin chains of the Haldane-Shastry-Inozemtsev type. First, we construct the R-matrix-valued Lax pairs for the third flow of the classical Calogero-Moser model. Then we notice that the scalar parts (in the auxiliary space) of the M-matrices corresponding to the second and third flows have form of special spin exchange operators. The freezing trick restricts them to quantum Hamiltonians of long-range spin chains. We show that for a special choice of the R-matrix these Hamiltonians reproduce those for the Inozemtsev chain. In the general case related to the Baxter's elliptic R-matrix we obtain a natural anisotropic extension of the Inozemtsev chain. Commutativity of the Hamiltonians is verified numerically. Trigonometric limits lead to the Haldane-Shastry chains and their anisotropic generalizations.

Effective lattice Hamiltonian for monolayer tin disulfide: Tailoring electronic structure with electric and magnetic fields

NASA Astrophysics Data System (ADS)

Yu, Jin; van Veen, Edo; Katsnelson, Mikhail I.; Yuan, Shengjun

2018-06-01

The electronic properties of monolayer tin dilsulfide (ML -Sn S2 ), a recently synthesized metal dichalcogenide, are studied by a combination of first-principles calculations and tight-binding (TB) approximation. An effective lattice Hamiltonian based on six hybrid s p -like orbitals with trigonal rotation symmetry are proposed to calculate the band structure and density of states for ML -Sn S2 , which demonstrates good quantitative agreement with relativistic density-functional-theory calculations in a wide energy range. We show that the proposed TB model can be easily applied to the case of an external electric field, yielding results consistent with those obtained from full Hamiltonian results. In the presence of a perpendicular magnetic field, highly degenerate equidistant Landau levels are obtained, showing typical two-dimensional electron gas behavior. Thus, the proposed TB model provides a simple way in describing properties in ML -Sn S2 .

Scalable free energy calculation of proteins via multiscale essential sampling

NASA Astrophysics Data System (ADS)

Moritsugu, Kei; Terada, Tohru; Kidera, Akinori

2010-12-01

A multiscale simulation method, "multiscale essential sampling (MSES)," is proposed for calculating free energy surface of proteins in a sizable dimensional space with good scalability. In MSES, the configurational sampling of a full-dimensional model is enhanced by coupling with the accelerated dynamics of the essential degrees of freedom. Applying the Hamiltonian exchange method to MSES can remove the biasing potential from the coupling term, deriving the free energy surface of the essential degrees of freedom. The form of the coupling term ensures good scalability in the Hamiltonian exchange. As a test application, the free energy surface of the folding process of a miniprotein, chignolin, was calculated in the continuum solvent model. Results agreed with the free energy surface derived from the multicanonical simulation. Significantly improved scalability with the MSES method was clearly shown in the free energy calculation of chignolin in explicit solvent, which was achieved without increasing the number of replicas in the Hamiltonian exchange.

Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity

NASA Astrophysics Data System (ADS)

Li, Qian; Matula, Thomas J.; Tu, Juan; Guo, Xiasheng; Zhang, Dong

2013-02-01

It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear ‘Cross law’ to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius-time curves and the numerical simulations demonstrate that the ‘compression-only’ behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., ‘shear-thinning’ and ‘strain-softening’) in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity.

Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity.

PubMed

Li, Qian; Matula, Thomas J; Tu, Juan; Guo, Xiasheng; Zhang, Dong

2013-02-21

It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear 'Cross law' to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius-time curves and the numerical simulations demonstrate that the 'compression-only' behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., 'shear-thinning' and 'strain-softening') in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity.

Lattice Virasoro algebra and corner transfer matrices in the Baxter eight-vertex model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Itoyama, H.; Thacker, H.B.

1987-04-06

A lattice Virasoro algebra is constructed for the Baxter eight-vertex model. The operator L/sub 0/ is obtained from the logarithm of the corner transfer matrix and is given by the first moment of the XYZ spin-chain Hamiltonian. The algebra is valid even when the Hamiltonian includes a mass term, in which case it represents lattice coordinate transformations which distinguish between even and odd sublattices. We apply the quantum inverse scattering method to demonstrate that the Virasoro algebra follows from the Yang-Baxter relations.

Hamiltonian chaos acts like a finite energy reservoir: accuracy of the Fokker-Planck approximation.

PubMed

Riegert, Anja; Baba, Nilüfer; Gelfert, Katrin; Just, Wolfram; Kantz, Holger

2005-02-11

The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic approximation on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.

Hamiltonian theory of guiding-center motion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Littlejohn, R.G.

1980-05-01

A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.

Non-perturbative RPA-method implemented in the Coulomb gauge QCD Hamiltonian: From quarks and gluons to baryons and mesons

NASA Astrophysics Data System (ADS)

Yepez-Martinez, Tochtli; Civitarese, Osvaldo; Hess, Peter O.

2018-02-01

Starting from an algebraic model based on the QCD-Hamiltonian and previously applied to study meson states, we have developed an extension of it in order to explore the structure of baryon states. In developing our approach we have adapted concepts taken from group theory and non-perturbative many-body methods to describe states built from effective quarks and anti-quarks degrees of freedom. As a Hamiltonian we have used the QCD Hamiltonian written in the Coulomb Gauge, and expressed it in terms of effective quark-antiquark, di-quarks and di-antiquark excitations. To gain some insights about the relevant interactions of quarks in hadronic states, the Hamiltonian was approximately diagonalized by mapping quark-antiquark pairs and di-quarks (di-antiquarks) onto phonon states. In dealing with the structure of the vacuum of the theory, color-scalar and color-vector states are introduced to account for ground-state correlations. While the use of a purely color-scalar ground state is an obvious choice, so that colorless hadrons contain at least three quarks, the presence of coupled color-vector pairs in the ground state allows for colorless excitations resulting from the action of color objects upon it.

Multibody dynamic analysis using a rotation-free shell element with corotational frame

NASA Astrophysics Data System (ADS)

Shi, Jiabei; Liu, Zhuyong; Hong, Jiazhen

2018-03-01

Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore, the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.

BRST theory without Hamiltonian and Lagrangian

NASA Astrophysics Data System (ADS)

Lyakhovich, S. L.; Sharapov, A. A.

2005-03-01

We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure or action principle is supposed to exist. For such a generic gauge system we construct a consistent BRST formulation, which includes the conventional BV Lagrangian and BFV Hamiltonian schemes as particular cases. If the original manifold carries a weak Poisson structure (a bivector field giving rise to a Poisson bracket on the space of physical observables) the generic gauge system is shown to admit deformation quantization by means of the Kontsevich formality theorem. A sigma-model interpretation of this quantization algorithm is briefly discussed.

Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom

NASA Astrophysics Data System (ADS)

Compelli, A.; Ivanov, R.; Todorov, M.

2017-12-01

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg-de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth. This article is part of the theme issue 'Nonlinear water waves'.

Finite T spectral function of a single carrier injected into an Ising chain: a comparison of 3 different models

NASA Astrophysics Data System (ADS)

Moeller, Mirko; Berciu, Mona

2015-03-01

When studying the properties of complex, magnetic materials it is often necessary to work with effective Hamiltonians. In many cases the effective Hamiltonian is obtained by mapping the full, multiband Hamiltonian onto a simpler, single band model. A prominent example is the use of Zhang-Rice singlets to map the multiband Emery model for cuprates onto the single band t - J -model. Such mappings are usually done at zero temperature (T) and it is implicitly assumed that they are justified at finite T, as well. We present results on 3 different models of a single charge carrier (electron or hole) injected into a ferromagnetic Ising chain. Model I is a two band, two sublattice model, Model II is a two band, single sublattice model, and Model III is a single band model, the so called t -Jz -model. Due to the absence of spin-flip terms, a numerically exact solution of all 3 Models is possible, even at finite T. At zero T a mapping between all 3 models results in the same low energy physics. However, this is no longer true at finite T. Here the low energy behavior of Model III is significantly different from that of Models I and II. The reasons for this discrepancy and its implications for more realistic models (higher dimension, inclusion of spin-flip terms) are discussed. This work was supported by NSERC, QMI and the UBC 4YF (M.M.).

Shapes and stability of algebraic nuclear models

NASA Technical Reports Server (NTRS)

Lopez-Moreno, Enrique; Castanos, Octavio

1995-01-01

A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.

Improvement of the Davydov theory of bioenergy transport in protein molecular systems.

PubMed

Pang, X F

2000-11-01

The Hamiltonian and the wave function in the Davydov theory have simultaneously been improved and extended, based on some physical and biological grounds and on results from other models. The equations of motion for the improved Davydov model with a quasicoherent two-quanta state and a new interaction term in the Hamiltonian describe bioenergy transport along the molecular chains in protein molecules by a soliton mechanism. Some elementary properties of the soliton, including the nonlinear coupling energy and greatly increased binding energy of the soliton, are also given. The results obtained suggest that the model could be a candidate for a bioenergy transport mechanism in protein molecules.

Classification of three-state Hamiltonians solvable by the coordinate Bethe ansatz

NASA Astrophysics Data System (ADS)

Crampé, N.; Frappat, L.; Ragoucy, E.

2013-10-01

We classify ‘all’ Hamiltonians with rank 1 symmetry and nearest-neighbour interactions, acting on a periodic three-state spin chain, and solvable through (generalization of) the coordinate Bethe ansatz (CBA). In this way we obtain four multi-parametric extensions of the known 19-vertex Hamiltonians (such as Zamolodchikov-Fateev, Izergin-Korepin and Bariev Hamiltonians). Apart from the 19-vertex Hamiltonians, there exist 17-vertex and 14-vertex Hamiltonians that cannot be viewed as subcases of the 19-vertex ones. In the case of 17-vertex Hamiltonians, we get a generalization of the genus 5 special branch found by Martins, plus three new ones. We also get two 14-vertex Hamiltonians. We solve all these Hamiltonians using CBA, and provide their spectrum, eigenfunctions and Bethe equations. Special attention is given to provide the specifications of our multi-parametric Hamiltonians that give back known Hamiltonians.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

DOE Office of Scientific and Technical Information (OSTI.GOV)

Park, Jae Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr; Department of Chemistry, Pohang University of Science and Technology

2014-04-28

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabaticmore » transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.« less

Dynamic analysis of rotor flex-structure based on nonlinear anisotropic shell models

NASA Astrophysics Data System (ADS)

Bauchau, Olivier A.; Chiang, Wuying

1991-05-01

In this paper an anisotropic shallow shell model is developed that accommodates transverse shearing deformations and arbitrarily large displacements and rotations, but strains are assumed to remain small. Two kinematic models are developed, the first using two DOF to locate the direction of the normal to the shell's midplane, the second using three. The latter model allows for an automatic compatibility of the shell model with beam models. The shell model is validated by comparing its predictions with several benchmark problems. In actual helicopter rotor blade problems, the shell model of the flex structure is shown to give very different results shown compared to beam models. The lead-lag and torsion modes in particular are strongly affected, whereas flapping modes seem to be less affected.

Crypto-Unitary Forms of Quantum Evolution Operators

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2013-06-01

The description of quantum evolution using unitary operator {u}(t)=exp(-i{h}t) requires that the underlying self-adjoint quantum Hamiltonian {h} remains time-independent. In a way extending the so called {PT}-symmetric quantum mechanics to the models with manifestly time-dependent "charge" {C}(t) we propose and describe an extension of such an exponential-operator approach to evolution to the manifestly time-dependent self-adjoint quantum Hamiltonians {h}(t).

Chain of point-like potentials in Script R3 and infiniteness of the number of bound states

NASA Astrophysics Data System (ADS)

Boitsev, A. A.; Popov, I. Yu; Sokolov, O. V.

2014-10-01

Infinite chain of point-like potentials having the Hamiltonian with infinite number of eigenvalues below the continuous spectrum is constructed. The background of the model is the theory of self-adjoint extensions of symmetric operators in the Hilbert space. The analogous example of the Hamiltonian is obtained for the system of three-dimensional waveguides coupled through point-like windows.

Mean energy of some interacting bosonic systems derived by virtue of the generalized Hellmann-Feynman theorem

NASA Astrophysics Data System (ADS)

Fan, Hong-yi; Xu, Xue-xiang

2009-06-01

By virtue of the generalized Hellmann-Feynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann-Feynman theorem and may enrich the theory of quantum statistics.

Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

2018-05-01

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

Effective Hamiltonian for protected edge states in graphene

DOE Office of Scientific and Technical Information (OSTI.GOV)

Winkler, R.; Deshpande, H.

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for bothmore » zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.« less

Investigation of electronic transport through a ladder-like graphene nanoribbon including random distributed impurities

NASA Astrophysics Data System (ADS)

Esmaili, Esmat; Mardaani, Mohammad; Rabani, Hassan

2018-01-01

The electronic transport of a ladder-like graphene nanoribbon which the on-site or hopping energies of a small part of it can be random is modeled by using the Green's function technique within the nearest neighbor tight-binding approach. We employ a unitary transformation in order to convert the Hamiltonian of the nanoribbon to the Hamiltonian of a tight-binding ladder-like network. In this case, the disturbed part of the system includes the second neighbor hopping interactions. While, the converted Hamiltonian of each ideal part is equivalent to the Hamiltonian of two periodic on-site chains. Therefore, we can insert the self-energies of the alternative on-site tight-binding chains to the inverse of the Green's function matrix of the ladder-like part. In this viewpoint, the conductance is constructed from two trans and cis contributions. The results show that increasing the disorder strength causes the increase and decrease of the conductance of the trans and cis contributions, respectively.

Effective Hamiltonian for protected edge states in graphene

DOE PAGES

Winkler, R.; Deshpande, H.

2017-06-15

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for bothmore » zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.« less

Accelerated and Airy-Bloch oscillations

NASA Astrophysics Data System (ADS)

Longhi, Stefano

2016-09-01

A quantum particle subjected to a constant force undergoes an accelerated motion following a parabolic path, which differs from the classical motion just because of wave packet spreading (quantum diffusion). However, when a periodic potential is added (such as in a crystal) the particle undergoes Bragg scattering and an oscillatory (rather than accelerated) motion is found, corresponding to the famous Bloch oscillations (BOs). Here, we introduce an exactly-solvable quantum Hamiltonian model, corresponding to a generalized Wannier-Stark Hamiltonian Ĥ, in which a quantum particle shows an intermediate dynamical behavior, namely an oscillatory motion superimposed to an accelerated one. Such a novel dynamical behavior is referred to as accelerated BOs. Analytical expressions of the spectrum, improper eigenfunctions and propagator of the generalized Wannier-Stark Hamiltonian Ĥ are derived. Finally, it is shown that acceleration and quantum diffusion in the generalized Wannier-Stark Hamiltonian are prevented for Airy wave packets, which undergo a periodic breathing dynamics that can be referred to as Airy-Bloch oscillations.

Analysis of Franck-Condon factors for CO+ molecule using the Fourier Grid Hamiltonian method

NASA Astrophysics Data System (ADS)

Syiemiong, Arnestar; Swer, Shailes; Jha, Ashok Kumar; Saxena, Atul

2018-04-01

Franck-Condon factors (FCFs) are important parameters and it plays a very important role in determining the intensities of the vibrational bands in electronic transitions. In this paper, we illustrate the Fourier Grid Hamiltonian (FGH) method, a relatively simple method to calculate the FCFs. The FGH is a method used for calculating the vibrational eigenvalues and eigenfunctions of bound electronic states of diatomic molecules. The obtained vibrational wave functions for the ground and the excited states are used to calculate the vibrational overlap integral and then the FCFs. In this computation, we used the Morse potential and Bi-Exponential potential model for constructing and diagonalizing the molecular Hamiltonians. The effects of the change in equilibrium internuclear distance (xe), dissociation energy (De), and the nature of the excited state electronic energy curve on the FCFs have been determined. Here we present our work for the qualitative analysis of Franck-Condon Factorsusing this Fourier Grid Hamiltonian Method.

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

NASA Astrophysics Data System (ADS)

Lampart, Jonas; Schmidt, Julian; Teufel, Stefan; Tumulka, Roderich

2018-06-01

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cut-off (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC.

Rib fractures under anterior-posterior dynamic loads: experimental and finite-element study.

PubMed

Li, Zuoping; Kindig, Matthew W; Kerrigan, Jason R; Untaroiu, Costin D; Subit, Damien; Crandall, Jeff R; Kent, Richard W

2010-01-19

The purpose of this study was to investigate whether using a finite-element (FE) mesh composed entirely of hexahedral elements to model cortical and trabecular bone (all-hex model) would provide more accurate simulations than those with variable thickness shell elements for cortical bone and hexahedral elements for trabecular bone (hex-shell model) in the modeling human ribs. First, quasi-static non-injurious and dynamic injurious experiments were performed using the second, fourth, and tenth human thoracic ribs to record the structural behavior and fracture tolerance of individual ribs under anterior-posterior bending loads. Then, all-hex and hex-shell FE models for the three ribs were developed using an octree-based and multi-block hex meshing approach, respectively. Material properties of cortical bone were optimized using dynamic experimental data and the hex-shell model of the fourth rib and trabecular bone properties were taken from the literature. Overall, the reaction force-displacement relationship predicted by both all-hex and hex-shell models with nodes in the offset middle-cortical surfaces compared well with those measured experimentally for all the three ribs. With the exception of fracture locations, the predictions from all-hex and offset hex-shell models of the second and fourth ribs agreed better with experimental data than those from the tenth rib models in terms of reaction force at fracture (difference <15.4%), ultimate failure displacement and time (difference <7.3%), and cortical bone strains. The hex-shell models with shell nodes in outer cortical surfaces increased static reaction forces up to 16.6%, compared to offset hex-shell models. These results indicated that both all-hex and hex-shell modeling strategies were applicable for simulating rib responses and bone fractures for the loading conditions considered, but coarse hex-shell models with constant or variable shell thickness were more computationally efficient and therefore preferred. Copyright 2009 Elsevier Ltd. All rights reserved.

Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional

NASA Astrophysics Data System (ADS)

Chacón, Enrique; Tarazona, Pedro

2016-06-01

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional.

PubMed

Chacón, Enrique; Tarazona, Pedro

2016-06-22

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

Theoretical research of the spin-Hamiltonian parameters for two rhombic W5+ centers in KTiOPO4 (KTP) crystal through a two-mechanism model

NASA Astrophysics Data System (ADS)

Mei, Yang; Chen, Bo-Wei; Wei, Chen-Fu; Zheng, Wen-Chen

2016-09-01

The high-order perturbation formulas based on the two-mechanism model are employed to calculate the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, where i=x, y, z) for two approximately rhombic W5+ centers in KTiOPO4 (KTP) crystal. In the model, both the widely-applied crystal-field (CF) mechanism concerning the interactions of CF excited states with the ground state and the generally-neglected charge-transfer (CT) mechanism concerning the interactions of CT excited states with the ground state are included. The calculated results agree with the experimental values, and the signs of constants Ai are suggested. The calculations indicate that (i) for the high valence state dn ions in crystals, the contributions to spin-Hamiltonian parameters should take into account both the CF and CT mechanisms and (ii) the large g-shifts |Δgi | (=|gi-ge |, where ge≈ 2.0023) for W5+ centers in crystals are due to the large spin-orbit parameter of free W5+ ion.

THREE-DIMENSIONAL MODELING OF THE DYNAMICS OF THERAPEUTIC ULTRASOUND CONTRAST AGENTS

PubMed Central

Hsiao, Chao-Tsung; Lu, Xiaozhen; Chahine, Georges

2010-01-01

A 3-D thick-shell contrast agent dynamics model was developed by coupling a finite volume Navier-Stokes solver and a potential boundary element method flow solver to simulate the dynamics of thick-shelled contrast agents subjected to pressure waves. The 3-D model was validated using a spherical thick-shell model validated by experimental observations. We then used this model to study shell break-up during nonspherical deformations resulting from multiple contrast agent interaction or the presence of a nearby solid wall. Our simulations indicate that the thick viscous shell resists the contrast agent from forming a re-entrant jet, as normally observed for an air bubble oscillating near a solid wall. Instead, the shell thickness varies significantly from location to location during the dynamics, and this could lead to shell break-up caused by local shell thinning and stretching. PMID:20950929

Non-singular black holes and the limiting curvature mechanism: a Hamiltonian perspective

NASA Astrophysics Data System (ADS)

Ben Achour, J.; Lamy, F.; Liu, H.; Noui, K.

2018-05-01

We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian structure of the theory. We write down the equations of motion that we solve in the regime deep inside the black hole, and we recover that the black hole has no singularity, due to the limiting curvature mechanism. Then, we study the relation between such black holes and effective polymer black holes which have been introduced in the context of loop quantum gravity. As expected, contrary to what happens in the cosmological sector, mimetic gravity with a limiting curvature fails to reproduce the usual effective dynamics of spherically symmetric loop quantum gravity which are generically not covariant. Nonetheless, we exhibit a theory in the class of extended mimetic gravity whose dynamics reproduces the general shape of the effective corrections of spherically symmetric polymer models, but in an undeformed covariant manner. These covariant effective corrections are found to be always metric dependent, i.e. within the bar mu-scheme, underlying the importance of this ingredient for inhomogeneous polymer models. In that respect, extended mimetic gravity can be viewed as an effective covariant theory which naturally implements a covariant notion of point wise holonomy-like corrections. The difference between the mimetic and polymer Hamiltonian formulations provides us with a guide to understand the deformation of covariance in inhomogeneous polymer models.

Fermion bag approach to Hamiltonian lattice field theories in continuous time

NASA Astrophysics Data System (ADS)

Huffman, Emilie; Chandrasekharan, Shailesh

2017-12-01

We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the 3 d Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find η =0.54 (6 ) and ν =0.88 (2 ) using lattices up to N =2304 sites. We argue that even sizes up to N =10 ,000 sites should be accessible with supercomputers available today.

Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom.

PubMed

Compelli, A; Ivanov, R; Todorov, M

2018-01-28

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg-de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

Landau problem with time dependent mass in time dependent electric and harmonic background fields

NASA Astrophysics Data System (ADS)

Lawson, Latévi M.; Avossevou, Gabriel Y. H.

2018-04-01

The spectrum of a Hamiltonian describing the dynamics of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field is obtained. The configuration space wave function of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian, we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce a unitary transformation in the framework of the algebraic formalism to construct the invariant operator of the system and then to obtain the exact solution of the Hamiltonian. We recover the solutions of the ordinary Landau problem in the absence of the electric and harmonic fields for a constant particle mass.

From Majorana fermions to topological order.

PubMed

Terhal, Barbara M; Hassler, Fabian; DiVincenzo, David P

2012-06-29

We consider a system consisting of a 2D network of links between Majorana fermions on superconducting islands. We show that the fermionic Hamiltonian modeling this system is topologically ordered in a region of parameter space: we show that Kitaev's toric code emerges in fourth-order perturbation theory. By using a Jordan-Wigner transformation we can map the model onto a family of signed 2D Ising models in a transverse field where the signs, ferromagnetic or antiferromagnetic, are determined by additional gauge bits. Our mapping allows an understanding of the nonperturbative regime and the phase transition to a nontopological phase. We discuss the physics behind a possible implementation of this model and argue how it can be used for topological quantum computation by adiabatic changes in the Hamiltonian.

A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian assisted with an ancillary qubit system

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Lee, Seung-Woo; Lee, Chang-Woo; Jeong, Hyunseok

2015-01-01

We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied to the initial state assisted with an ancillary qubit. The fraction of the lowest eigenstate in the initial state is then amplified up to 1. We prove that our algorithm can faithfully work for any arbitrary Hamiltonian in the theoretical analysis. Numerical analyses are also carried out. We firstly provide a numerical proof-of-principle demonstration with a simple Hamiltonian in order to compare our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently proposed in Xu (Nat Photonics 8:113, 2014). The result shows a good agreement with our theoretical analysis, exhibiting the comparable behavior to the best `cooling' with the DLAC method. We then consider a random Hamiltonian model for further analysis of our algorithm. By numerical simulations, we show that the total number of iterations is proportional to , where is the difference between the two lowest eigenvalues and is an error defined as the probability that the finally obtained system state is in an unexpected (i.e., not the lowest) eigenstate.

On the structure of the two-stream instability–complex G-Hamiltonian structure and Krein collisions between positive- and negative-action modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Ruili; Liu, Jian; Xiao, Jianyuan

2016-07-15

The two-stream instability is probably the most important elementary example of collective instabilities in plasma physics and beam-plasma systems. For a warm plasma with two charged particle species, the instability diagram of the two-stream instability based on a 1D warm-fluid model exhibits an interesting band structure that has not been explained. We show that the band structure for this instability is the consequence of the Hamiltonian nature of the warm two-fluid system. Interestingly, the Hamiltonian nature manifests as a complex G-Hamiltonian structure in wave-number space, which directly determines the instability diagram. Specifically, it is shown that the boundaries between themore » stable and unstable regions are locations for Krein collisions between eigenmodes with different Krein signatures. In terms of physics, this rigorously implies that the system is destabilized when a positive-action mode resonates with a negative-action mode, and that this is the only mechanism by which the system can be destabilized. It is anticipated that this physical mechanism of destabilization is valid for other collective instabilities in conservative systems in plasma physics, accelerator physics, and fluid dynamics systems, which admit infinite-dimensional Hamiltonian structures.« less

Superfield Hamiltonian quantization in terms of quantum antibrackets

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.

2016-04-01

We develop a new version of the superfield Hamiltonian quantization. The main new feature is that the BRST-BFV charge and the gauge fixing Fermion are introduced on equal footing within the sigma model approach, which provides for the actual use of the quantum/derived antibrackets. We study in detail the generating equations for the quantum antibrackets and their primed counterparts. We discuss the finite quantum anticanonical transformations generated by the quantum antibracket.

Experiments in Quantum Coherence and Computation With Single Cooper-Pair Electronics

DTIC Science & Technology

2006-01-22

through the cavity. In the absence of damping, exact diagonalization of the Jaynes - Cumming Hamiltonian yields the excited eigenstates (dressed states...neglecting rapidly oscillating terms and omitting damping for the moment, Eq. (16) reduces to the Jaynes - Cummings Hamiltonian (1) with V=EJ /" and cou...is therefore little entanglement between the field and qubit in this situation and the rotation fidelity is high. To model the effect of the drive on

The direct reaction field hamiltonian: Analysis of the dispersion term and application to the water dimer

NASA Astrophysics Data System (ADS)

Thole, B. T.; Van Duijnen, P. Th.

1982-10-01

The induction and dispersion terms obtained from quantum-mechanical calculations with a direct reaction field hamiltonian are compared to second order perturbation theory expressions. The dispersion term is shown to give an upper bound which is a generalization of Alexander's upper bound. The model is illustrated by a calculation on the interactions in the water dimer. The long range Coulomb, induction and dispersion interactions are reasonably reproduced.

Hamiltonian description and quantization of dissipative systems

NASA Astrophysics Data System (ADS)

Enz, Charles P.

1994-09-01

Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.

First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics

NASA Astrophysics Data System (ADS)

Bagarello, F.; Haven, E.

2016-02-01

We discuss a non linear extension of a model of alliances in politics, recently proposed by one of us. The model is constructed in terms of operators, describing the interest of three parties to form, or not, some political alliance with the other parties. The time evolution of what we call the decision functions is deduced by introducing a suitable Hamiltonian, which describes the main effects of the interactions of the parties amongst themselves and with their environments, which are generated by their electors and by people who still have no clear idea for which party to vote (or even if to vote). The Hamiltonian contains some non-linear effects, which takes into account the role of a party in the decision process of the other two parties. Moreover, we show how the same Hamiltonian can also be used to construct a formal structure which can describe the dynamics of buying and selling financial assets (without however implying a specific price setting mechanism).

Analysis of repeated signals during shell fights in the hermit crab Pagurus bernhardus

PubMed Central

Briffa, M.; Elwood, R. W.; Dick, J. T. A.

1998-01-01

Shell exchanges between hermit crabs may occur after a period of shell rapping, when the initiating or attacking crab brings its shell rapidly and repeatedly into contact with the shell of the non-initiator or defender, in a series of bouts. There are two opposing models of hermit crab shell exchange and the function of shell rapping. The negotiation model views shell exchange as a mutualistic activity, in which the initiator supplies information about the quality of its shell via the fundamental frequency of the rapping sound. The aggression model views shell rapping as either detrimental to the defending crab, or as providing it with information about the initiator's ability or motivation to continue, or both. The negotiation model makes no predictions about the temporal pattern of rapping, but under the aggression model it would be expected that crabs that rapped more vigorously would be more likely to effect an exchange. Repeating the signal could be expected under either model. Crabs that achieve an exchange rap more vigorously, rapping is more persistent when a clear gain in shell quality may be achieved, and the vigour is greater when the relative resource-holding potential (or 'fighting ability') is high. These findings support the aggression model rather than the negotiation model. Contrary to the predictions of game theory, crabs that do not effect an exchange appear to signal that they are about to give up. The data suggest that rapping is performed repeatedly because the accumulation of all of the performances acts as a signal of stamina.

Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Szalay, Viktor, E-mail: szalay.viktor@wigner.mta.hu

A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, T-hat, is presented. It is in the Eckart frame and it is of the same form as Watson’s normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact T-hat given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.

Phase transitions in the sdg interacting boson model

NASA Astrophysics Data System (ADS)

Van Isacker, P.; Bouldjedri, A.; Zerguine, S.

2010-05-01

A geometric analysis of the sdg interacting boson model is performed. A coherent state is used in terms of three types of deformation: axial quadrupole ( β), axial hexadecapole ( β) and triaxial ( γ). The phase-transitional structure is established for a schematic sdg Hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical U(5)⊗U(9), the (prolate and oblate) deformed SU(3) and the γ-soft SO(15) limits. For realistic choices of the Hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the sd version of the model and, in particular, no transition towards a stable triaxial shape is found.

A Thin Lens Model for Charged-Particle RF Accelerating Gaps

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allen, Christopher K.

Presented is a thin-lens model for an RF accelerating gap that considers general axial fields without energy dependence or other a priori assumptions. Both the cosine and sine transit time factors (i.e., Fourier transforms) are required plus two additional functions; the Hilbert transforms the transit-time factors. The combination yields a complex-valued Hamiltonian rotating in the complex plane with synchronous phase. Using Hamiltonians the phase and energy gains are computed independently in the pre-gap and post-gap regions then aligned using the asymptotic values of wave number. Derivations of these results are outlined, examples are shown, and simulations with the model aremore » presented.« less

The Abelian Higgs model on Optical Lattice?

NASA Astrophysics Data System (ADS)

Meurice, Yannick; Tsai, Shan-Wen; Bazavov, Alexei; Zhang, Jin

2015-03-01

We study the Lattice Gauge Theory of the U(1)-Higgs model in 1+1 dimensions in the strongly coupled regime. We discuss the plaquette corrections to the effective theory where link variables are integrated out. We discuss matching with the second-order perturbation theory effective Hamiltonian for various Bose-Hubbard models. This correspondence can be exploited for building a lattice gauge theory simulator on optical lattices. We propose to implement the quantum rotors which appear in the Hamiltonian formulation using Bose mixtures or p-orbitals. Recent progress on magnetic effects in 2+1 dimensions will be discussed. Supported by the Army Research Office of the Department of Defense under Award Number W911NF-13-1-0119.

Equivalent Hamiltonian for the Lee model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jones, H. F.

2008-03-15

Using the techniques of quasi-Hermitian quantum mechanics and quantum field theory we use a similarity transformation to construct an equivalent Hermitian Hamiltonian for the Lee model. In the field theory confined to the V/N{theta} sector it effectively decouples V, replacing the three-point interaction of the original Lee model by an additional mass term for the V particle and a four-point interaction between N and {theta}. While the construction is originally motivated by the regime where the bare coupling becomes imaginary, leading to a ghost, it applies equally to the standard Hermitian regime where the bare coupling is real. In thatmore » case the similarity transformation becomes a unitary transformation.« less

On a new class of completely integrable nonlinear wave equations. II. Multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.

1987-11-01

The multi-Hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed. Infinitely many conservation laws had earlier been obtained for these equations. Starting from a (primary) Hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi-Hamiltonian structure are obtained and it is shown that the second Hamiltonian operator can be constructed solely through a knowledge of the first Hamiltonian function. The recursion operator which first appears at the level of bi-Hamiltonian structure gives rise to an infinite sequence of conserved Hamiltonians. It is found that in general there exist two different infinite sequences of conserved quantities for these equations. The recursion relation defining higher Hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the (k+1)st Hamiltonian operator which depends on the kth Hamiltonian function. The infinite sequence of conserved Hamiltonians are common to all the higher Hamiltonian structures. The equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri-Hamiltonian structure with two distinct infinite sets of conserved quantities. The isothermal case of γ=1 is an exceptional one that requires separate treatment. This corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to Poisson's equation in nonlinear acoustics.

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Holm, Darryl D.

2018-01-01

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Holm, Darryl D.

2018-06-01

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

The complexity of translationally invariant low-dimensional spin lattices in 3D

NASA Astrophysics Data System (ADS)

Bausch, Johannes; Piddock, Stephen

2017-11-01

In this theoretical paper, we consider spin systems in three spatial dimensions and consider the computational complexity of estimating the ground state energy, known as the local Hamiltonian problem, for translationally invariant Hamiltonians. We prove that the local Hamiltonian problem for 3D lattices with face-centered cubic unit cells and 4-local translationally invariant interactions between spin-3/2 particles and open boundary conditions is QMAEXP-complete, where QMAEXP is the class of problems which can be verified in exponential time on a quantum computer. We go beyond a mere embedding of past hard 1D history state constructions, for which the local spin dimension is enormous: even state-of-the-art constructions have local dimension 42. We avoid such a large local dimension by combining some different techniques in a novel way. For the verifier circuit which we embed into the ground space of the local Hamiltonian, we utilize a recently developed computational model, called a quantum ring machine, which is especially well suited for translationally invariant history state constructions. This is encoded with a new and particularly simple universal gate set, which consists of a single 2-qubit gate applied only to nearest-neighbour qubits. The Hamiltonian construction involves a classical Wang tiling problem as a binary counter which translates one cube side length into a binary description for the encoded verifier input and a carefully engineered history state construction that implements the ring machine on the cubic lattice faces. These novel techniques allow us to significantly lower the local spin dimension, surpassing the best translationally invariant result to date by two orders of magnitude (in the number of degrees of freedom per coupling). This brings our models on par with the best non-translationally invariant construction.

Resource Letter NSM-1: New insights into the nuclear shell model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dean, David Jarvis; Hamilton, J. H.

2011-01-01

This Resource Letter provides a guide to the literature on the spherical shell model as applied to nuclei. The nuclear shell model describes the structure of nuclei starting with a nuclear core developed by the classical neutron and proton magic numbers N,Z=2,8,20,28,50,82, 126, where gaps occur in the single-particle energies as a shell is filled, and the interactions of valence nucleons that reside beyond that core. Various modern extensions of this model for spherical nuclei are likewise described. Significant extensions of the nuclear shell model include new magic numbers for spherical nuclei and now for deformed nuclei as well. Whenmore » both protons and neutrons have shell gaps at the same spherical or deformed shapes, they can reinforce each other to give added stability to that shape and lead to new magic numbers. The vanishings of the classical spherical shell model energy gaps and magic numbers in new neutron-rich nuclei are described. Spherical and deformed shell gaps are seen to be critical for the existence of elements with Z > 100.« less

Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: A local mean-field analysis

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Lookman, Turab; Shenoy, Subodh R.

2010-09-01

We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local mean-field approximation of their pseudospin Hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their NOP -component order parameters, with Landau free energies that have a single zero-strain “austenite” minimum at high temperatures, and spontaneous-strain “martensite” minima of NV structural variants at low temperatures. The total free energy also has gradient terms, and power-law anisotropic effective interactions, induced by “no-dislocation” St Venant compatibility constraints. In a reduced description, the strains at Landau minima induce temperature dependent, clocklike ZNV+1 Hamiltonians, with NOP -component strain-pseudospin vectors S⃗ pointing to NV+1 discrete values (including zero). We study elastic texturing in five such first-order structural transitions through a local mean-field approximation of their pseudospin Hamiltonians, that include the power-law interactions. As a prototype, we consider the two-variant square/rectangle transition, with a one-component pseudospin taking NV+1=3 values of S=0,±1 , as in a generalized Blume-Capel model. We then consider transitions with two-component (NOP=2) pseudospins: the equilateral to centered rectangle (NV=3) ; the square to oblique polygon (NV=4) ; the triangle to oblique (NV=6) transitions; and finally the three-dimensional (3D) cubic to tetragonal transition (NV=3) . The local mean-field solutions in two-dimensional and 3D yield oriented domain-wall patterns as from continuous-variable strain dynamics, showing the discrete-variable models capture the essential ferroelastic texturings. Other related Hamiltonians illustrate that structural transitions in materials science can be the source of interesting spin models in statistical mechanics.

Competition Between Two Large-Amplitude Motion Models: New Hybrid Hamiltonian Versus Old Pure-Tunneling Hamiltonian

NASA Astrophysics Data System (ADS)

Kleiner, Isabelle; Hougen, Jon T.

2017-06-01

In this talk we report on our progress in trying to make the hybrid Hamiltonian competitive with the pure-tunneling Hamiltonian for treating large-amplitude motions in methylamine. A treatment using the pure-tunneling model has the advantages of: (i) requiring relatively little computer time, (ii) working with relatively uncorrelated fitting parameters, and (iii) yielding in the vast majority of cases fits to experimental measurement accuracy. These advantages are all illustrated in the work published this past year on a gigantic v_{t} = 1 data set for the torsional fundamental band in methyl amine. A treatment using the hybrid model has the advantages of: (i) being able to carry out a global fit involving both v_{t} = 0 and v_{t} = 1 energy levels and (ii) working with fitting parameters that have a clearer physical interpretation. Unfortunately, a treatment using the hybrid model has the great disadvantage of requiring a highly correlated set of fitting parameters to achieve reasonable fitting accuracy, which complicates the search for a good set of molecular fitting parameters and a fit to experimental accuracy. At the time of writing this abstract, we have been able to carry out a fit with J up to 15 that includes all available infrared data in the v_{t} = 1-0 torsional fundamental band, all ground-state microwave data with K up to 10 and J up to 15, and about a hundred microwave lines within the v_{t} = 1 torsional state, achieving weighted root-mean-square (rms) deviations of about 1.4, 2.8, and 4.2 for these three categories of data. We will give an update of this situation at the meeting. I. Gulaczyk, M. Kreglewski, V.-M. Horneman, J. Mol. Spectrosc., in Press (2017).

Particle in a box in PT-symmetric quantum mechanics and an electromagnetic analog

NASA Astrophysics Data System (ADS)

Dasarathy, Anirudh; Isaacson, Joshua P.; Jones-Smith, Katherine; Tabachnik, Jason; Mathur, Harsh

2013-06-01

In PT-symmetric quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be Hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time reversal. Here we study the role of boundary conditions in PT-symmetric quantum mechanics by constructing a simple model that is the PT-symmetric analog of a particle in a box. The model has the usual particle-in-a-box Hamiltonian but boundary conditions that respect PT symmetry rather than Hermiticity. We find that for a broad class of PT-symmetric boundary conditions the model respects the condition of unbroken PT symmetry, namely, that the Hamiltonian and the symmetry operator PT have simultaneous eigenfunctions, implying that the energy eigenvalues are real. We also find that the Hamiltonian is self-adjoint under the PT-symmetric inner product. Thus we obtain a simple soluble model that fulfills all the requirements of PT-symmetric quantum mechanics. In the second part of this paper we formulate a variational principle for PT-symmetric quantum mechanics that is the analog of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic analogs of the PT-symmetric particle in a box. We show that the isolated particle in a box may be realized as a Fabry-Perot cavity between an absorbing medium and its conjugate gain medium. Coupling the cavity to an external continuum of incoming and outgoing states turns the energy levels of the box into sharp resonances. Remarkably we find that the resonances have a Breit-Wigner line shape in transmission and a Fano line shape in reflection; by contrast, in the corresponding Hermitian case the line shapes always have a Breit-Wigner form in both transmission and reflection.

Extreme ultraviolet and soft x-ray spectral lines in Rb XXIX

NASA Astrophysics Data System (ADS)

Indu, Khatri; Arun, Goyal; Sunny, Aggarwal; A, K. Singh; Man, Mohan

2016-03-01

An extensive theoretical set of atomic data for Rb XXIX in a wide range with L-shell electron excitations to the M-shell has been reported. We have computed energy levels for the lowest 113 fine structure levels of Rb XXIX. The fully relativistic multiconfigurational Dirac-Fock method (MCDF) within the framework of Dirac-Coulomb Hamiltonian taking quantum electrodynamics (QED) and Breit corrections into account has been adopted for calculations. Radiative data are reported for electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions from the ground level, although calculations have been performed for a much larger number of levels. To assess the accuracy of results, we performed analogous calculations using flexible atomic code (FAC). Comparisons are made with existing available results and a good agreement has been achieved. Most of the wavelengths calculated lie in the soft x-ray (SXR) region. Lifetimes for all 113 levels have also been provided for the first time. Additionally, we have provided the spectra for allowed transitions from n = 2 to n = 3 within the x-ray region and also compared our SXR photon wavelengths with experimentally recognized wavelengths. We hope that our results will be beneficial in fusion plasma research and astrophysical applications.

Parameterized Finite Element Modeling and Buckling Analysis of Six Typical Composite Grid Cylindrical Shells

NASA Astrophysics Data System (ADS)

Lai, Changliang; Wang, Junbiao; Liu, Chuang

2014-10-01

Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.

Possible treatment of the ghost states in the Lee-Wick standard model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shalaby, Abouzeid M.; Physics Department, Faculty of Science, Qassim University

2009-07-15

In this work, we employ the techniques used to cure the indefinite norm problem in pseudo-Hermitian Hamiltonians to show that the ghost states in a higher derivative scalar field theory are not real ghosts. For the model under investigation, an imaginary auxiliary field is introduced to have an equivalent non-Hermitian two-field scalar theory. We were able to calculate exactly the positive definite metric operator {eta} for the quantum mechanical as well as the quantum field versions of the theory. While the equivalent Hamiltonian is non-Hermitian in a Hilbert space characterized by the Dirac sense inner product, it is, however, amore » Hermitian in a Hilbert space endowed with the inner product . The main feature of the latter Hilbert space is that the propagator has the correct sign (no Lee-Wick fields). Moreover, the calculated metric operator diagonalizes the Hamiltonian in the two fields (no mixing). We found that the Hermiticity of the calculated metric operator to lead to the constrain M>2m for the two Higgs masses, in agreement with other calculations in the literature. Besides, our mass formulas coincide with those obtained in other works (obtained by a very different regime but with the existence of ghost states), which means that our positive normed Hamiltonian form preserves the mass spectra.« less

Toward Hamiltonian Adaptive QM/MM: Accurate Solvent Structures Using Many-Body Potentials.

PubMed

Boereboom, Jelle M; Potestio, Raffaello; Donadio, Davide; Bulo, Rosa E

2016-08-09

Adaptive quantum mechanical (QM)/molecular mechanical (MM) methods enable efficient molecular simulations of chemistry in solution. Reactive subregions are modeled with an accurate QM potential energy expression while the rest of the system is described in a more approximate manner (MM). As solvent molecules diffuse in and out of the reactive region, they are gradually included into (and excluded from) the QM expression. It would be desirable to model such a system with a single adaptive Hamiltonian, but thus far this has resulted in distorted structures at the boundary between the two regions. Solving this long outstanding problem will allow microcanonical adaptive QM/MM simulations that can be used to obtain vibrational spectra and dynamical properties. The difficulty lies in the complex QM potential energy expression, with a many-body expansion that contains higher order terms. Here, we outline a Hamiltonian adaptive multiscale scheme within the framework of many-body potentials. The adaptive expressions are entirely general, and complementary to all standard (nonadaptive) QM/MM embedding schemes available. We demonstrate the merit of our approach on a molecular system defined by two different MM potentials (MM/MM'). For the long-range interactions a numerical scheme is used (particle mesh Ewald), which yields energy expressions that are many-body in nature. Our Hamiltonian approach is the first to provide both energy conservation and the correct solvent structure everywhere in this system.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vakili, Hajar; Rahvar, Sohrab; Kroupa, Pavel, E-mail: vakili@physics.sharif.edu

Shell galaxies are understood to form through the collision of a dwarf galaxy with an elliptical galaxy. Shell structures and kinematics have been noted to be independent tools to measure the gravitational potential of the shell galaxies. We compare theoretically the formation of shells in Type I shell galaxies in different gravity theories in this work because this is so far missing in the literature. We include Newtonian plus dark halo gravity, and two non-Newtonian gravity models, MOG and MOND, in identical initial systems. We investigate the effect of dynamical friction, which by slowing down the dwarf galaxy in themore » dark halo models limits the range of shell radii to low values. Under the same initial conditions, shells appear on a shorter timescale and over a smaller range of distances in the presence of dark matter than in the corresponding non-Newtonian gravity models. If galaxies are embedded in a dark matter halo, then the merging time may be too rapid to allow multi-generation shell formation as required by observed systems because of the large dynamical friction effect. Starting from the same initial state, the observation of small bright shells in the dark halo model should be accompanied by large faint ones, while for the case of MOG, the next shell generation patterns iterate with a specific time delay. The first shell generation pattern shows a degeneracy with the age of the shells and in different theories, but the relative distance of the shells and the shell expansion velocity can break this degeneracy.« less

An Informal Overview of the Unitary Group Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sonnad, V.; Escher, J.; Kruse, M.

The Unitary Groups Approach (UGA) is an elegant and conceptually unified approach to quantum structure calculations. It has been widely used in molecular structure calculations, and holds the promise of a single computational approach to structure calculations in a variety of different fields. We explore the possibility of extending the UGA to computations in atomic and nuclear structure as a simpler alternative to traditional Racah algebra-based approaches. We provide a simple introduction to the basic UGA and consider some of the issues in using the UGA with spin-dependent, multi-body Hamiltonians requiring multi-shell bases adapted to additional symmetries. While the UGAmore » is perfectly capable of dealing with such problems, it is seen that the complexity rises dramatically, and the UGA is not at this time, a simpler alternative to Racah algebra-based approaches.« less

Analytical spectrum for a Hamiltonian of quantum dots with Rashba spin-orbit coupling

NASA Astrophysics Data System (ADS)

Dossa, Anselme F.; Avossevou, Gabriel Y. H.

2014-12-01

We determine the analytical solution for a Hamiltonian describing a confined charged particle in a quantum dot, including Rashba spin-orbit coupling and Zeeman splitting terms. The approach followed in this paper is straightforward and uses the symmetrization of the wave function's components. The eigenvalue problem for the Hamiltonian in Bargmann's Hilbert space reduces to a system of coupled first-order differential equations. Then we exploit the symmetry in the system to obtain uncoupled second-order differential equations, which are found to be the Whittaker-Ince limit of the confluent Heun equations. Analytical expressions as well as numerical results are obtained for the spectrum. One of the main features of such models, namely, the level splitting, is present through the spectrum obtained in this paper.

RPA treatment of a motivated QCD Hamiltonian in the SO(4) (2 + 1)-flavor limit: Light and strange mesons

NASA Astrophysics Data System (ADS)

Yepez-Martinez, Tochtli; Civitarese, Osvaldo; Hess, Peter O.

The SO(4) symmetry of a sector of the quantum chromodynamics (QCD) Hamiltonian was analyzed in a previous work. The numerical calculations were then restricted to a particle-hole (ph) space and the comparison with experimental data was reasonable in spite of the complexity of the QCD spectrum at low energy. Here on, we continue along this line of research and show our new results of the treatment of the QCD Hamiltonian in the SO(4) representation, including ground state correlations by means of the Random Phase Approximation (RPA). We are able to identify, within this model, states which may be associated to physical pseudo-scalar and vector mesons, like η,η‧,K,ρ,ω,ϕ, as well as the pion (π).

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

NASA Astrophysics Data System (ADS)

Bukov, Marin; Polkovnikov, Anatoli

2014-10-01

We study the stroboscopic and nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian. We show that the former produces the evolution expected in the high-frequency limit only for observables, which commute with the operator to which the driving protocol couples. On the contrary, nonstroboscopic dynamics is capable of capturing the evolution governed by the Floquet Hamiltonian of any observable associated with the effective high-frequency model. We provide exact numerical simulations for the dynamics of the number operator following a quantum cyclotron orbit on a 2×2 plaquette, as well as the chiral current operator flowing along the legs of a 2×20 ladder. The exact evolution is compared with its stroboscopic and nonstroboscopic counterparts, including finite-frequency corrections.

Full f-p Shell Calculation of {sup 51}Ca and {sup 51}Sc

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novoselsky, A.; Vallieres, M.; Laadan, O.

The spectra and the electromagnetic transitions of the nuclei {sup 51}Ca and {sup 51}Sc with 11 nucleons in the {ital f-p} shell are described in the nuclear shell-model approach by using two different two-body effective interactions. The full {ital f-p} shell basis functions are used with no truncation. The new parallel shell-model computer code DUPSM (Drexel University parallel shell model), that we recently developed, has been used. The calculations have been done on the MOSIX parallel machine at the Hebrew University of Jerusalem. {copyright} {ital 1997} {ital The American Physical Society}

Hamilton-Jacobi modelling of relative motion for formation flying.

PubMed

Kolemen, Egemen; Kasdin, N Jeremy; Gurfil, Pini

2005-12-01

A precise analytic model for the relative motion of a group of satellites in slightly elliptic orbits is introduced. With this aim, we describe the relative motion of an object relative to a circular or slightly elliptic reference orbit in the rotating Hill frame via a low-order Hamiltonian, and solve the Hamilton-Jacobi equation. This results in a first-order solution to the relative motion identical to the Clohessy-Wiltshire approach; here, however, rather than using initial conditions as our constants of the motion, we utilize the canonical momenta and coordinates. This allows us to treat perturbations in an identical manner, as in the classical Delaunay formulation of the two-body problem. A precise analytical model for the base orbit is chosen with the included effect of zonal harmonics (J(2), J(3), J(4)). A Hamiltonian describing the real relative motion is formed and by differing this from the nominal Hamiltonian, the perturbing Hamiltonian is obtained. Using the Hamilton equations, the variational equations for the new constants are found. In a manner analogous to the center manifold reduction procedure, the non-periodic part of the motion is canceled through a magnitude analysis leading to simple boundedness conditions that cancel the drift terms due to the higher order perturbations. Using this condition, the variational equations are integrated to give periodic solutions that closely approximate the results from numerical integration (1 mm/per orbit for higher order and eccentricity perturbations and 30 cm/per orbit for zonal perturbations). This procedure provides a compact and insightful analytic description of the resulting relative motion.

Semiclassical stochastic mechanics for the Coulomb potential with applications to modelling dark matter

NASA Astrophysics Data System (ADS)

Neate, Andrew; Truman, Aubrey

2016-05-01

Little is known about dark matter particles save that their most important interactions with ordinary matter are gravitational and that, if they exist, they are stable, slow moving and relatively massive. Based on these assumptions, a semiclassical approximation to the Schrödinger equation under the action of a Coulomb potential should be relevant for modelling their behaviour. We investigate the semiclassical limit of the Schrödinger equation for a particle of mass M under a Coulomb potential in the context of Nelson's stochastic mechanics. This is done using a Freidlin-Wentzell asymptotic series expansion in the parameter ɛ = √{ ħ / M } for the Nelson diffusion. It is shown that for wave functions ψ ˜ exp((R + iS)/ɛ2) where R and S are real valued, the ɛ = 0 behaviour is governed by a constrained Hamiltonian system with Hamiltonian Hr and constraint Hi = 0 where the superscripts r and i denote the real and imaginary parts of the Bohr correspondence limit of the quantum mechanical Hamiltonian, independent of Nelson's ideas. Nelson's stochastic mechanics is restored in dealing with the nodal surface singularities and by computing (correct to first order in ɛ) the relevant diffusion process in terms of Jacobi fields thereby revealing Kepler's laws in a new light. The key here is that the constrained Hamiltonian system has just two solutions corresponding to the forward and backward drifts in Nelson's stochastic mechanics. We discuss the application of this theory to modelling dark matter particles under the influence of a large gravitating point mass.

Improving long time behavior of Poisson bracket mapping equation: A non-Hamiltonian approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Hyun Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr

2014-05-14

Understanding nonadiabatic dynamics in complex systems is a challenging subject. A series of semiclassical approaches have been proposed to tackle the problem in various settings. The Poisson bracket mapping equation (PBME) utilizes a partial Wigner transform and a mapping representation for its formulation, and has been developed to describe nonadiabatic processes in an efficient manner. Operationally, it is expressed as a set of Hamilton's equations of motion, similar to more conventional classical molecular dynamics. However, this original Hamiltonian PBME sometimes suffers from a large deviation in accuracy especially in the long time limit. Here, we propose a non-Hamiltonian variant ofmore » PBME to improve its behavior especially in that limit. As a benchmark, we simulate spin-boson and photosynthetic model systems and find that it consistently outperforms the original PBME and its Ehrenfest style variant. We explain the source of this improvement by decomposing the components of the mapping Hamiltonian and by assessing the energy flow between the system and the bath. We discuss strengths and weaknesses of our scheme with a viewpoint of offering future prospects.« less

Interest rates in quantum finance: the Wilson expansion and Hamiltonian.

PubMed

Baaquie, Belal E

2009-10-01

Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field A(t,x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor phi(t,x) is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated.

Quantum-like dynamics applied to cognition: a consideration of available options

NASA Astrophysics Data System (ADS)

Broekaert, Jan; Basieva, Irina; Blasiak, Pawel; Pothos, Emmanuel M.

2017-10-01

Quantum probability theory (QPT) has provided a novel, rich mathematical framework for cognitive modelling, especially for situations which appear paradoxical from classical perspectives. This work concerns the dynamical aspects of QPT, as relevant to cognitive modelling. We aspire to shed light on how the mind's driving potentials (encoded in Hamiltonian and Lindbladian operators) impact the evolution of a mental state. Some existing QPT cognitive models do employ dynamical aspects when considering how a mental state changes with time, but it is often the case that several simplifying assumptions are introduced. What kind of modelling flexibility does QPT dynamics offer without any simplifying assumptions and is it likely that such flexibility will be relevant in cognitive modelling? We consider a series of nested QPT dynamical models, constructed with a view to accommodate results from a simple, hypothetical experimental paradigm on decision-making. We consider Hamiltonians more complex than the ones which have traditionally been employed with a view to explore the putative explanatory value of this additional complexity. We then proceed to compare simple models with extensions regarding both the initial state (e.g. a mixed state with a specific orthogonal decomposition; a general mixed state) and the dynamics (by introducing Hamiltonians which destroy the separability of the initial structure and by considering an open-system extension). We illustrate the relations between these models mathematically and numerically. This article is part of the themed issue `Second quantum revolution: foundational questions'.

Effects of cluster-shell competition and BCS-like pairing in 12C

NASA Astrophysics Data System (ADS)

Matsuno, H.; Itagaki, N.

2017-12-01

The antisymmetrized quasi-cluster model (AQCM) was proposed to describe α-cluster and jj-coupling shell models on the same footing. In this model, the cluster-shell transition is characterized by two parameters, R representing the distance between α clusters and Λ describing the breaking of α clusters, and the contribution of the spin-orbit interaction, very important in the jj-coupling shell model, can be taken into account starting with the α-cluster model wave function. Not only the closure configurations of the major shells but also the subclosure configurations of the jj-coupling shell model can be described starting with the α-cluster model wave functions; however, the particle-hole excitations of single particles have not been fully established yet. In this study we show that the framework of AQCM can be extended even to the states with the character of single-particle excitations. For ^{12}C, two-particle-two-hole (2p2h) excitations from the subclosure configuration of 0p_{3/2} corresponding to a BCS-like pairing are described, and these shell model states are coupled with the three α-cluster model wave functions. The correlation energy from the optimal configuration can be estimated not only in the cluster part but also in the shell model part. We try to pave the way to establish a generalized description of the nuclear structure.

Quantum memories and Landauer's principle

NASA Astrophysics Data System (ADS)

Alicki, Robert

2011-10-01

Two types of arguments concerning (im)possibility of constructing a scalable, exponentially stable quantum memory equipped with Hamiltonian controls are discussed. The first type concerns ergodic properties of open Kitaev models which are considered as promising candidates for such memories. It is shown that, although the 4D Kitaev model provides stable qubit observables, the Hamiltonian control is not possible. The thermodynamical approach leads to the new proposal of the revised version of Landauer's principle and suggests that the existence of quantum memory implies the existence of the perpetuum mobile of the second kind. Finally, a discussion of the stability property of information and its implications is presented.

Influence of Aromatic Molecules on the Structure and Spectroscopy of Water Clusters

NASA Astrophysics Data System (ADS)

Tabor, Daniel P.; Sibert, Edwin; Walsh, Patrick S.; Zwier, Timothy S.

2016-06-01

Isomer-specific resonant ion-dip infrared spectra are presented for benzene-(water)_n, 1-2-diphenoxyethane-(water)_n, and tricyclophane-(water)_n clusters. The IR spectra are modeled with a local mode Hamiltonian that was originally formulated for the analysis of benzene-(water)_n clusters with up to seven waters. The model accounts for stretch-bend Fermi coupling, which can complicate the IR spectra in the 3150-3300 cm-1 region. When the water clusters interact with each of the solutes, the hydrogen bond lengths between the water molecules change in a characteristic way, reflecting the strength of the solute-water interaction. These structural effects are also reflected spectroscopically in the shifts of the local mode OH stretch frequencies. When diphenoxyethane is the solute, the water clusters distort more significantly than when bound to benzene. Tricyclophane's structure provides an aromatic-rich binding pocket for the water clusters. The local mode model is used to extract Hamiltonians for individual water molecules. These monomer Hamiltonians divide into groups based on their local H-bonding architecture, allowing for further classification of the wide variety of water environments encountered in this study.

Steady state model for the thermal regimes of shells of airships and hot air balloons

NASA Astrophysics Data System (ADS)

Luchev, Oleg A.

1992-10-01

A steady state model of the temperature regime of airships and hot air balloons shells is developed. The model includes three governing equations: the equation of the temperature field of airships or balloons shell, the integral equation for the radiative fluxes on the internal surface of the shell, and the integral equation for the natural convective heat exchange between the shell and the internal gas. In the model the following radiative fluxes on the shell external surface are considered: the direct and the earth reflected solar radiation, the diffuse solar radiation, the infrared radiation of the earth surface and that of the atmosphere. For the calculations of the infrared external radiation the model of the plane layer of the atmosphere is used. The convective heat transfer on the external surface of the shell is considered for the cases of the forced and the natural convection. To solve the mentioned set of the equations the numerical iterative procedure is developed. The model and the numerical procedure are used for the simulation study of the temperature fields of an airship shell under the forced and the natural convective heat transfer.

γ-unstable nuclei in the sdg boson model

NASA Astrophysics Data System (ADS)

Kuyucak, S.; Lac, V.-S.; Morrison, I.; Barrett, B. R.

1991-07-01

Following the recent Pt(p, p‧) experiments which indicated the need for g bosons to reproduce the E4 data, we have extended the O(6) limit of the sd boson model to include g bosons. It is shown that a γ-unstable hamiltonian in the sdg model consisting of a quadrupole interaction and a g boson energy leads to results that are very similar to the O(6) limit. Deviations from the empirical energy spectrum that stem from the γ-unstable nature of the hamiltonian can be improved by including a consistent hexadecapole interaction which induces triaxiality. The same hexadecapole operator can also account for the strong E4 transitions. Applications are made to the Xe and Pt isotopes.

Statistical transmutation in doped quantum dimer models.

PubMed

Lamas, C A; Ralko, A; Cabra, D C; Poilblanc, D; Pujol, P

2012-07-06

We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular, and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e., bosonic into fermionic or vice versa) of the holes and of the signs of all the dimer resonance loops. This exact transformation enables us to define the duality equivalence between doped quantum dimer Hamiltonians and provides the analytic framework to analyze dynamical statistical transmutations. We investigate numerically the doping of the triangular quantum dimer model with special focus on the topological Z(2) dimer liquid. Doping leads to four (instead of two for the square lattice) inequivalent families of Hamiltonians. Competition between phase separation, superfluidity, supersolidity, and fermionic phases is investigated in the four families.

A Hamiltonian electromagnetic gyrofluid model

NASA Astrophysics Data System (ADS)

Waelbroeck, F. L.; Hazeltine, R. D.; Morrison, P. J.

2009-11-01

An isothermal truncation of the electromagnetic gyrofluid model of Snyder and Hammett [Phys. Plasmas 8, 3199 (2001)] is shown to be Hamiltonian. The corresponding noncanonical Lie-Poisson bracket and its Casimir invariants are presented. The model describes the evolution of the density, the electrostatic potential, and the component of the vector potential along a strong background field. This makes it suitable for describing such phenomena as the propagation of kinetic-Alfv'en modons, the nonlinear saturation of drift-tearing modes, and the diamagnetic stabilization of the internal kink. The invariants are used to obtain a set of coupled Grad-Shafranov equations describing equilibria and propagating coherent structures. They also lead to a Lagrangian formulation of the equations of motion that is well suited to solution with the PIC method.

Universal Low-energy Behavior in a Quantum Lorentz Gas with Gross-Pitaevskii Potentials

NASA Astrophysics Data System (ADS)

Basti, Giulia; Cenatiempo, Serena; Teta, Alessandro

2018-06-01

We consider a quantum particle interacting with N obstacles, whose positions are independently chosen according to a given probability density, through a two-body potential of the form N 2 V ( N x) (Gross-Pitaevskii potential). We show convergence of the N dependent one-particle Hamiltonian to a limiting Hamiltonian where the quantum particle experiences an effective potential depending only on the scattering length of the unscaled potential and the density of the obstacles. In this sense our Lorentz gas model exhibits a universal behavior for N large. Moreover we explicitely characterize the fluctuations around the limit operator. Our model can be considered as a simplified model for scattering of slow neutrons from condensed matter.

Microscopic Shell Model Calculations for sd-Shell Nuclei

NASA Astrophysics Data System (ADS)

Barrett, Bruce R.; Dikmen, Erdal; Maris, Pieter; Shirokov, Andrey M.; Smirnova, Nadya A.; Vary, James P.

Several techniques now exist for performing detailed and accurate calculations of the structure of light nuclei, i.e., A ≤ 16. Going to heavier nuclei requires new techniques or extensions of old ones. One of these is the so-called No Core Shell Model (NCSM) with a Core approach, which involves an Okubo-Lee-Suzuki (OLS) transformation of a converged NCSM result into a single major shell, such as the sd-shell. The obtained effective two-body matrix elements can be separated into core and single-particle (s.p.) energies plus residual two-body interactions, which can be used for performing standard shell-model (SSM) calculations. As an example, an application of this procedure will be given for nuclei at the beginning ofthe sd-shell.

Improvement of Progressive Damage Model to Predicting Crashworthy Composite Corrugated Plate

NASA Astrophysics Data System (ADS)

Ren, Yiru; Jiang, Hongyong; Ji, Wenyuan; Zhang, Hanyu; Xiang, Jinwu; Yuan, Fuh-Gwo

2018-02-01

To predict the crashworthy composite corrugated plate, different single and stacked shell models are evaluated and compared, and a stacked shell progressive damage model combined with continuum damage mechanics is proposed and investigated. To simulate and predict the failure behavior, both of the intra- and inter- laminar failure behavior are considered. The tiebreak contact method, 1D spot weld element and cohesive element are adopted in stacked shell model, and a surface-based cohesive behavior is used to capture delamination in the proposed model. The impact load and failure behavior of purposed and conventional progressive damage models are demonstrated. Results show that the single shell could simulate the impact load curve without the delamination simulation ability. The general stacked shell model could simulate the interlaminar failure behavior. The improved stacked shell model with continuum damage mechanics and cohesive element not only agree well with the impact load, but also capture the fiber, matrix debonding, and interlaminar failure of composite structure.

The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

DOE PAGES

Dubček, Tena; Lelas, Karlo; Jukić, Dario; ...

2015-12-07

Here we propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. Lastly, we compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.

Towards development of enhanced fully-Lagrangian mesh-free computational methods for fluid-structure interaction

NASA Astrophysics Data System (ADS)

Khayyer, Abbas; Gotoh, Hitoshi; Falahaty, Hosein; Shimizu, Yuma

2018-02-01

Simulation of incompressible fluid flow-elastic structure interactions is targeted by using fully-Lagrangian mesh-free computational methods. A projection-based fluid model (moving particle semi-implicit (MPS)) is coupled with either a Newtonian or a Hamiltonian Lagrangian structure model (MPS or HMPS) in a mathematically-physically consistent manner. The fluid model is founded on the solution of Navier-Stokes and continuity equations. The structure models are configured either in the framework of Newtonian mechanics on the basis of conservation of linear and angular momenta, or Hamiltonian mechanics on the basis of variational principle for incompressible elastodynamics. A set of enhanced schemes are incorporated for projection-based fluid model (Enhanced MPS), thus, the developed coupled solvers for fluid structure interaction (FSI) are referred to as Enhanced MPS-MPS and Enhanced MPS-HMPS. Besides, two smoothed particle hydrodynamics (SPH)-based FSI solvers, being developed by the authors, are considered and their potential applicability and comparable performance are briefly discussed in comparison with MPS-based FSI solvers. The SPH-based FSI solvers are established through coupling of projection-based incompressible SPH (ISPH) fluid model and SPH-based Newtonian/Hamiltonian structure models, leading to Enhanced ISPH-SPH and Enhanced ISPH-HSPH. A comparative study is carried out on the performances of the FSI solvers through a set of benchmark tests, including hydrostatic water column on an elastic plate, high speed impact of an elastic aluminum beam, hydroelastic slamming of a marine panel and dam break with elastic gate.

Communication: Fragment-based Hamiltonian model of electronic charge-excitation gaps and gap closure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valone, S. M.; Pilania, G.; Liu, X. Y.

2015-11-14

Capturing key electronic properties such as charge excitation gaps within models at or above the atomic scale presents an ongoing challenge to understanding molecular, nanoscale, and condensed phase systems. One strategy is to describe the system in terms of properties of interacting material fragments, but it is unclear how to accomplish this for charge-excitation and charge-transfer phenomena. Hamiltonian models such as the Hubbard model provide formal frameworks for analyzing gap properties but are couched purely in terms of states of electrons, rather than the states of the fragments at the scale of interest. The recently introduced Fragment Hamiltonian (FH) modelmore » uses fragments in different charge states as its building blocks, enabling a uniform, quantum-mechanical treatment that captures the charge-excitation gap. These gaps are preserved in terms of inter-fragment charge-transfer hopping integrals T and on-fragment parameters U{sup (FH)}. The FH model generalizes the standard Hubbard model (a single intra-band hopping integral t and on-site repulsion U) from quantum states for electrons to quantum states for fragments. We demonstrate that even for simple two-fragment and multi-fragment systems, gap closure is enabled once T exceeds the threshold set by U{sup (FH)}, thus providing new insight into the nature of metal-insulator transitions. This result is in contrast to the standard Hubbard model for 1d rings, for which Lieb and Wu proved that gap closure was impossible, regardless of the choices for t and U.« less

PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics

NASA Astrophysics Data System (ADS)

Fring, Andreas; Jones, Hugh; Znojil, Miloslav

2008-06-01

Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong interactions at high energies via Regge models, in condensed matter physics in the context of the XXZ-spin chain, in interacting boson models in nuclear physics, in integrable quantum field theories as Toda field theories with complex coupling constants, and also very recently in a field theoretical scenario in the quantization procedure of strings on an AdS5 x S5 background. Concrete experimental realizations of these types of systems in the form of optical lattices have been proposed in 2007. In the area of mathematical physics similar non-systematic results appeared sporadically over the years. However, intensive and more systematic investigation of these types of non- Hermitian Hamiltonians with real eigenvalue spectra only began about ten years ago, when the surprising discovery was made that a large class of one-particle systems perturbed by a simple non-Hermitian potential term possesses a real energy spectrum. Since then regular international workshops devoted to this theme have taken place. This special issue is centred around the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics held in July 2007 at City University London. All the contributions contain significant new results or alternatively provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants were also invited. Meanwhile many interesting results have been obtained and consensus has been reached on various central conceptual issues in the growing community of this subject. It is, for instance, well understood that the reality of the spectrum can be attributed either to the unbroken PT-symmetry of the entire system, that is, invariance of the Hamiltonian and the corresponding wavefunctions under a simultaneous parity transformation and time reversal, or more generally to its pseudo-Hermiticity . When the spectrum is real and discrete the Hamiltonian is actually quasi-Hermitian, with a positive-definite metric operator, and can in principle be related by a similarity transformation to an isospectral Hermitian counterpart. For all approaches well-defined procedures have been developed, which allow one to construct metric operators and therefore a consistent description of the underlying quantum mechanical observables. Even though the general principles have been laid out, it remains a challenge in most concrete cases to implement the entire procedure. Solvable models in this sense, some of which may be found in this issue, remain a rare exception. Nonetheless, despite this progress some important questions are still unanswered. For instance, according to the current understanding the non-Hermitian Hamiltonian does not uniquely define the physics of the system since a meaningful metric can no longer be associated with the system in a non-trivial and unambiguous manner. A fully consistent scattering theory has also not yet been formulated. Other issues remain controversial, such as the quantum brachistochrone problem, the problem of forming a mixture between a Hermitian and non-Hermitian system, the new phenomenological possibilities of forming a kind of worm-hole effect, etc. We would like to acknowledge the financial support of the London Mathematical Society, the Institute of Physics, the Doppler Institute in Prague and the School of Engineering and Mathematical Science of City University London. We hope this special issue will be useful to the newcomer as well as to the expert in the subject. Workshop photograph Participants of the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics.

Inclusion of orbital relaxation and correlation through the unitary group adapted open shell coupled cluster theory using non-relativistic and scalar relativistic Hamiltonians to study the core ionization potential of molecules containing light to medium-heavy elements

NASA Astrophysics Data System (ADS)

Sen, Sangita; Shee, Avijit; Mukherjee, Debashis

2018-02-01

The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J. Chem. Phys. 137, 074104 (2012)], is very effective in capturing orbital relaxation accompanying ionization or excitation of both the core and the valence electrons [S. Sen et al., Mol. Phys. 111, 2625 (2013); A. Shee et al., J. Chem. Theory Comput. 9, 2573 (2013)] while preserving the spin-symmetry of the target states and using the neutral closed-shell spatial orbitals of the ground state. Our Ansatz invokes a normal-ordered exponential representation of spin-free cluster-operators. The orbital relaxation induced by a specific set of cluster operators in our Ansatz is good enough to eliminate the need for different sets of orbitals for the ground and the core-ionized states. We call the single configuration state function (CSF) limit of this theory the Unitary Group Adapted Open-Shell Coupled Cluster (UGA-OSCC) theory. The aim of this paper is to comprehensively explore the efficacy of our Ansatz to describe orbital relaxation, using both theoretical analysis and numerical performance. Whenever warranted, we also make appropriate comparisons with other coupled-cluster theories. A physically motivated truncation of the chains of spin-free T-operators is also made possible by the normal-ordering, and the operational resemblance to single reference coupled-cluster theory allows easy implementation. Our test case is the prediction of the 1s core IP of molecules containing a single light- to medium-heavy nucleus and thus, in addition to demonstrating the orbital relaxation, we have addressed the scalar relativistic effects on the accuracy of the IPs by using a hierarchy of spin-free Hamiltonians in conjunction with our theory. Additionally, the contribution of the spin-free component of the two-electron Gaunt term, not usually taken into consideration, has been estimated at the Self-Consistent Field (ΔSCF) level and is found to become increasingly important and eventually quite prominent for molecules with third period atoms and below. The accuracies of the IPs computed using UGA-OSCC are found to be of the same order as the Coupled Cluster Singles Doubles (ΔCCSD) values while being free from spin contamination. Since the UGA-OSCC uses a common set of orbitals for the ground state and the ion, it obviates the need of two N5 AO to MO transformation in contrast to the ΔCCSD method.

Inclusion of orbital relaxation and correlation through the unitary group adapted open shell coupled cluster theory using non-relativistic and scalar relativistic Hamiltonians to study the core ionization potential of molecules containing light to medium-heavy elements.

PubMed

Sen, Sangita; Shee, Avijit; Mukherjee, Debashis

2018-02-07

The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J. Chem. Phys. 137, 074104 (2012)], is very effective in capturing orbital relaxation accompanying ionization or excitation of both the core and the valence electrons [S. Sen et al., Mol. Phys. 111, 2625 (2013); A. Shee et al., J. Chem. Theory Comput. 9, 2573 (2013)] while preserving the spin-symmetry of the target states and using the neutral closed-shell spatial orbitals of the ground state. Our Ansatz invokes a normal-ordered exponential representation of spin-free cluster-operators. The orbital relaxation induced by a specific set of cluster operators in our Ansatz is good enough to eliminate the need for different sets of orbitals for the ground and the core-ionized states. We call the single configuration state function (CSF) limit of this theory the Unitary Group Adapted Open-Shell Coupled Cluster (UGA-OSCC) theory. The aim of this paper is to comprehensively explore the efficacy of our Ansatz to describe orbital relaxation, using both theoretical analysis and numerical performance. Whenever warranted, we also make appropriate comparisons with other coupled-cluster theories. A physically motivated truncation of the chains of spin-free T-operators is also made possible by the normal-ordering, and the operational resemblance to single reference coupled-cluster theory allows easy implementation. Our test case is the prediction of the 1s core IP of molecules containing a single light- to medium-heavy nucleus and thus, in addition to demonstrating the orbital relaxation, we have addressed the scalar relativistic effects on the accuracy of the IPs by using a hierarchy of spin-free Hamiltonians in conjunction with our theory. Additionally, the contribution of the spin-free component of the two-electron Gaunt term, not usually taken into consideration, has been estimated at the Self-Consistent Field (ΔSCF) level and is found to become increasingly important and eventually quite prominent for molecules with third period atoms and below. The accuracies of the IPs computed using UGA-OSCC are found to be of the same order as the Coupled Cluster Singles Doubles (ΔCCSD) values while being free from spin contamination. Since the UGA-OSCC uses a common set of orbitals for the ground state and the ion, it obviates the need of two N 5 AO to MO transformation in contrast to the ΔCCSD method.

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

NASA Astrophysics Data System (ADS)

Hermes, Matthew R.; Dukelsky, Jorge; Scuseria, Gustavo E.

2017-06-01

The failures of single-reference coupled-cluster theory for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled-cluster theory fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled-cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a test bed [J. Chem. Phys. 146, 054110 (2017), 10.1063/1.4974989]. We generalize the concept of a symmetry-projected mean-field wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled-cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled-cluster theory is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.

Solvable Family of Driven-Dissipative Many-Body Systems.

PubMed

Foss-Feig, Michael; Young, Jeremy T; Albert, Victor V; Gorshkov, Alexey V; Maghrebi, Mohammad F

2017-11-10

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.

Solvable Family of Driven-Dissipative Many-Body Systems

NASA Astrophysics Data System (ADS)

Foss-Feig, Michael; Young, Jeremy T.; Albert, Victor V.; Gorshkov, Alexey V.; Maghrebi, Mohammad F.

2017-11-01

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.

PubMed

Pang, Shengshi; Jordan, Andrew N

2017-03-09

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T 2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T 4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

PubMed Central

Pang, Shengshi; Jordan, Andrew N.

2017-01-01

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case. PMID:28276428

Application of the Shell/3D Modeling Technique for the Analysis of Skin-Stiffener Debond Specimens

NASA Technical Reports Server (NTRS)

Krueger, Ronald; O'Brien, T. Kevin; Minguet, Pierre J.

2002-01-01

The application of a shell/3D modeling technique for the simulation of skin/stringer debond in a specimen subjected to three-point bending is demonstrated. The global structure was modeled with shell elements. A local three-dimensional model, extending to about three specimen thicknesses on either side of the delamination front was used to capture the details of the damaged section. Computed total strain energy release rates and mixed-mode ratios obtained from shell/13D simulations were in good agreement with results obtained from full solid models. The good correlations of the results demonstrated the effectiveness of the shell/3D modeling technique for the investigation of skin/stiffener separation due to delamination in the adherents.

Electronic transport properties of inner and outer shells in near ohmic-contacted double-walled carbon nanotube transistors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Yuchun; Zhou, Liyan; Zhao, Shangqian

2014-06-14

We investigate electronic transport properties of field-effect transistors based on double-walled carbon nanotubes, of which inner shells are metallic and outer shells are semiconducting. When both shells are turned on, electron-phonon scattering is found to be the dominant phenomenon. On the other hand, when outer semiconducting shells are turned off, a zero-bias anomaly emerges in the dependence of differential conductance on the bias voltage, which is characterized according to the Tomonaga-Luttinger liquid model describing tunneling into one-dimensional materials. We attribute these behaviors to different contact conditions for outer and inner shells of the double-walled carbon nanotubes. A simple model combiningmore » Luttinger liquid model for inner metallic shells and electron-phonon scattering in outer semiconducting shells is given here to explain our transport data at different temperatures.« less

Propagation of flexural and membrane waves with fluid loaded NASTRAN plate and shell elements

NASA Technical Reports Server (NTRS)

Kalinowski, A. J.; Wagner, C. A.

1983-01-01

Modeling of flexural and membrane type waves existing in various submerged (or in vacuo) plate and/or shell finite element models that are excited with steady state type harmonic loadings proportioned to e(i omega t) is discussed. Only thin walled plates and shells are treated wherein rotary inertia and shear correction factors are not included. More specifically, the issue of determining the shell or plate mesh size needed to represent the spatial distribution of the plate or shell response is of prime importance towards successfully representing the solution to the problem at hand. To this end, a procedure is presented for establishing guide lines for determining the mesh size based on a simple test model that can be used for a variety of plate and shell configurations such as, cylindrical shells with water loading, cylindrical shells in vacuo, plates with water loading, and plates in vacuo. The procedure for doing these four cases is given, with specific numerical examples present only for the cylindrical shell case.

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

NASA Astrophysics Data System (ADS)

Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

2018-05-01

A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

Work distributions for random sudden quantum quenches

NASA Astrophysics Data System (ADS)

Łobejko, Marcin; Łuczka, Jerzy; Talkner, Peter

2017-05-01

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of Hermitian matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature. The same work distribution as for a sudden random quench is obtained for an adiabatic, i.e., infinitely slow, protocol connecting the same initial and final Hamiltonians.

Hamiltonian dynamics of extended objects

NASA Astrophysics Data System (ADS)

Capovilla, R.; Guven, J.; Rojas, E.

2004-12-01

We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.

Theoretical research on the spin-Hamiltonian parameters of the rhombic W5+ centers in CaWO4:Y3+ crystal

NASA Astrophysics Data System (ADS)

Mei, Yang; Wei, Cheng-Fu; Zheng, Wen-Chen

2016-02-01

Detailed theoretical calculations for the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, where i=x, y, z) of the rhombic W5+ center in CaWO4:Y3+ crystal are performed by using the high-order perturbation formulas for d1 ions in rhombic tetrahedral clusters with the ground state |dz2>. These formulas consist of the contributions from two mechanisms, the crystal-field (CF) mechanism connected with CF excited states in the vastly-used CF theory and the frequently-neglected charge-transfer (CT) mechanism related to CT excited states. The calculated results agree well with the experimental values. The calculations indicate that for W5+ ion (or other high valence state dn ions) in crystals, the model calculations of spin-Hamiltonian parameters should take both the CF and CT mechanisms into account. The signs of hyperfine structure constants Ai are suggested and the forming (or defect model) of rhombic W5+ center in CaWO4:Y3+ crystal is confirmed from the calculations.

On the domain of the Nelson Hamiltonian

NASA Astrophysics Data System (ADS)

Griesemer, M.; Wünsch, A.

2018-04-01

The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.

Light-Front Holography, Light-Front Wavefunctions, and Novel QCD Phenomena

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; de Teramond, Guy F.

2012-02-16

Light-Front Holography is one of the most remarkable features of the AdS/CFT correspondence. In spite of its present limitations it provides important physical insights into the nonperturbative regime of QCD and its transition to the perturbative domain. This novel framework allows hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time. The model leads to an effective confining light-front QCD Hamiltonian and a single-variable light-front Schroedinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z inmore » AdS space is uniquely identified with a Lorentz-invariant coordinate {zeta} which measures the separation of the constituents within a hadron at equal light-front time and determines the off-shell dynamics of the bound-state wavefunctions, and thus the fall-off as a function of the invariant mass of the constituents. The soft-wall holographic model modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics - a semi-classical frame-independent first approximation to the spectra and light-front wavefunctions of meson and baryons. The model predicts a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum L of hadrons and the radial quantum number n. The hadron eigensolutions projected on the free Fock basis provides the complete set of valence and non-valence light-front Fock state wavefunctions {Psi}{sub n/H} (x{sub i}, k{sub {perpendicular}i}, {lambda}{sub i}) which describe the hadron's momentum and spin distributions needed to compute the direct measures of hadron structure at the quark and gluon level, such as elastic and transition form factors, distribution amplitudes, structure functions, generalized parton distributions and transverse momentum distributions. The effective confining potential also creates quark-antiquark pairs from the amplitude q {yields} q{bar q}q. Thus in holographic QCD higher Fock states can have any number of extra q{bar q} pairs. We discuss the relevance of higher Fock-states for describing the detailed structure of space and time-like form factors. The AdS/QCD model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms. A new perspective on quark and gluon condensates is also obtained.« less

Generalized Bloch theorem and topological characterization

NASA Astrophysics Data System (ADS)

Dobardžić, E.; Dimitrijević, M.; Milovanović, M. V.

2015-03-01

The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with the translational group. Based on a group theory analysis we present a generalization of the Bloch theorem that incorporates all additional symmetries of a crystal. The generalized Bloch theorem constrains the form of the Hamiltonian which becomes manifestly invariant under additional symmetries. In the case of isotropic interactions the generalized Bloch theorem gives a unique Hamiltonian. This Hamiltonian coincides with the Hamiltonian in the periodic gauge. In the case of anisotropic interactions the generalized Bloch theorem allows a family of Hamiltonians. Due to the continuity argument we expect that even in this case the Hamiltonian in the periodic gauge defines observables, such as Berry curvature, in the inverse space. For both cases we present examples and demonstrate that the average of the Berry curvatures of all possible Hamiltonians in the Bloch gauge is the Berry curvature in the periodic gauge.

Experimental analysis and numerical modeling of mollusk shells as a three dimensional integrated volume.

PubMed

Faghih Shojaei, M; Mohammadi, V; Rajabi, H; Darvizeh, A

2012-12-01

In this paper, a new numerical technique is presented to accurately model the geometrical and mechanical features of mollusk shells as a three dimensional (3D) integrated volume. For this purpose, the Newton method is used to solve the nonlinear equations of shell surfaces. The points of intersection on the shell surface are identified and the extra interior parts are removed. Meshing process is accomplished with respect to the coordinate of each point of intersection. The final 3D generated mesh models perfectly describe the spatial configuration of the mollusk shells. Moreover, the computational model perfectly matches with the actual interior geometry of the shells as well as their exterior architecture. The direct generation technique is employed to generate a 3D finite element (FE) model in ANSYS 11. X-ray images are taken to show the close similarity of the interior geometry of the models and the actual samples. A scanning electron microscope (SEM) is used to provide information on the microstructure of the shells. In addition, a set of compression tests were performed on gastropod shell specimens to obtain their ultimate compressive strength. A close agreement between experimental data and the relevant numerical results is demonstrated. Copyright © 2012 Elsevier Ltd. All rights reserved.

A Method for Quantifying, Visualising, and Analysing Gastropod Shell Form

PubMed Central

Liew, Thor-Seng; Schilthuizen, Menno

2016-01-01

Quantitative analysis of organismal form is an important component for almost every branch of biology. Although generally considered an easily-measurable structure, the quantification of gastropod shell form is still a challenge because many shells lack homologous structures and have a spiral form that is difficult to capture with linear measurements. In view of this, we adopt the idea of theoretical modelling of shell form, in which the shell form is the product of aperture ontogeny profiles in terms of aperture growth trajectory that is quantified as curvature and torsion, and of aperture form that is represented by size and shape. We develop a workflow for the analysis of shell forms based on the aperture ontogeny profile, starting from the procedure of data preparation (retopologising the shell model), via data acquisition (calculation of aperture growth trajectory, aperture form and ontogeny axis), and data presentation (qualitative comparison between shell forms) and ending with data analysis (quantitative comparison between shell forms). We evaluate our methods on representative shells of the genera Opisthostoma and Plectostoma, which exhibit great variability in shell form. The outcome suggests that our method is a robust, reproducible, and versatile approach for the analysis of shell form. Finally, we propose several potential applications of our methods in functional morphology, theoretical modelling, taxonomy, and evolutionary biology. PMID:27280463

A Hybrid Program for Fitting Rotationally Resolved Spectra of Floppy Molecules with One Large-Amplitude Rotatory Motion and One Large-Amplitude Oscillatory Motion

PubMed Central

Kleiner, Isabelle; Hougen, Jon T.

2015-01-01

A new hybrid-model fitting program for methylamine-like molecules has been developed, based on an effective Hamiltonian in which the ammonia-like inversion motion is treated using a tunneling formalism, while the internal-rotation motion is treated using an explicit kinetic energy operator and potential energy function. The Hamiltonian in the computer program is set up as a 2×2 partitioned matrix, where each diagonal block contains a traditional torsion-rotation Hamiltonian (as in the earlier program BELGI), and the two off-diagonal blocks contain tunneling terms. This hybrid formulation permits the use of the permutation-inversion group G6 (isomorphic to C3v) for terms in the two diagonal blocks, but requires G12 for terms in the off-diagonal blocks. The first application of the new program is to 2-methylmalonaldehyde. Microwave data for this molecule were previously fit using an all-tunneling Hamiltonian formalism to treat both large-amplitude-motions. For 2-methylmalonaldehyde, the hybrid program achieves the same quality of fit as was obtained with the all-tunneling program, but fits with the hybrid program eliminate a large discrepancy between internal rotation barriers in the OH and OD isotopologs of 2-methylmalonaldehyde that arose in fits with the all-tunneling program. This large isotopic shift in internal rotation barrier is thus almost certainly an artifact of the all-tunneling model. Other molecules for application of the hybrid program are mentioned. PMID:26439709

Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański

NASA Astrophysics Data System (ADS)

Sheftel, Mikhail; Yazıcı, Devrim

2016-09-01

We present first heavenly equation of Plebański in a two-component evolutionary form and obtain Lagrangian and Hamiltonian representations of this system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We derive two linearly independent recursion operators for symmetries of this system related by a discrete symmetry of both the two-component system and its symmetry condition. Acting by these operators on the first Hamiltonian operator J_0 we obtain second and third Hamiltonian operators. However, we were not able to find Hamiltonian densities corresponding to the latter two operators. Therefore, we construct two recursion operators, which are either even or odd, respectively, under the above-mentioned discrete symmetry. Acting with them on J_0, we generate another two Hamiltonian operators J_+ and J_- and find the corresponding Hamiltonian densities, thus obtaining second and third Hamiltonian representations for the first heavenly equation in a two-component form. Using P. Olver's theory of the functional multi-vectors, we check that the linear combination of J_0, J_+ and J_- with arbitrary constant coefficients satisfies Jacobi identities. Since their skew symmetry is obvious, these three operators are compatible Hamiltonian operators and hence we obtain a tri-Hamiltonian representation of the first heavenly equation. Our well-founded conjecture applied here is that P. Olver's method works fine for nonlocal operators and our proof of the Jacobi identities and bi-Hamiltonian structures crucially depends on the validity of this conjecture.

A shell-neutral modeling approach yields sustainable oyster harvest estimates: a retrospective analysis of the Louisiana state primary seed grounds

USGS Publications Warehouse

Soniat, Thomas M.; Klinck, John M.; Powell, Eric N.; Cooper, Nathan; Abdelguerfi, Mahdi; Hofmann, Eileen E.; Dahal, Janak; Tu, Shengru; Finigan, John; Eberline, Benjamin S.; La Peyre, Jerome F.; LaPeyre, Megan K.; Qaddoura, Fareed

2012-01-01

A numerical model is presented that defines a sustainability criterion as no net loss of shell, and calculates a sustainable harvest of seed (<75 mm) and sack or market oysters (≥75 mm). Stock assessments of the Primary State Seed Grounds conducted east of the Mississippi from 2009 to 2011 show a general trend toward decreasing abundance of sack and seed oysters. Retrospective simulations provide estimates of annual sustainable harvests. Comparisons of simulated sustainable harvests with actual harvests show a trend toward unsustainable harvests toward the end of the time series. Stock assessments combined with shell-neutral models can be used to estimate sustainable harvest and manage cultch through shell planting when actual harvest exceeds sustainable harvest. For exclusive restoration efforts (no fishing allowed), the model provides a metric for restoration success-namely, shell accretion. Oyster fisheries that remove shell versus reef restorations that promote shell accretion, although divergent in their goals, are convergent in their management; both require vigilant attention to shell budgets.

Bohr Hamiltonian for γ = 30° with Davidson potential

NASA Astrophysics Data System (ADS)

Yigitoglu, Ibrahim; Gokbulut, Melek

2018-03-01

A γ-rigid solution of the Bohr Hamiltonian for γ = 30° is constructed with the Davidson potential in the β part. This solution is going to be called Z(4)-D. The energy eigenvalues and wave functions are obtained by using the analytic method developed by Nikiforov and Uvarov. The calculated intraband and interband B(E2) transitions rates are presented and compared with the Z(4) model predictions. The staggering behavior in γ-bands is considered to search Z(4) -D candidate nuclei. A variational procedure is applied to demonstrate that the Z(4) model is a solution of the critical point at the shape phase transition from spherical to rigid triaxial rotor.

Spacetime emergence of the robertson-walker universe from a matrix model.

PubMed

Erdmenger, Johanna; Meyer, René; Park, Jeong-Hyuck

2007-06-29

Using a novel, string theory-inspired formalism based on a Hamiltonian constraint, we obtain a conformal mechanical system for the spatially flat four-dimensional Robertson-Walker Universe. Depending on parameter choices, this system describes either a relativistic particle in the Robertson-Walker background or metric fluctuations of the Robertson-Walker geometry. Moreover, we derive a tree-level M theory matrix model in this time-dependent background. Imposing the Hamiltonian constraint forces the spacetime geometry to be fuzzy near the big bang, while the classical Robertson-Walker geometry emerges as the Universe expands. From our approach, we also derive the temperature of the Universe interpolating between the radiation and matter dominated eras.

Small traveling clusters in attractive and repulsive Hamiltonian mean-field models.

PubMed

Barré, Julien; Yamaguchi, Yoshiyuki Y

2009-03-01

Long-lasting small traveling clusters are studied in the Hamiltonian mean-field model by comparing between attractive and repulsive interactions. Nonlinear Landau damping theory predicts that a Gaussian momentum distribution on a spatially homogeneous background permits the existence of traveling clusters in the repulsive case, as in plasma systems, but not in the attractive case. Nevertheless, extending the analysis to a two-parameter family of momentum distributions of Fermi-Dirac type, we theoretically predict the existence of traveling clusters in the attractive case; these findings are confirmed by direct N -body numerical simulations. The parameter region with the traveling clusters is much reduced in the attractive case with respect to the repulsive case.

On the Magnitude of the Nonadiabatic Error for Highly Coupled Radicals

NASA Astrophysics Data System (ADS)

Stanton, J. F.

2009-06-01

A review is given of recent advances in the construction of (quasi)diabatic model Hamiltonians and their application to analyzing the spectroscopy of molecules with strong vibronic coupling. A numerical application to the vibronic levels of the BNB radical below 0.6 eV is presented, together with corresponding adiabatic (quantum chemistry) calculations. The agreement with the experimental levels is nearly quantitative with the model Hamiltonian, attesting to the power of the approach. On the contrary, it is also revealed that the magnitude of the nonadiabatic contributions to the zero-point energy and the lowest fundamental frequency of the coupling mode are considerably larger than expected, at least by your narrator.

Open source integrated modeling environment Delta Shell

NASA Astrophysics Data System (ADS)

Donchyts, G.; Baart, F.; Jagers, B.; van Putten, H.

2012-04-01

In the last decade, integrated modelling has become a very popular topic in environmental modelling since it helps solving problems, which is difficult to model using a single model. However, managing complexity of integrated models and minimizing time required for their setup remains a challenging task. The integrated modelling environment Delta Shell simplifies this task. The software components of Delta Shell are easy to reuse separately from each other as well as a part of integrated environment that can run in a command-line or a graphical user interface mode. The most components of the Delta Shell are developed using C# programming language and include libraries used to define, save and visualize various scientific data structures as well as coupled model configurations. Here we present two examples showing how Delta Shell simplifies process of setting up integrated models from the end user and developer perspectives. The first example shows coupling of a rainfall-runoff, a river flow and a run-time control models. The second example shows how coastal morphological database integrates with the coastal morphological model (XBeach) and a custom nourishment designer. Delta Shell is also available as open-source software released under LGPL license and accessible via http://oss.deltares.nl.

Gamma-unstable nuclei in the sdg boson model

NASA Astrophysics Data System (ADS)

Kuyucak, S.; Lac, V.-S.; Morrison, I.; Barret, B. R.

Following the recent Pt(p,p') experiments which indicated the need for high angular momentum (g) bosons to reproduce the E4 data, we have extended the O(6) limit of the sd boson model to the sdg bosons. It is shown that a gamma-unstable Hamiltonian in the sdg model consisting of a quadrupole interaction and a g boson energy leads to results that are very similar to the O(6) limit. Deviations from the empirical energy spectrum that stem from the gamma-unstable nature of the Hamiltonian can be improved by including a consistent hexadecapole interaction which induces triaxiality. The same hexadecapole operator can also account for the strong E4 transitions to the 4(sup +) states presumed to be g boson states. Specific applications are made to the Xe and Pt isotopes.

Hamiltonian BFV-BRST theory of closed quantum cosmological models

NASA Astrophysics Data System (ADS)

Kamenshchik, A. Yu.; Lyakhovich, S. L.

1997-02-01

We introduce and study a new discrete basis of gravity constraints by making use of harmonic expansion for closed cosmological models. The full set of constraints is split into area-preserving spatial diffeomorphisms, forming closed subalgebra, and Virasoro-like generators. Operational Hamiltonian BFV-BRST quantization is performed in the framework of perturbative expansion in the dimensionless parameter, which is a positive power of the ratio of Planckian volume to the volume of the Universe. For the (N + 1)-dimensional generalization of stationary closed Bianchi-I cosmology the nilpotency condition for the BRST operator is examined in the first quantum approximation. It turns out that a certain relationship between the dimensionality of the space and the spectrum of matter fields emerges from the requirement of quantum consistency of the model.

Hamiltonian BFV-BRST theory of closed quantum cosmological models

NASA Astrophysics Data System (ADS)

Kamenshchik, A. Yu.; Lyakhovich, S. L.

1997-08-01

We introduce and study a new discrete basis of gravity constraints by making use of the harmonic expansion for closed cosmological models. The full set of constraints is split into area-preserving spatial diffeomorphisms, forming a closed subalgebra, and Virasoro-like generators. The operatorial Hamiltonian BFV-BRST quantization is performed in the framework of a perturbative expansion in the dimensionless parameter which is a positive power of the ratio of the Planck volume to the volume of the Universe. For the (N + 1) - dimensional generalization of a stationary closed Bianchi-I cosmology the nilpotency condition for the BRST operator is examined in the first quantum approximation. It turns out that a relationship between the dimensionality of the space and the spectrum of matter fields emerges from the requirement of quantum consistency of the model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Yang; Xiao, Jianyuan; Zhang, Ruili

Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature.

Influence of corneal thickness on the intraocular pressure readings for Maklakoff's tonometer of different weight

NASA Astrophysics Data System (ADS)

Franus, D. V.

2018-05-01

Research is conducted into variation in the stress-strain state of the corneoscleral shell of the human eye under loading by a flat base stamp of varying weight. A three-dimensional finite-element model of the contact problem of loading of the corneoscleral shell in the ANSYS program package is presented. Cornea and sclera are modeled as conjugated transversely isotropic spherical shells. The cornea is modeled as a multilayer shell with variable thickness in which all modeled layers have their own individual elastic properties. The research deals with the numerical calculation of the diameter of the contact zone between the shell and the stamp. Values of correction coefficients for intraocular pressure are obtained depending on the thickness of the corneal shell in its center, allowing the true intraocular pressure to be determined more accurately.

Mixing of t2 g-eg orbitals in 4 d and 5 d transition metal oxides

NASA Astrophysics Data System (ADS)

Stamokostas, Georgios L.; Fiete, Gregory A.

2018-02-01

Using exact diagonalization, we study the spin-orbit coupling and interaction-induced mixing between t2 g and egd -orbital states in a cubic crystalline environment, as commonly occurs in transition metal oxides. We make a direct comparison with the widely used t2 g-only or eg-only models, depending on electronic filling. We consider all electron fillings of the d shell and compute the total magnetic moment, the spin, the occupancy of each orbital, and the effective spin-orbit coupling strength (renormalized through interaction effects) in terms of the bare interaction parameters, spin-orbit coupling, and crystal-field splitting, focusing on the parameter ranges relevant to 4 d and 5 d transition metal oxides. In various limits, we provide perturbative results consistent with our numerical calculations. We find that the t2 g-eg mixing can be large, with up to 20% occupation of orbitals that are nominally "empty," which has experimental implications for the interpretation of the branching ratio in experiments, and can impact the effective local moment Hamiltonian used to study magnetic phases and magnetic excitations in transition metal oxides. Our results can aid the theoretical interpretation of experiments on these materials, which often fall in a regime of intermediate coupling with respect to electron-electron interactions.

Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Degroote, M.; Henderson, T. M.; Zhao, J.

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero.more » Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.« less

Unifying perspective: Solitary traveling waves as discrete breathers in Hamiltonian lattices and energy criteria for their stability

NASA Astrophysics Data System (ADS)

Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna; Xu, Haitao

2017-09-01

In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H''(c0) evaluated at the critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.

Zero-field splitting in the isoelectronic aqueous Gd(III) and Eu(II) complexes from a first principles analysis

NASA Astrophysics Data System (ADS)

Khan, S.; Peters, V.; Kowalewski, J.; Odelius, M.

2018-03-01

The zero-field splitting (ZFS) of the ground state octet in aqueous Eu(II) and Gd(III) solutions was investigated through multi- configurational quantum chemical calculations and ab initio molecular dynamics (AIMD) simulations. Investigation of the ZFS of the lanthanide ions is essential to understand the electron spin dynamics and nuclear spin relaxation around paramagnetic ions and consequently the mechanisms underlying applications like magnetic resonance imaging. We found by comparing clusters at identical geometries but different metallic centres that there is not a simple relationship for their ZFS, in spite of the complexes being isoelectronic - each containing 7 unpaired f electrons. Through sampling it was established that inclusion of the first hydration shell has a dominant (over 90 %) influence on the ZFS. Extended sampling of aqueous Gd(III) showed that the 2 nd order spin Hamiltonian formalism is valid and that the rhombic ZFS component is decisive.

Is the addition of an assisted driving Hamiltonian always useful for adiabatic evolution?

NASA Astrophysics Data System (ADS)

Sun, Jie; Lu, Songfeng; Li, Li

2017-04-01

It has been known that when an assisted driving item is added to the main system Hamiltonian, the efficiency of the resultant adiabatic evolution can be significantly improved. In some special cases, it can be seen that only through adding an assisted driving Hamiltonian can the resulting adiabatic evolution be made not to fail. Thus the additional driving Hamiltonian plays an important role in adiabatic computing. In this paper, we show that if the driving Hamiltonian is chosen inappropriately, the adiabatic computation may still fail. More importantly, we find that the adiabatic computation can only succeed if the assisted driving Hamiltonian has a relatively fixed form. This may help us understand why in the related literature all of the driving Hamiltonians used share the same form.

Universality class of non-Fermi-liquid behavior in mixed-valence systems

NASA Astrophysics Data System (ADS)

Zhang, Guang-Ming; Su, Zhao-Bin; Yu, Lu

1996-01-01

A generalized Anderson single-impurity model with off-site Coulomb interactions is derived from the extended three-band Hubbard model, originally proposed to describe the physics of the copper oxides. Using the Abelian bosonization technique and canonical transformations, an effective Hamiltonian is derived in the strong-coupling limit, which is essentially analogous to the Toulouse limit of the ordinary Kondo problem. In this limit, the effective Hamiltonian can be exactly solved, with a mixed-valence quantum critical point separating two different Fermi-liquid phases, i.e., the Kondo phase and the empty orbital phase. In the mixed-valence quantum critical regime, the local moment is only partially quenched and x-ray edge singularities are generated. Around the quantum critical point, a type of non-Fermi-liquid behavior is predicted with an extra specific heat Cimp~T1/4 and a singular spin susceptibility χimp~T-3/4. At the same time, the effective Hamiltonian under single occupancy is transformed into a resonant-level model, from which the correct Kondo physical properties (specific heat, spin susceptibility, and an enhanced Wilson ratio) are easily rederived. Finally, a brief discussion is given to relate these theoretical results to observations in UPdxCu5-x (x=1,1.5) alloys, which show single-impurity critical behavior consistent with our predictions.

Glass shell manufacturing in space

NASA Technical Reports Server (NTRS)

Downs, R. L.; Ebner, M. A.; Nolen, R. L., Jr.

1981-01-01

Highly-uniform, hollow glass spheres (shells), which are used for inertial confinement fusion targets, were formed from metal-organic gel powder feedstock in a vertical furnace. As a result of the rapid pyrolysis caused by the furnace, the gel is transformed to a shell in five distinct stages: (a) surface closure of the porous gel; (b) generation of a closed-cell foam structure in the gel; (c) spheridization of the gel and further expansion of the foam; (d) coalescence of the closed-cell foam to a single-void shell; and (e) fining of the glass shell. The heat transfer from the furnace to the falling gel particle was modeled to determine the effective heating rate of the gel. The model predicts the temperature history for a particle as a function of mass, dimensions, specific heat, and absorptance as well as furnace temperature profile and thermal conductivity of the furnace gas. A model was developed that predicts the gravity-induced degradation of shell concentricity in falling molten shells as a function of shell characteristics and time.

Isothermal Circumstellar Dust Shell Model for Teaching

ERIC Educational Resources Information Center

Robinson, G.; Towers, I. N.; Jovanoski, Z.

2009-01-01

We introduce a model of radiative transfer in circumstellar dust shells. By assuming that the shell is both isothermal and its thickness is small compared to its radius, the model is simple enough for students to grasp and yet still provides a quantitative description of the relevant physical features. The isothermal model can be used in a…

Geodynamic Modeling of Planetary Ice-Oceans: Evolution of Ice-Shell Thickness in Convecting Two-Phase Systems

NASA Astrophysics Data System (ADS)

Allu Peddinti, D.; McNamara, A. K.

2016-12-01

Along with the newly unveiled icy surface of Pluto, several icy planetary bodies show indications of an active surface perhaps underlain by liquid oceans of some size. This augments the interest to explore the evolution of an ice-ocean system and its surface implications. The geologically young surface of the Jovian moon Europa lends much speculation to variations in ice-shell thickness over time. Along with the observed surface features, it suggests the possibility of episodic convection and conduction within the ice-shell as it evolved. What factors would control the growth of the ice-shell as it forms? If and how would those factors determine the thickness of the ice-shell and consequently the heat transfer? Would parameters such as tidal heating or initial temperature affect how the ice-shell grows and to what significance? We perform numerical experiments using geodynamical models of the two-phase ice-water system to study the evolution of planetary ice-oceans such as that of Europa. The models evolve self-consistently from an initial liquid ocean as it cools with time. The effects of presence, absence and magnitude of tidal heating on ice-shell thickness are studied in different models. The vigor of convection changes as the ice-shell continues to thicken. Initial modeling results track changes in the growth rate of the ice-shell as the vigor of the convection changes. The magnitude and temporal location of the rate change varies with different properties of tidal heating and values of initial temperature. A comparative study of models is presented to demonstrate how as the ice-shell is forming, its growth rate and convection are affected by processes such as tidal heating.

Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians

NASA Astrophysics Data System (ADS)

Subasi, Yigit; Jarzynski, Christopher

The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary k-body interactions, their use is limited to small k because the strength of interaction is k'th order in perturbation theory. Here we develop a nonperturbative technique for obtaining effective k-body interactions using Hamiltonians consisting of at most l-body interactions with l < k . This technique works best for Hamiltonians with a few interactions with very large k and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme. We gratefully acknowledge financial support from the Lockheed Martin Corporation under Contract U12001C.

Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems

NASA Astrophysics Data System (ADS)

Tonni, Erik; Rodríguez-Laguna, Javier; Sierra, Germán

2018-04-01

Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson.

PubMed

Miller, Michael I; Trouvé, Alain; Younes, Laurent

2015-01-01

The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

Nonlinear Quantum Metrology of Many-Body Open Systems

NASA Astrophysics Data System (ADS)

Beau, M.; del Campo, A.

2017-07-01

We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k -body Hamiltonian and p -body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N-[k -(p /2 )], surpassing the shot-noise limit for 2 k >p +1 . Metrology equivalence between initial product states and maximally entangled states is established for p ≥1 . We further show that one can estimate the system-environment coupling parameter with precision N-(p /2 ), while many-body decoherence enhances the precision to N-k in the noise-amplitude estimation of a fluctuating k -body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.

Exponentially-Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians

NASA Technical Reports Server (NTRS)

Mandra, Salvatore

2017-01-01

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated to a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.

Communication: Fragment-based Hamiltonian model of electronic charge-excitation gaps and gap closure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valone, Steven Michael; Pilania, Ghanshyam; Liu, Xiang-Yang

Capturing key electronic properties such as charge excitation gaps within models at or above the atomic scale presents an ongoing challenge to understanding molecular, nanoscale, and condensed phase systems. One strategy is to describe the system in terms of properties of interacting material fragments, but it is unclear how to accomplish this for charge-excitation and charge-transfer phenomena. Hamiltonian models such as the Hubbard model provide formal frameworks for analyzing gap properties but are couched purely in terms of states of electrons, rather than the states of the fragments at the scale of interest. The recently introduced Fragment Hamiltonian (FH) modelmore » uses fragments in different charge states as its building blocks, enabling a uniform, quantum-mechanical treatment that captures the charge-excitation gap. These gaps are preserved in terms of inter-fragment charge-transferhopping integrals T and on-fragment parameters U (FH). The FH model generalizes the standard Hubbard model (a single intra-band hopping integral t and on-site repulsion U) from quantum states for electrons to quantum states for fragments. In this paper, we demonstrate that even for simple two-fragment and multi-fragment systems, gap closure is enabled once T exceeds the threshold set by U (FH), thus providing new insight into the nature of metal-insulator transitions. Finally, this result is in contrast to the standard Hubbard model for 1d rings, for which Lieb and Wu proved that gap closure was impossible, regardless of the choices for t and U.« less

Communication: Fragment-based Hamiltonian model of electronic charge-excitation gaps and gap closure

DOE PAGES

Valone, Steven Michael; Pilania, Ghanshyam; Liu, Xiang-Yang; ...

2015-11-13

Capturing key electronic properties such as charge excitation gaps within models at or above the atomic scale presents an ongoing challenge to understanding molecular, nanoscale, and condensed phase systems. One strategy is to describe the system in terms of properties of interacting material fragments, but it is unclear how to accomplish this for charge-excitation and charge-transfer phenomena. Hamiltonian models such as the Hubbard model provide formal frameworks for analyzing gap properties but are couched purely in terms of states of electrons, rather than the states of the fragments at the scale of interest. The recently introduced Fragment Hamiltonian (FH) modelmore » uses fragments in different charge states as its building blocks, enabling a uniform, quantum-mechanical treatment that captures the charge-excitation gap. These gaps are preserved in terms of inter-fragment charge-transferhopping integrals T and on-fragment parameters U (FH). The FH model generalizes the standard Hubbard model (a single intra-band hopping integral t and on-site repulsion U) from quantum states for electrons to quantum states for fragments. In this paper, we demonstrate that even for simple two-fragment and multi-fragment systems, gap closure is enabled once T exceeds the threshold set by U (FH), thus providing new insight into the nature of metal-insulator transitions. Finally, this result is in contrast to the standard Hubbard model for 1d rings, for which Lieb and Wu proved that gap closure was impossible, regardless of the choices for t and U.« less

Topological order following a quantum quench

NASA Astrophysics Data System (ADS)

Tsomokos, Dimitris I.; Hamma, Alioscia; Zhang, Wen; Haas, Stephan; Fazio, Rosario

2009-12-01

We determine the conditions under which topological order survives a rapid quantum quench. Specifically, we consider the case where a quantum spin system is prepared in the ground state of the toric code model and, after the quench, it evolves with a Hamiltonian that does not support topological order. We provide analytical results supported by numerical evidence for a variety of quench Hamiltonians. The robustness of topological order under nonequilibrium situations is tested by studying the topological entropy and a dynamical measure, which makes use of the similarity between partial density matrices obtained from different topological sectors.

Effect of Floquet engineering on the p-wave superconductor with second-neighbor couplings

NASA Astrophysics Data System (ADS)

Li, X. P.; Li, C. F.; Wang, L. C.; Zhou, L.

2018-06-01

The influence of the Floquet engineering on a particular one-dimensional p-wave superconductor, Kitaev model, with second-neighbor couplings is investigated in this paper. The effective Hamiltonians in the rotated reference frames have been obtained, and the convergent regions of the approximated Hamiltonian as well as the topological phase diagrams have been analyzed and discussed. We show that by modulating the external driving field amplitude, frequency as well as the second-neighbor hopping amplitude, the rich phase diagrams and transitions between different topological phases can be obtained.

An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation.

PubMed

Ilias, Miroslav; Saue, Trond

2007-02-14

The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.

Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mandal, Anirban; Hunt, Katharine L. C.

In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gaugemore » dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels identically with a gauge-dependent term in the usual form of the field Hamiltonian. We treat the electromagnetic field classically and treat the molecule quantum mechanically, but nonrelativistically. Our derivation starts from the Lagrangian for a set of charged particles and an electromagnetic field, with the particle coordinates, the vector potential, the scalar potential, and their time derivatives treated as the variables in the Lagrangian. We construct the full Hamiltonian using a Lagrange multiplier method originally suggested by Dirac, partition this Hamiltonian into a molecular term H{sub m} and a field term H{sub f}, and show that both H{sub m} and H{sub f} have gauge-independent expectation values. Any gauge may be chosen for the calculations; but following our partitioning, the expectation values of the molecular Hamiltonian are identical to those obtained directly in the Coulomb gauge. As a corollary of this result, the power absorbed by a molecule from a time-dependent, applied electromagnetic field is equal to the time derivative of the non-adiabatic term in the molecular energy, in any gauge.« less

A Study of Charge Transport: Correlated Energetic Disorder in Organic Semiconductors, and the Fragment Hamiltonian

NASA Astrophysics Data System (ADS)

Allen, Jonathan Robert

This dissertation details work done on two different descriptions of charge transport. The first topic is energetic disorder in organic semiconductors, and its effect on charge transport. This is motivated primarily by solar cells, which can be broadly classified as either inorganic or organic. The inorganic class of solar cells is older, and more well-developed, with the most common type being constructed from crystalline silicon. The large silicon crystals required for these cells are expensive to manufacture, which gave rise to interest in photovoltaic cells made from much less costly organic polymers. These organic materials are also less efficient than their silicon counterparts, due to a large degree of spatial and energetic disorder. In this document, the sources and structure of energetic disorder in organic semiconductors are explored, with an emphasis on spatial correlations in energetic disorder. In order for an organic photovoltaic device to function, there must be photogeneration of an exciton (a bound electron-hole pair), exciton transport, exciton dissociation, and transport of the individual charges to their respective terminals. In the case of this thesis, the main focus is exciton dissociation. The effects of correlation on exciton dissociation are examined through computer simulation, and compared to the theory and simulations of previous researchers. We conclude that energetic disorder in organic semiconductors is spatially correlated, and that this correlation improves the ability of excitons to dissociate. The second topic of this dissertation is the Fragment Hamiltonian model. This is a model currently in development as a means of describing charge transport across a range of systems. Currently there are many different systems which exhibit various charge transport behaviors, which are described by several different models. The overarching goal of the Fragment Hamiltonian model is to construct a description of charge transport which accurately describes the behavior of multiple different materials (i.e. metallic conductors or ceramic insulators) in the appropriate limits. The Fragment Hamiltonian model is explored in the context of the tight-binding model, and properties such as the conductivity of several different systems are deduced.

General phase spaces: from discrete variables to rotor and continuum limits

NASA Astrophysics Data System (ADS)

Albert, Victor V.; Pascazio, Saverio; Devoret, Michel H.

2017-12-01

We provide a basic introduction to discrete-variable, rotor, and continuous-variable quantum phase spaces, explaining how the latter two can be understood as limiting cases of the first. We extend the limit-taking procedures used to travel between phase spaces to a general class of Hamiltonians (including many local stabilizer codes) and provide six examples: the Harper equation, the Baxter parafermionic spin chain, the Rabi model, the Kitaev toric code, the Haah cubic code (which we generalize to qudits), and the Kitaev honeycomb model. We obtain continuous-variable generalizations of all models, some of which are novel. The Baxter model is mapped to a chain of coupled oscillators and the Rabi model to the optomechanical radiation pressure Hamiltonian. The procedures also yield rotor versions of all models, five of which are novel many-body extensions of the almost Mathieu equation. The toric and cubic codes are mapped to lattice models of rotors, with the toric code case related to U(1) lattice gauge theory.

Finite Rotation Analysis of Highly Thin and Flexible Structures

NASA Technical Reports Server (NTRS)

Clarke, Greg V.; Lee, Keejoo; Lee, Sung W.; Broduer, Stephen J. (Technical Monitor)

2001-01-01

Deployable space structures such as sunshields and solar sails are extremely thin and highly flexible with limited bending rigidity. For analytical investigation of their responses during deployment and operation in space, these structures can be modeled as thin shells. The present work examines the applicability of the solid shell element formulation to modeling of deployable space structures. The solid shell element formulation that models a shell as a three-dimensional solid is convenient in that no rotational parameters are needed for the description of kinematics of deformation. However, shell elements may suffer from element locking as the thickness becomes smaller unless special care is taken. It is shown that, when combined with the assumed strain formulation, the solid shell element formulation results in finite element models that are free of locking even for extremely thin structures. Accordingly, they can be used for analysis of highly flexible space structures undergoing geometrically nonlinear finite rotations.

Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles.

PubMed

Doinikov, Alexander A; Haac, Jillian F; Dayton, Paul A

2009-02-01

A general theoretical approach to the development of zero-thickness encapsulation models for contrast microbubbles is proposed. The approach describes a procedure that allows one to recast available rheological laws from the bulk form to a surface form which is used in a modified Rayleigh-Plesset equation governing the radial dynamics of a contrast microbubble. By the use of the proposed procedure, the testing of different rheological laws for encapsulation can be carried out. Challenges of existing shell models for lipid-encapsulated microbubbles, such as the dependence of shell parameters on the initial bubble radius and the "compression-only" behavior, are discussed. Analysis of the rheological behavior of lipid encapsulation is made by using experimental radius-time curves for lipid-coated microbubbles with radii in the range 1.2-2.5 microm. The curves were acquired for a research phospholipid-coated contrast agent insonified with a 20 cycle, 3.0 MHz, 100 kPa acoustic pulse. The fitting of the experimental data by a model which treats the shell as a viscoelastic solid gives the values of the shell surface viscosity increasing from 0.30 x 10(-8) kg/s to 2.63 x 10(-8) kg/s for the range of bubble radii, indicated above. The shell surface elastic modulus increases from 0.054 N/m to 0.37 N/m. It is proposed that this increase may be a result of the lipid coating possessing the properties of both a shear-thinning and a strain-softening material. We hypothesize that these complicated rheological properties do not allow the existing shell models to satisfactorily describe the dynamics of lipid encapsulation. In the existing shell models, the viscous and the elastic shell terms have the linear form which assumes that the viscous and the elastic stresses acting inside the lipid shell are proportional to the shell shear rate and the shell strain, respectively, with constant coefficients of proportionality. The analysis performed in the present paper suggests that a more general, nonlinear theory may be more appropriate. It is shown that the use of the nonlinear theory for shell viscosity allows one to model the "compression-only" behavior. As an example, the results of the simulation for a 2.03 microm radius bubble insonified with a 6 cycle, 1.8 MHz, 100 kPa acoustic pulse are given. These parameters correspond to the acoustic conditions under which the "compression-only" behavior was observed by de Jong et al. [Ultrasound Med. Biol. 33 (2007) 653-656]. It is also shown that the use of the Cross law for the modeling of the shear-thinning behavior of shell viscosity reduces the variance of experimentally estimated values of the shell viscosity and its dependence on the initial bubble radius.

Verification of Orthogrid Finite Element Modeling Techniques

NASA Technical Reports Server (NTRS)

Steeve, B. E.

1996-01-01

The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.

A new multi-layer approach for progressive damage simulation in composite laminates based on isogeometric analysis and Kirchhoff-Love shells. Part II: impact modeling

NASA Astrophysics Data System (ADS)

Pigazzini, M. S.; Bazilevs, Y.; Ellison, A.; Kim, H.

2017-11-01

In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on isogeometric analysis, where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff-Love thin shell. Continuum damage mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations.

A new multi-layer approach for progressive damage simulation in composite laminates based on isogeometric analysis and Kirchhoff-Love shells. Part I: basic theory and modeling of delamination and transverse shear

NASA Astrophysics Data System (ADS)

Bazilevs, Y.; Pigazzini, M. S.; Ellison, A.; Kim, H.

2017-11-01

In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on Isogeometric Analysis (IGA), where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff-Love thin shell. Continuum Damage Mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations.

Oscillator-like coherent states for the Jaynes-Cummings Model

NASA Technical Reports Server (NTRS)

Berubelauziere, Y.; Hussin, V.; Nieto, Michael M.

1995-01-01

A new way of diagonalizing the Jaynes-Cummings Hamiltonian is proposed, which allows the definition of annihilation operators and coherent states for this model. Mean values and dispersions over these states are computed and interpreted.

Constructing Dense Graphs with Unique Hamiltonian Cycles

ERIC Educational Resources Information Center

Lynch, Mark A. M.

2012-01-01

It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

Combined first-principles and model Hamiltonian study of the perovskite series R MnO 3 (R =La ,Pr ,Nd ,Sm ,Eu , and Gd )

NASA Astrophysics Data System (ADS)

Kováčik, Roman; Murthy, Sowmya Sathyanarayana; Quiroga, Carmen E.; Ederer, Claude; Franchini, Cesare

2016-02-01

We merge advanced ab initio schemes (standard density functional theory, hybrid functionals, and the G W approximation) with model Hamiltonian approaches (tight-binding and Heisenberg Hamiltonian) to study the evolution of the electronic, magnetic, and dielectric properties of the manganite family R MnO3 (R =La,Pr,Nd,Sm,Eu, and Gd) . The link between first principles and tight binding is established by downfolding the physically relevant subset of 3 d bands with eg character by means of maximally localized Wannier functions (MLWFs) using the VASP2WANNIER90 interface. The MLWFs are then used to construct a general tight-binding Hamiltonian written as a sum of the kinetic term, the Hund's rule coupling, the JT coupling, and the electron-electron interaction. The dispersion of the tight-binding (TB) eg bands at all levels are found to match closely the MLWFs. We provide a complete set of TB parameters which can serve as guidance for the interpretation of future studies based on many-body Hamiltonian approaches. In particular, we find that the Hund's rule coupling strength, the Jahn-Teller coupling strength, and the Hubbard interaction parameter U remain nearly constant for all the members of the R MnO3 series, whereas the nearest-neighbor hopping amplitudes show a monotonic attenuation as expected from the trend of the tolerance factor. Magnetic exchange interactions, computed by mapping a large set of hybrid functional total energies onto an Heisenberg Hamiltonian, clarify the origin of the A-type magnetic ordering observed in the early rare-earth manganite series as arising from a net negative out-of-plane interaction energy. The obtained exchange parameters are used to estimate the Néel temperature by means of Monte Carlo simulations. The resulting data capture well the monotonic decrease of the ordering temperature down the series from R =La to Gd, in agreement with experiments. This trend correlates well with the modulation of structural properties, in particular with the progressive reduction of the Mn-O-Mn bond angle which is associated with the quenching of the volume and the decrease of the tolerance factor due to the shrinkage of the ionic radii of R going from La to Gd.

Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

NASA Astrophysics Data System (ADS)

Bagarello, F.

2011-12-01

We have recently proposed a strategy to produce, starting from a given Hamiltonian h and a certain operator x for which [h,xx]=0 and xx is invertible, a second Hamiltonian h with the same eigenvalues as h and whose eigenvectors are related to those of h by x. Here we extend this procedure to build up a second Hamiltonian, whose eigenvalues are different from those of h, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian Hamiltonians.

Analysis of Composite Skin-Stiffener Debond Specimens Using a Shell/3D Modeling Technique and Submodeling

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin (Technical Monitor); Krueger, Ronald; Minguet, Pierre J.

2004-01-01

The application of a shell/3D modeling technique for the simulation of skin/stringer debond in a specimen subjected to tension and three-point bending was studied. The global structure was modeled with shell elements. A local three-dimensional model, extending to about three specimen thicknesses on either side of the delamination front was used to model the details of the damaged section. Computed total strain energy release rates and mixed-mode ratios obtained from shell/3D simulations were in good agreement with results obtained from full solid models. The good correlation of the results demonstrated the effectiveness of the shell/3D modeling technique for the investigation of skin/stiffener separation due to delamination in the adherents. In addition, the application of the submodeling technique for the simulation of skin/stringer debond was also studied. Global models made of shell elements and solid elements were studied. Solid elements were used for local submodels, which extended between three and six specimen thicknesses on either side of the delamination front to model the details of the damaged section. Computed total strain energy release rates and mixed-mode ratios obtained from the simulations using the submodeling technique were not in agreement with results obtained from full solid models.

Ergodicity and model quality in template-restrained canonical and temperature/Hamiltonian replica exchange coarse-grained molecular dynamics simulations of proteins.

PubMed

Karczyńska, Agnieszka S; Czaplewski, Cezary; Krupa, Paweł; Mozolewska, Magdalena A; Joo, Keehyoung; Lee, Jooyoung; Liwo, Adam

2017-12-05

Molecular simulations restrained to single or multiple templates are commonly used in protein-structure modeling. However, the restraints introduce additional barriers, thus impairing the ergodicity of simulations, which can affect the quality of the resulting models. In this work, the effect of restraint types and simulation schemes on ergodicity and model quality was investigated by performing template-restrained canonical molecular dynamics (MD), multiplexed replica-exchange molecular dynamics, and Hamiltonian replica exchange molecular dynamics (HREMD) simulations with the coarse-grained UNRES force field on nine selected proteins, with pseudo-harmonic log-Gaussian (unbounded) or Lorentzian (bounded) restraint functions. The best ergodicity was exhibited by HREMD. It has been found that non-ergodicity does not affect model quality if good templates are used to generate restraints. However, when poor-quality restraints not covering the entire protein are used, the improved ergodicity of HREMD can lead to significantly improved protein models. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Error suppression for Hamiltonian quantum computing in Markovian environments

NASA Astrophysics Data System (ADS)

Marvian, Milad; Lidar, Daniel A.

2017-03-01

Hamiltonian quantum computing, such as the adiabatic and holonomic models, can be protected against decoherence using an encoding into stabilizer subspace codes for error detection and the addition of energy penalty terms. This method has been widely studied since it was first introduced by Jordan, Farhi, and Shor (JFS) in the context of adiabatic quantum computing. Here, we extend the original result to general Markovian environments, not necessarily in Lindblad form. We show that the main conclusion of the original JFS study holds under these general circumstances: Assuming a physically reasonable bath model, it is possible to suppress the initial decay out of the encoded ground state with an energy penalty strength that grows only logarithmically in the system size, at a fixed temperature.

Implementing the SU(2) Symmetry for the DMRG

NASA Astrophysics Data System (ADS)

Alvarez, Gonzalo

2010-03-01

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992), Hamiltonian symmetries play an important role. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This talk will explain how the DMRG++ codefootnotetextarXiv:0902.3185 or Computer Physics Communications 180 (2009) 1572-1578. has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries will be discussed for typical tight-binding models of strongly correlated electronic systems. The computational bottleneck of the algorithm, and the use of shared memory parallelization will also be addressed. Finally, a roadmap for future work on DMRG++ will be presented.

Superradiant phase transition with graphene embedded in one dimensional optical cavity

NASA Astrophysics Data System (ADS)

Li, Benliang; Liu, Tao; Hewak, Daniel W.; Wang, Qi Jie

2018-01-01

We theoretically investigate the cavity QED of graphene embedded in an optical cavity under perpendicular magnetic field. We consider the coupling of cyclotron transition and a multimode cavity described by a multimode Dicke model. This model exhibits a superradiant quantum phase transition, which we describe exactly in an effective Hamiltonian approach. The complete excitation spectrum in both the normal phase and superradiant phase regimes is given. In contrast to the single mode case, multimode coupling of cavity photon and cyclotron transition can greatly reduce the critical vacuum Rabi frequency required for quantum phase transition, and dramatically enhance the superradiant emission by fast modulating the Hamiltonian. Our work paves a way to experimental explorations of quantum phase transitions in solid state systems.

Interest Rates and Coupon Bonds in Quantum Finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2009-09-01

1. Synopsis; 2. Interest rates and coupon bonds; 3. Options and option theory; 4. Interest rate and coupon bond options; 5. Quantum field theory of bond forward interest rates; 6. Libor Market Model of interest rates; 7. Empirical analysis of forward interest rates; 8. Libor Market Model of interest rate options; 9. Numeraires for bond forward interest rates; 10. Empirical analysis of interest rate caps; 11. Coupon bond European and Asian options; 12. Empirical analysis of interest rate swaptions; 13. Correlation of coupon bond options; 14. Hedging interest rate options; 15. Interest rate Hamiltonian and option theory; 16. American options for coupon bonds and interest rates; 17. Hamiltonian derivation of coupon bond options; Appendixes; Glossaries; List of symbols; Reference; Index.

Lower bounds for the ground state energy for the PPP and Hubbard models of the benzene molecule

NASA Astrophysics Data System (ADS)

Číẑek, J.; Vinette, F.

1988-09-01

The optimized inner projection (OIP) technique, which is equivalent to the method of intermediate Hamiltonians (MIH), is applied to the PPP and Hubbard models of the benzene molecule. Both these methods are applicable since the electrostatic part of the PPP and Hubbard Hamiltonians is positive definite. Lower energy bounds are calculated using OIP and MIH for all values of the resonance integral β. In this study, β plays the role of a coupling constant. The deviation of the OIP results from exact ones is smaller than 7% for all values of β. The OIP results are also compared with the correlation energies obtained by other techniques. The OIP method gives surprisingly good results even for small |β| values.

Numerical studies of various Néel-VBS transitions in SU(N) anti-ferromagnets

NASA Astrophysics Data System (ADS)

Kaul, Ribhu K.; Block, Matthew S.

2015-09-01

In this manuscript we review recent developments in the numerical simulations of bipartite SU(N) spin models by quantum Monte Carlo (QMC) methods. We provide an account of a large family of newly discovered sign-problem free spin models which can be simulated in their ground states on large lattices, containing O(105) spins, using the stochastic series expansion method with efficient loop algorithms. One of the most important applications so far of these Hamiltonians are to unbiased studies of quantum criticality between Neel and valence bond phases in two dimensions - a summary of this body of work is provided. The article concludes with an overview of the current status of and outlook for future studies of the “designer” Hamiltonians.

Quantum Dynamics of Multi Harmonic Oscillators Described by Time Variant Conic Hamiltonian and their Use in Contemporary Sciences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Demiralp, Metin

This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if themore » dynamic of the system is related to a set of ODEs.« less

Stability and Hamiltonian formulation of higher derivative theories

NASA Astrophysics Data System (ADS)

Schmidt, Hans-Jürgen

1994-06-01

We analyze the presuppositions leading to instabilities in theories of order higher than second. The type of fourth-order gravity which leads to an inflationary (quasi-de Sitter) period of cosmic evolution by inclusion of one curvature-squared term (i.e., the Starobinsky model) is used as an example. The corresponding Hamiltonian formulation (which is necessary for deducing the Wheeler-DeWitt equation) is found both in the Ostrogradski approach and in another form. As an example, a closed form solution of the Wheeler-DeWitt equation for a spatially flat Friedmann model and L=R2 is found. The method proposed by Simon to bring fourth order gravity to second order can be (if suitably generalized) applied to bring sixth-order gravity to second order.

One-Shot Decoupling and Page Curves from a Dynamical Model for Black Hole Evaporation.

PubMed

Brádler, Kamil; Adami, Christoph

2016-03-11

One-shot decoupling is a powerful primitive in quantum information theory and was hypothesized to play a role in the black hole information paradox. We study black hole dynamics modeled by a trilinear Hamiltonian whose semiclassical limit gives rise to Hawking radiation. An explicit numerical calculation of the discretized path integral of the S matrix shows that decoupling is exact in the continuous limit, implying that quantum information is perfectly transferred from the black hole to radiation. A striking consequence of decoupling is the emergence of an output radiation entropy profile that follows Page's prediction. We argue that information transfer and the emergence of Page curves is a robust feature of any multilinear interaction Hamiltonian with a bounded spectrum.

Close-packed structure dynamics with finite-range interaction: computational mechanics with individual layer interaction.

PubMed

Rodriguez-Horta, Edwin; Estevez-Rams, Ernesto; Lora-Serrano, Raimundo; Neder, Reinhard

2017-09-01

This is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. A Hamiltonian introduced by Ahmad & Khan [Phys. Status Solidi B (2000), 218, 425-430] avoids the unphysical assignment of interaction terms to fictitious entities given by spins in the Hägg coding of the stacking arrangement. In this paper an analysis of polytype generation and disorder in close-packed structures is made for such a Hamiltonian. Results are compared with a previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed. The competing effects of disorder and structure, as given by entropy density and excess entropy, respectively, are discussed. It is argued that the Ahmad & Khan model is simpler and predicts a larger set of polytypes than previous treatments.

On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions

NASA Astrophysics Data System (ADS)

Hagendorf, Christian; Liénardy, Jean

2018-03-01

The square-lattice eight-vertex model with vertex weights a, b, c, d obeying the relation (a^2+ab)(b^2+ab) = (c^2+ab)(d^2+ab) and periodic boundary conditions is considered. It is shown that the transfer matrix of the model for L  =  2n  +  1 vertical lines and periodic boundary conditions along the horizontal direction possesses the doubly degenerate eigenvalue \\Thetan = (a+b){\\hspace{0pt}}2n+1 . This proves a conjecture by Stroganov from 2001. The proof uses the supersymmetry of a related XYZ spin-chain Hamiltonian. The eigenstates of the transfer matrix corresponding to \\Thetan are shown to be the ground states of the spin-chain Hamiltonian. Moreover, for positive vertex weights \\Thetan is the largest eigenvalue of the transfer matrix.

Lie algebraic similarity transformed Hamiltonians for lattice model systems

NASA Astrophysics Data System (ADS)

Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.

2015-01-01

We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.

Self-dual gravity is completely integrable

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sheftel, M. B.; Kalayci, J.; Yazıcı, D.

2008-10-01

We discover a multi-Hamiltonian structure of a complex Monge-Ampère equation (CMA) set in a real first-order 2-component form. Therefore, by Magri's theorem this is a completely integrable system in four real dimensions. We start with Lagrangian and Hamiltonian densities and obtain a symplectic form and the Hamiltonian operator that determines the Dirac bracket. We have calculated all point symmetries of the 2-component CMA system and Hamiltonians of the symmetry flows. We have found two new real recursion operators for symmetries which commute with the operator of a symmetry condition on solutions of the CMA system. These operators form two Lax pairs for the 2-component system. The recursion operators, applied to the first Hamiltonian operator, generate infinitely many real Hamiltonian structures. We show how to construct an infinite hierarchy of higher commuting flows together with the corresponding infinite chain of their Hamiltonians.

Perspective: Quantum Hamiltonians for optical interactions

NASA Astrophysics Data System (ADS)

Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy

2018-01-01

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Optical properties of light absorbing carbon aggregates mixed with sulfate: assessment of different model geometries for climate forcing calculations.

PubMed

Kahnert, Michael; Nousiainen, Timo; Lindqvist, Hannakaisa; Ebert, Martin

2012-04-23

Light scattering by light absorbing carbon (LAC) aggregates encapsulated into sulfate shells is computed by use of the discrete dipole method. Computations are performed for a UV, visible, and IR wavelength, different particle sizes, and volume fractions. Reference computations are compared to three classes of simplified model particles that have been proposed for climate modeling purposes. Neither model matches the reference results sufficiently well. Remarkably, more realistic core-shell geometries fall behind homogeneous mixture models. An extended model based on a core-shell-shell geometry is proposed and tested. Good agreement is found for total optical cross sections and the asymmetry parameter. © 2012 Optical Society of America

Isospin symmetry breaking and large-scale shell-model calculations with the Sakurai-Sugiura method

NASA Astrophysics Data System (ADS)

Mizusaki, Takahiro; Kaneko, Kazunari; Sun, Yang; Tazaki, Shigeru

2015-05-01

Recently isospin symmetry breaking for mass 60-70 region has been investigated based on large-scale shell-model calculations in terms of mirror energy differences (MED), Coulomb energy differences (CED) and triplet energy differences (TED). Behind these investigations, we have encountered a subtle problem in numerical calculations for odd-odd N = Z nuclei with large-scale shell-model calculations. Here we focus on how to solve this subtle problem by the Sakurai-Sugiura (SS) method, which has been recently proposed as a new diagonalization method and has been successfully applied to nuclear shell-model calculations.

Symplectic no-core shell-model approach to intermediate-mass nuclei

NASA Astrophysics Data System (ADS)

Tobin, G. K.; Ferriss, M. C.; Launey, K. D.; Dytrych, T.; Draayer, J. P.; Dreyfuss, A. C.; Bahri, C.

2014-03-01

We present a microscopic description of nuclei in the intermediate-mass region, including the proximity to the proton drip line, based on a no-core shell model with a schematic many-nucleon long-range interaction with no parameter adjustments. The outcome confirms the essential role played by the symplectic symmetry to inform the interaction and the winnowing of shell-model spaces. We show that it is imperative that model spaces be expanded well beyond the current limits up through 15 major shells to accommodate particle excitations, which appear critical to highly deformed spatial structures and the convergence of associated observables.

Monte Carlo simulations of nematic and chiral nematic shells

NASA Astrophysics Data System (ADS)

Wand, Charlie R.; Bates, Martin A.

2015-01-01

We present a systematic Monte Carlo simulation study of thin nematic and cholesteric shells with planar anchoring using an off-lattice model. The results obtained using the simple model correspond with previously published results for lattice-based systems, with the number, type, and position of defects observed dependent on the shell thickness with four half-strength defects in a tetrahedral arrangement found in very thin shells and a pair of defects in a bipolar (boojum) configuration observed in thicker shells. A third intermediate defect configuration is occasionally observed for intermediate thickness shells, which is stabilized in noncentrosymmetric shells of nonuniform thickness. Chiral nematic (cholesteric) shells are investigated by including a chiral term in the potential. Decreasing the pitch of the chiral nematic leads to a twisted bipolar (chiral boojum) configuration with the director twist increasing from the inner to the outer surface.

Deriving the nuclear shell model from first principles

NASA Astrophysics Data System (ADS)

Barrett, Bruce R.; Dikmen, Erdal; Vary, James P.; Maris, Pieter; Shirokov, Andrey M.; Lisetskiy, Alexander F.

2014-09-01

The results of an 18-nucleon No Core Shell Model calculation, performed in a large basis space using a bare, soft NN interaction, can be projected into the 0 ℏω space, i.e., the sd -shell. Because the 16 nucleons in the 16O core are frozen in the 0 ℏω space, all the correlations of the 18-nucleon system are captured by the two valence, sd -shell nucleons. By the projection, we obtain microscopically the sd -shell 2-body effective interactions, the core energy and the sd -shell s.p. energies. Thus, the input for standard shell-model calculations can be determined microscopically by this approach. If the same procedure is then applied to 19-nucleon systems, the sd -shell 3-body effective interactions can also be obtained, indicating the importance of these 3-body effective interactions relative to the 2-body effective interactions. Applications to A = 19 and heavier nuclei with different intrinsic NN interactions will be presented and discussed. The results of an 18-nucleon No Core Shell Model calculation, performed in a large basis space using a bare, soft NN interaction, can be projected into the 0 ℏω space, i.e., the sd -shell. Because the 16 nucleons in the 16O core are frozen in the 0 ℏω space, all the correlations of the 18-nucleon system are captured by the two valence, sd -shell nucleons. By the projection, we obtain microscopically the sd -shell 2-body effective interactions, the core energy and the sd -shell s.p. energies. Thus, the input for standard shell-model calculations can be determined microscopically by this approach. If the same procedure is then applied to 19-nucleon systems, the sd -shell 3-body effective interactions can also be obtained, indicating the importance of these 3-body effective interactions relative to the 2-body effective interactions. Applications to A = 19 and heavier nuclei with different intrinsic NN interactions will be presented and discussed. Supported by the US NSF under Grant No. 0854912, the US DOE under Grants Nos. DESC0008485 and DE-FG02-87ER40371, the Higher Education Council of Turkey(YOK), and the Ministry of Education and Science of Russian Fed. under contracts P521 and 14.v37.21.1297.

Where Is the Electronic Oscillator Strength? Mapping Oscillator Strength across Molecular Absorption Spectra.

PubMed

Zheng, Lianjun; Polizzi, Nicholas F; Dave, Adarsh R; Migliore, Agostino; Beratan, David N

2016-03-24

The effectiveness of solar energy capture and conversion materials derives from their ability to absorb light and to transform the excitation energy into energy stored in free carriers or chemical bonds. The Thomas-Reiche-Kuhn (TRK) sum rule mandates that the integrated (electronic) oscillator strength of an absorber equals the total number of electrons in the structure. Typical molecular chromophores place only about 1% of their oscillator strength in the UV-vis window, so individual chromophores operate at about 1% of their theoretical limit. We explore the distribution of oscillator strength as a function of excitation energy to understand this circumstance. To this aim, we use familiar independent-electron model Hamiltonians as well as first-principles electronic structure methods. While model Hamiltonians capture the qualitative electronic spectra associated with π electron chromophores, these Hamiltonians mistakenly focus the oscillator strength in the fewest low-energy transitions. Advanced electronic structure methods, in contrast, spread the oscillator strength over a very wide excitation energy range, including transitions to Rydberg and continuum states, consistent with experiment. Our analysis rationalizes the low oscillator strength in the UV-vis spectral region in molecules, a step toward the goal of oscillator strength manipulation and focusing.

Synergy and destructive interferences between local magnetic anisotropies in binuclear complexes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guihéry, Nathalie; Ruamps, Renaud; Maurice, Rémi

2015-12-31

Magnetic anisotropy is responsible for the single molecule magnet behavior of transition metal complexes. This behavior is characterized by a slow relaxation of the magnetization for low enough temperatures, and thus for a possible blocking of the magnetization. This bistable behavior can lead to possible technological applications in the domain of data storage or quantum computing. Therefore, the understanding of the microscopic origin of magnetic anisotropy has received a considerable interest during the last two decades. The presentation focuses on the determination of the anisotropy parameters of both mono-nuclear and bi-nuclear types of complexes and on the control and optimizationmore » of the anisotropic properties. The validity of the model Hamiltonians commonly used to characterize such complexes has been questioned and it is shown that neither the standard multispin Hamiltonian nor the giant spin Hamiltonian are appropriate for weakly coupled ions. Alternative models have been proposed and used to properly extract the relevant parameters. Rationalizations of the magnitude and nature of both local anisotropies of single ions and the molecular anisotropy of polynuclear complexes are provided. The synergy and interference effects between local magnetic anisotropies are studied in a series of binuclear complexes.« less

Quasi-equilibria in reduced Liouville spaces.

PubMed

Halse, Meghan E; Dumez, Jean-Nicolas; Emsley, Lyndon

2012-06-14

The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.

An algorithm for finding a similar subgraph of all Hamiltonian cycles

NASA Astrophysics Data System (ADS)

Wafdan, R.; Ihsan, M.; Suhaimi, D.

2018-01-01

This paper discusses an algorithm to find a similar subgraph called findSimSubG algorithm. A similar subgraph is a subgraph with a maximum number of edges, contains no isolated vertex and is contained in every Hamiltonian cycle of a Hamiltonian Graph. The algorithm runs only on Hamiltonian graphs with at least two Hamiltonian cycles. The algorithm works by examining whether the initial subgraph of the first Hamiltonian cycle is a subgraph of comparison graphs. If the initial subgraph is not in comparison graphs, the algorithm will remove edges and vertices of the initial subgraph that are not in comparison graphs. There are two main processes in the algorithm, changing Hamiltonian cycle into a cycle graph and removing edges and vertices of the initial subgraph that are not in comparison graphs. The findSimSubG algorithm can find the similar subgraph without using backtracking method. The similar subgraph cannot be found on certain graphs, such as an n-antiprism graph, complete bipartite graph, complete graph, 2n-crossed prism graph, n-crown graph, n-möbius ladder, prism graph, and wheel graph. The complexity of this algorithm is O(m|V|), where m is the number of Hamiltonian cycles and |V| is the number of vertices of a Hamiltonian graph.

Non-commuting two-local Hamiltonians for quantum error suppression

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Rieffel, Eleanor G.

2017-04-01

Physical constraints make it challenging to implement and control many-body interactions. For this reason, designing quantum information processes with Hamiltonians consisting of only one- and two-local terms is a worthwhile challenge. Enabling error suppression with two-local Hamiltonians is particularly challenging. A no-go theorem of Marvian and Lidar (Phys Rev Lett 113(26):260504, 2014) demonstrates that, even allowing particles with high Hilbert space dimension, it is impossible to protect quantum information from single-site errors by encoding in the ground subspace of any Hamiltonian containing only commuting two-local terms. Here, we get around this no-go result by encoding in the ground subspace of a Hamiltonian consisting of non-commuting two-local terms arising from the gauge operators of a subsystem code. Specifically, we show how to protect stored quantum information against single-qubit errors using a Hamiltonian consisting of sums of the gauge generators from Bacon-Shor codes (Bacon in Phys Rev A 73(1):012340, 2006) and generalized-Bacon-Shor code (Bravyi in Phys Rev A 83(1):012320, 2011). Our results imply that non-commuting two-local Hamiltonians have more error-suppressing power than commuting two-local Hamiltonians. While far from providing full fault tolerance, this approach improves the robustness achievable in near-term implementable quantum storage and adiabatic quantum computations, reducing the number of higher-order terms required to encode commonly used adiabatic Hamiltonians such as the Ising Hamiltonians common in adiabatic quantum optimization and quantum annealing.

Thin Shell Model for NIF capsule stagnation studies

NASA Astrophysics Data System (ADS)

Hammer, J. H.; Buchoff, M.; Brandon, S.; Field, J. E.; Gaffney, J.; Kritcher, A.; Nora, R. C.; Peterson, J. L.; Spears, B.; Springer, P. T.

2015-11-01

We adapt the thin shell model of Ott et al. to asymmetric ICF capsule implosions on NIF. Through much of an implosion, the shell aspect ratio is large so the thin shell approximation is well satisfied. Asymmetric pressure drive is applied using an analytic form for ablation pressure as a function of the x-ray flux, as well as time-dependent 3D drive asymmetry from hohlraum calculations. Since deviations from a sphere are small through peak velocity, we linearize the equations, decompose them by spherical harmonics and solve ODE's for the coefficients. The model gives the shell position, velocity and areal mass variations at the time of peak velocity, near 250 microns radius. The variables are used to initialize 3D rad-hydro calculations with the HYDRA and ARES codes. At link time the cold fuel shell and ablator are each characterized by a density, adiabat and mass. The thickness, position and velocity of each point are taken from the thin shell model. The interior of the shell is filled with a uniform gas density and temperature consistent with the 3/2PV energy found from 1D rad-hydro calculations. 3D linked simulations compare favorably with integrated simulations of the entire implosion. Through generating synthetic diagnostic data, the model offers a method for quickly testing hypothetical sources of asymmetry and comparing with experiment. Prepared by LLNL under Contract DE-AC52-07NA27344.

HR Del REMNANT ANATOMY USING TWO-DIMENSIONAL SPECTRAL DATA AND THREE-DIMENSIONAL PHOTOIONIZATION SHELL MODELS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moraes, Manoel; Diaz, Marcos

2009-12-15

The HR Del nova remnant was observed with the IFU-GMOS at Gemini North. The spatially resolved spectral data cube was used in the kinematic, morphological, and abundance analysis of the ejecta. The line maps show a very clumpy shell with two main symmetric structures. The first one is the outer part of the shell seen in H{alpha}, which forms two rings projected in the sky plane. These ring structures correspond to a closed hourglass shape, first proposed by Harman and O'Brien. The equatorial emission enhancement is caused by the superimposed hourglass structures in the line of sight. The second structuremore » seen only in the [O III] and [N II] maps is located along the polar directions inside the hourglass structure. Abundance gradients between the polar caps and equatorial region were not found. However, the outer part of the shell seems to be less abundant in oxygen and nitrogen than the inner regions. Detailed 2.5-dimensional photoionization modeling of the three-dimensional shell was performed using the mass distribution inferred from the observations and the presence of mass clumps. The resulting model grids are used to constrain the physical properties of the shell as well as the central ionizing source. A sequence of three-dimensional clumpy models including a disk-shaped ionization source is able to reproduce the ionization gradients between polar and equatorial regions of the shell. Differences between shell axial ratios in different lines can also be explained by aspherical illumination. A total shell mass of 9 x 10{sup -4} M {sub sun} is derived from these models. We estimate that 50%-70% of the shell mass is contained in neutral clumps with density contrast up to a factor of 30.« less

Adiabatic quantum computing with spin qubits hosted by molecules.

PubMed

Yamamoto, Satoru; Nakazawa, Shigeaki; Sugisaki, Kenji; Sato, Kazunobu; Toyota, Kazuo; Shiomi, Daisuke; Takui, Takeji

2015-01-28

A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs. We exemplify the utilization of an adiabatic factorization problem of 21, compared with the corresponding nuclear magnetic resonance (NMR) case. Two molecular spins are selected: one is a molecular spin composed of three exchange-coupled electrons as electron-only qubits and the other an electron-bus qubit with two client nuclear spin qubits. Their electronic spin structures are well characterized in terms of the quantum mechanical behaviour in the spin Hamiltonian. The implementation of adiabatic quantum computing/computation (AQC) has, for the first time, been achieved by establishing ESR/MR pulse sequences for effective spin Hamiltonians in a fully controlled manner of spin manipulation. The conquered pulse sequences have been compared with the NMR experiments and shown much faster CPU times corresponding to the interaction strength between the spins. Significant differences are shown in rotational operations and pulse intervals for ESR/MR operations. As a result, we suggest the advantages and possible utilization of the time-evolution based AQC approach for molecular spin quantum computers and molecular spin quantum simulators underlain by sophisticated ESR/MR pulsed spin technology.

Shell effects in a multinucleon transfer process

NASA Astrophysics Data System (ADS)

Zhu, Long; Wen, Pei-Wei; Lin, Cheng-Jian; Bao, Xiao-Jun; Su, Jun; Li, Cheng; Guo, Chen-Chen

2018-04-01

The shell effects in multinucleon transfer process are investigated in the systems 136Xe + 198Pt and 136Xe + 208Pb within the dinuclear system (DNS) model. The temperature dependence of shell corrections on potential energy surface is taken into account in the DNS model and remarkable improvement for description of experimental data is noticed. The reactions 136Xe + 186W and 150Nd + 186W are also studied. It is found that due to shell effects the projectile 150Nd is more promising for producing transtarget nuclei rather than 136Xe with neutron shell closure.

A New Scheme of Integrability for (bi)Hamiltonian PDE

NASA Astrophysics Data System (ADS)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2016-10-01

We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.

Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2013-10-01

The Euclidean action with acceleration has been analyzed in Ref. 1, and referred to henceforth as Paper I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation and destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.

Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles

PubMed Central

Doinikov, Alexander A.; Haac, Jillian F.; Dayton, Paul A.

2009-01-01

A general theoretical approach to the development of zero-thickness encapsulation models for contrast microbubbles is proposed. The approach describes a procedure that allows one to recast available rheological laws from the bulk form to a surface form which is used in a modified Rayleigh-Plesset equation governing the radial dynamics of a contrast microbubble. By the use of the proposed procedure, the testing of different rheological laws for encapsulation can be carried out. Challenges of existing shell models for lipid-encapsulated microbubbles, such as the dependence of shell parameters on the initial bubble radius and the “compression-only” behavior, are discussed. Analysis of the rheological behavior of lipid encapsulation is made by using experimental radius-time curves for lipid-coated microbubbles with radii in the range 1.2 – 2.5 μm. The curves were acquired for a research phospholipid-coated contrast agent insonified with a 20-cycle, 3.0 MHz, 100 kPa acoustic pulse. The fitting of the experimental data by a model which treats the shell as a viscoelastic solid gives the values of the shell surface viscosity increasing from 0.30×10-8 kg/s to 2.63×10-8 kg/s for the range of bubble radii indicated above. The shell surface elastic modulus increases from 0.054 N/m to 0.37 N/m. It is proposed that this increase may be a result of the lipid coating possessing the properties of both a shear-thinning and a strain-softening material. We hypothesize that these complicated rheological properties do not allow the existing shell models to satisfactorily describe the dynamics of lipid encapsulation. In the existing shell models, the viscous and the elastic shell terms have the linear form which assumes that the viscous and the elastic stresses acting inside the lipid shell are proportional to the shell shear rate and the shell strain, respectively, with constant coefficients of proportionality. The analysis performed in the present paper suggests that a more general, nonlinear theory may be more appropriate. It is shown that the use of the nonlinear theory for shell viscosity allows one to model the “compression-only” behavior. As an example, the results of the simulation for a 2.03- μm-radius bubble insonified with a 6-cycle, 1.8 MHz, 100 kPa acoustic pulse are given. These parameters correspond to the acoustic conditions under which the “compression-only” behavior was observed by de Jong et al. [Ultrasound Med. Biol. 33 (2007) 653–656]. It is also shown that the use of the Cross law for the modeling of the shear-thinning behavior of shell viscosity reduces the variance of experimentally estimated values of the shell viscosity and its dependence on the initial bubble radius. PMID:18990417

A compact circumstellar shell as the source of high-velocity features in SN 2011fe

NASA Astrophysics Data System (ADS)

Mulligan, Brian W.; Wheeler, J. Craig

2018-05-01

High-velocity features (HVFs), especially of Ca II, are frequently seen in Type Ia supernova observed prior to B-band maximum (Bmax). These HVFs evolve in velocity from more than 25 000 km s-1, in the days after first light, to about 18 000 km s-1 near Bmax. To recreate the evolution of the Ca II near-infrared triplet (CaNIR) HVFs in SN 2011fe, we consider the interaction between a model Type Ia supernova and compact circumstellar shells with masses between 0.003 and 0.012 M⊙. We fit the observed CaNIR feature using synthetic spectra generated from the models using SYN++. The CaNIR feature is better explained by the supernova model interacting with a shell than the model without a shell, with a shell of mass 0.005 M⊙ tending to be better fitting than the other shells. The evolution of the optical depth of CaNIR suggests that the ionization state of calcium within the ejecta and shell is not constant. We discuss the method used to measure the observed velocity of CaNIR and other features and conclude that HVFs or other components can be falsely identified. We briefly discuss the possible origin of the shells and the implications for the progenitor system of the supernova.

Inner-shell radiation from wire array implosions on the Zebra generator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ouart, N. D.; Giuliani, J. L.; Dasgupta, A.

2014-03-15

Implosions of brass wire arrays on Zebra have produced L-shell radiation as well as inner-shell Kα and Kβ transitions. The L-shell radiation comes from ionization stages around the Ne-like charge state that is largely populated by a thermal electron energy distribution function, while the K-shell photons are a result of high-energy electrons ionizing or exciting an inner-shell (1s) electron from ionization stages around Ne-like. The K- and L-shell radiations were captured using two time-gated and two axially resolved time-integrated spectrometers. The electron beam was measured using a Faraday cup. A multi-zone non-local thermodynamic equilibrium pinch model with radiation transport ismore » used to model the x-ray emission from experiments for the purpose of obtaining plasma conditions. These plasma conditions are used to discuss some properties of the electron beam generated by runaway electrons. A simple model for runaway electrons is examined to produce the Kα radiation, but it is found to be insufficient.« less

Irreducible Brillouin conditions and contracted Schrödinger equations for n-electron systems. III. Systems of noninteracting electrons.

PubMed

Kutzelnigg, Werner; Mukherjee, Debashis

2004-04-22

We analyze the structure and the solutions of the irreducible k-particle Brillouin conditions (IBCk) and the irreducible contracted Schrödinger equations (ICSEk) for an n-electron system without electron interaction. This exercise is very instructive in that it gives one both the perspective and the strategies to be followed in applying the IBC and ICSE to physically realistic systems with electron interaction. The IBC1 leads to a Liouville equation for the one-particle density matrix gamma1=gamma, consistent with our earlier analysis that the IBC1 holds both for a pure and an ensemble state. The IBC1 or the ICSE1 must be solved subject to the constraints imposed by the n-representability condition, which is particularly simple for gamma. For a closed-shell state gamma is idempotent, i.e., all natural spin orbitals (NSO's) have occupation numbers 0 or 1, and all cumulants lambdak with k> or =2 vanish. For open-shell states there are NSO's with fractional occupation number, and at the same time nonvanishing elements of lambda2, which are related to spin and symmetry coupling. It is often useful to describe an open-shell state by a totally symmetric ensemble state. If one wants to treat a one-particle perturbation by means of perturbation theory, this mainly as a run-up for the study of a two-particle perturbation, one is faced with the problem that the perturbation expansion of the Liouville equation gives information only on the nondiagonal elements (in a basis of the unperturbed states) of gamma. There are essentially three possibilities to construct the diagonal elements of gamma: (i) to consider the perturbation expansion of the characteristic polynomial of gamma, especially the idempotency for closed-shell states, (ii) to rely on the ICSE1, which (at variance with the IBC1) also gives information on the diagonal elements, though not in a very efficient manner, and (iii) to formulate the perturbation theory in terms of a unitary transformation in Fock space. The latter is particularly powerful, especially, when one wishes to study realistic Hamiltonians with a two-body interaction. (c) 2004 American Institute of Physics

A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture

NASA Astrophysics Data System (ADS)

Marmottant, Philippe; van der Meer, Sander; Emmer, Marcia; Versluis, Michel; de Jong, Nico; Hilgenfeldt, Sascha; Lohse, Detlef

2005-12-01

We present a model applicable to ultrasound contrast agent bubbles that takes into account the physical properties of a lipid monolayer coating on a gas microbubble. Three parameters describe the properties of the shell: a buckling radius, the compressibility of the shell, and a break-up shell tension. The model presents an original non-linear behavior at large amplitude oscillations, termed compression-only, induced by the buckling of the lipid monolayer. This prediction is validated by experimental recordings with the high-speed camera Brandaris 128, operated at several millions of frames per second. The effect of aging, or the resultant of repeated acoustic pressure pulses on bubbles, is predicted by the model. It corrects a flaw in the shell elasticity term previously used in the dynamical equation for coated bubbles. The break-up is modeled by a critical shell tension above which gas is directly exposed to water.

Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians.

PubMed

Vidmar, Lev; Hackl, Lucas; Bianchi, Eugenio; Rigol, Marcos

2017-07-14

In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291], Page proved that the average entanglement entropy of subsystems of random pure states is S_{ave}≃lnD_{A}-(1/2)D_{A}^{2}/D for 1≪D_{A}≤sqrt[D], where D_{A} and D are the Hilbert space dimensions of the subsystem and the system, respectively. Hence, typical pure states are (nearly) maximally entangled. We develop tools to compute the average entanglement entropy ⟨S⟩ of all eigenstates of quadratic fermionic Hamiltonians. In particular, we derive exact bounds for the most general translationally invariant models lnD_{A}-(lnD_{A})^{2}/lnD≤⟨S⟩≤lnD_{A}-[1/(2ln2)](lnD_{A})^{2}/lnD. Consequently, we prove that (i) if the subsystem size is a finite fraction of the system size, then ⟨S⟩

Gyroaverage effects on nontwist Hamiltonians: Separatrix reconnection and chaos suppression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del-Castillo-Negrete, Diego B; Martinell, J.

2012-01-01

A study of finite Larmor radius (FLR) effects on E x B test particle chaotic transport in non-monotonic zonal flows with drift waves in magnetized plasmas is presented. Due to the non-monotonicity of the zonal flow, the Hamiltonian does not satisfy the twist condition. The electrostatic potential is modeled as a linear superposition of a zonal flow and the regular neutral modes of the Hasegawa-Mima equation. FLR effects are incorporated by gyro-averaging the E x B Hamiltonian. It is shown that there is a critical value of the Larmor radius for which the zonal flow transitions from a profile withmore » one maximum to a profile with two maxima and a minimum. This bifurcation leads to the creation of additional shearless curves and resonances. The gyroaveraged nontwist Hamiltonian exhibits complex patterns of separatrix reconnection. A change in the Larmor radius can lead to heteroclinic-homoclinic bifurcations and dipole formation. For Larmor radii for which the zonal flow has bifurcated, double heteroclinic-heteroclinic, homoclinic-homoclinic and heteroclinic-homoclinic separatrix topologies are observed. It is also shown that chaotic transport is typically reduced as the Larmor radius increases. Poincare sections show that, for large enough Larmor radius, chaos can be practically suppressed. In particular, changes of the Larmor radius can restore the shearless curve.« less

Gyroaverage effects on nontwist Hamiltonians: separatrix reconnection and chaos suppression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del-Castillo-Negrete, Diego B; Martinell, J.

2012-01-01

A study of nite Larmor radius (FLR) eects on E B test particle chaotic transport in non- monotonic zonal ows with drift waves in magnetized plasmas is presented. Due to the non- monotonicity of the zonal ow, the Hamiltonian does not satisfy the twist condition. The electro- static potential is modeled as a linear superposition of a zonal ow and regular neutral modes of the Hasegawa-Mima equation. FLR eects are incorporated by gyro-averaging the EB Hamiltonian. It is shown that there is a critical value the Larmor radius for which the zonal ow transitions from a prole with one maximummore » to a prole with two maxima and a minimum. This bifurcation leads to the creation of additional shearless curves and resonances. The gyroaveraged nontwist Hamiltonian exhibits complex patterns of separatrix reconnection. A change in the Larmor ra- dius can lead to heteroclinic-homoclinic bifurcations and dipole formation. For Larmor radii for which the zonal ow has bifurcated, double heteroclinic-heteroclinic, homoclinic-homoclinic and heteroclinic-homoclinic topologies are observed. It is also shown that chaotic transport is typically reduced as the Larmor radius increases. Poincare sections shows that, for large enough Larmor radius, chaos can be practically suppressed. In particular, small changes on the Larmor radius can restore the shearless curve.« less

Formalism for the solution of quadratic Hamiltonians with large cosine terms

NASA Astrophysics Data System (ADS)

Ganeshan, Sriram; Levin, Michael

2016-02-01

We consider quantum Hamiltonians of the form H =H0-U ∑jcos(Cj) , where H0 is a quadratic function of position and momentum variables {x1,p1,x2,p2,⋯} and the Cj's are linear in these variables. We allow H0 and Cj to be completely general with only two restrictions: we require that (1) the Cj's are linearly independent and (2) [Cj,Ck] is an integer multiple of 2 π i for all j ,k so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low-energy spectrum in the limit U →∞ . This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite U limit, we also discuss how to analyze these systems when U is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

Updating the Jovian Proton Radiation Environment - 2015

NASA Technical Reports Server (NTRS)

Garrett, Henry; Martinez-Sierra, Luz Maria; Evans, Robin

2015-01-01

Since publication in 1983 by N. Divine and H. Garrett, the Jet Propulsion Laboratory's plasma and radiation models have been the design standard for NASA's missions to Jupiter. These models consist of representations of the cold plasma and electrons, the warm and auroral electrons and protons, and the radiation environment (electron, proton, and heavy ions). To date, however, the high-energy proton model has been limited to an L-shell of 12. With the requirement to compute the effects of the high energy protons and other heavy ions on the proposed Europa mission, the extension of the high energy proton model from approximately 12 L-shell to approximately 50 L-shell has become necessary. In particular, a model of the proton environment over that range is required to estimate radiation effects on the solar arrays for the mission. This study describes both the steps taken to extend the original Divine proton model out to an approximately 50 L-shell and the resulting model developed to accomplish that goal. In addition to hydrogen, the oxygen, sulfur, and helium heavy ion environments have also been added between approximately 6 L-shell and approximately 50 L-shell. Finally, selected examples of the model's predictions are presented to illustrate the uses of the tool.

Exactly Solvable Models for Topological Phases of Matter

NASA Astrophysics Data System (ADS)

Tarantino, Nicolas Alessandro

Topological systems are characterized by some collection of features which remain unchanged under deformations of the Hamiltonian which leave the band gap open. The earliest examples of these were free fermion systems, allowing us to study the band structure to determine if a candidate material supports topological features. However, we can also ask the reversed question, i.e. Given a band gap, what topological features can be engineered? This classification problem proved to have numerous answers depending on which extra assumptions we allow, producing many candidate phases. While free fermion topological features could be classified by their band structures (culminating in the 10-fold way), strongly interacting systems defied this approach, and so classification outstripped the construction of even the most elementary Hamiltonians, leaving us with a number of phases which could exist, but do not have a single strongly interacting representative. The purpose of this thesis is to resolve this in certain cases by constructing commuting projector models (CPM), a class of exactly solvable models, for two types of topological phases, known as symmetry enriched topological (SET) order and fermionic symmetry protected topological (SPT) phases respectively. After introducing the background and history of commuting projector models, we will move on to the details of how these Hamiltonians are built. In the first case, we construct a CPM for a SET, showing how to encode the necessary group cohomology data into a lattice model. In the second, we construct a CPM for a fermionic SPT, and find that we must include a combinatorial representation of a spin structure to make the model consistent. While these two projects were independent, they are linked thematically by a technique known as decoration, where extra data is encoded onto simple models to generate exotic phases.

Ghost busting: PT-symmetric interpretation of the Lee model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bender, Carl M.; Brandt, Sebastian F.; Chen, J.-H.

2005-01-15

The Lee model was introduced in the 1950s as an elementary quantum field theory in which mass, wave function, and charge renormalization could be carried out exactly. In early studies of this model it was found that there is a critical value of g{sup 2}, the square of the renormalized coupling constant, above which g{sub 0}{sup 2}, the square of the unrenormalized coupling constant, is negative. Thus, for g{sup 2} larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. It was also discovered that in this non-Hermitian regime a new state appears whose norm is negative.more » This state is called a ghost state. It has always been assumed that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess PT symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having PT symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a new time-independent operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore, it has been shown that time evolution in such a theory is unitary. In this paper the C operator for the Lee model in the ghost regime is constructed in the V/N{theta} sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum field theory for all values of g{sup 2}.« less

Exactly solvable model of transitional nuclei based on dual algebraic structure for the three level pairing model in the framework of sdg interacting boson model

NASA Astrophysics Data System (ADS)

Jafarizadeh, M. A.; Ranjbar, Z.; Fouladi, N.; Ghapanvari, M.

2018-01-01

In this paper, a successful algebraic method based on the dual algebraic structure for three level pairing model in the framework of sdg IBM is proposed for transitional nuclei which show transitional behavior from spherical to gamma-unstable quantum shape phase transition. In this method complicated sdg Hamiltonian, which is a three level pairing Hamiltonian is determined easily via the exactly solvable method. This description provides a better interpretation of some observables such as BE (4) in nuclei which exhibits the necessity of inclusion of g boson in the sd IBM, while BE (4) cannot be explained in the sd boson model. Some observables such as Energy levels, BE (2), BE (4), the two neutron separation energies signature splitting of the γ-vibrational band and expectation values of the g-boson number operator are calculated and examined for 46 104 - 110Pd isotopes.

Unified formalism for higher order non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2012-03-01

This work is devoted to giving a geometric framework for describing higher order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.

Quantum Hamiltonian identification from measurement time traces.

PubMed

Zhang, Jun; Sarovar, Mohan

2014-08-22

Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.

Effects of Combined Loads on the Nonlinear Response and Residual Strength of Damaged Stiffened Shells

NASA Technical Reports Server (NTRS)

Starnes, James H., Jr.; Rose, Cheryl A.; Rankin, Charles C.

1996-01-01

The results of an analytical study of the nonlinear response of stiffened fuselage shells with long cracks are presented. The shells are modeled with a hierarchical modeling strategy and analyzed with a nonlinear shell analysis code that maintains the shell in a nonlinear equilibrium state while the crack is grown. The analysis accurately accounts for global and local structural response phenomena. Results are presented for various combinations of internal pressure and mechanical loads, and the effects of crack orientation on the shell response are described. The effects of combined loading conditions and the effects of varying structural parameters on the stress-intensity factors associated with a crack are presented.

Flexible configuration-interaction shell-model many-body solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Calvin W.; Ormand, W. Erich; McElvain, Kenneth S.

BIGSTICK Is a flexible configuration-Interaction open-source shell-model code for the many-fermion problem In a shell model (occupation representation) framework. BIGSTICK can generate energy spectra, static and transition one-body densities, and expectation values of scalar operators. Using the built-in Lanczos algorithm one can compute transition probabflity distributions and decompose wave functions into components defined by group theory.

The Vibration Analysis of Tube Bundles Induced by Fluid Elastic Excitation in Shell Side of Heat Exchanger

NASA Astrophysics Data System (ADS)

Bao, Minle; Wang, Lu; Li, Wenyao; Gao, Tianze

2017-09-01

Fluid elastic excitation in shell side of heat exchanger was deduced theoretically in this paper. Model foundation was completed by using Pro / Engineer software. The finite element model was constructed and imported into the FLUENT module. The flow field simulation adopted the dynamic mesh model, RNG k-ε model and no-slip boundary conditions. Analysing different positions vibration of tube bundles by selecting three regions in shell side of heat exchanger. The results show that heat exchanger tube bundles at the inlet of the shell side are more likely to be failure due to fluid induced vibration.

Integrated Hamiltonian sampling: a simple and versatile method for free energy simulations and conformational sampling.

PubMed

Mori, Toshifumi; Hamers, Robert J; Pedersen, Joel A; Cui, Qiang

2014-07-17

Motivated by specific applications and the recent work of Gao and co-workers on integrated tempering sampling (ITS), we have developed a novel sampling approach referred to as integrated Hamiltonian sampling (IHS). IHS is straightforward to implement and complementary to existing methods for free energy simulation and enhanced configurational sampling. The method carries out sampling using an effective Hamiltonian constructed by integrating the Boltzmann distributions of a series of Hamiltonians. By judiciously selecting the weights of the different Hamiltonians, one achieves rapid transitions among the energy landscapes that underlie different Hamiltonians and therefore an efficient sampling of important regions of the conformational space. Along this line, IHS shares similar motivations as the enveloping distribution sampling (EDS) approach of van Gunsteren and co-workers, although the ways that distributions of different Hamiltonians are integrated are rather different in IHS and EDS. Specifically, we report efficient ways for determining the weights using a combination of histogram flattening and weighted histogram analysis approaches, which make it straightforward to include many end-state and intermediate Hamiltonians in IHS so as to enhance its flexibility. Using several relatively simple condensed phase examples, we illustrate the implementation and application of IHS as well as potential developments for the near future. The relation of IHS to several related sampling methods such as Hamiltonian replica exchange molecular dynamics and λ-dynamics is also briefly discussed.

Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wahlen-Strothman, J. M.; Henderson, T. H.; Hermes, M. R.

Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems, but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories.more » We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.« less

An Efficient Analysis Methodology for Fluted-Core Composite Structures

NASA Technical Reports Server (NTRS)

Oremont, Leonard; Schultz, Marc R.

2012-01-01

The primary loading condition in launch-vehicle barrel sections is axial compression, and it is therefore important to understand the compression behavior of any structures, structural concepts, and materials considered in launch-vehicle designs. This understanding will necessarily come from a combination of test and analysis. However, certain potentially beneficial structures and structural concepts do not lend themselves to commonly used simplified analysis methods, and therefore innovative analysis methodologies must be developed if these structures and structural concepts are to be considered. This paper discusses such an analysis technique for the fluted-core sandwich composite structural concept. The presented technique is based on commercially available finite-element codes, and uses shell elements to capture behavior that would normally require solid elements to capture the detailed mechanical response of the structure. The shell thicknesses and offsets using this analysis technique are parameterized, and the parameters are adjusted through a heuristic procedure until this model matches the mechanical behavior of a more detailed shell-and-solid model. Additionally, the detailed shell-and-solid model can be strategically placed in a larger, global shell-only model to capture important local behavior. Comparisons between shell-only models, experiments, and more detailed shell-and-solid models show excellent agreement. The discussed analysis methodology, though only discussed in the context of fluted-core composites, is widely applicable to other concepts.

Hamiltonian structure of the Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-03-01

The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

Does finite-temperature decoding deliver better optima for noisy Hamiltonians?

NASA Astrophysics Data System (ADS)

Ochoa, Andrew J.; Nishimura, Kohji; Nishimori, Hidetoshi; Katzgraber, Helmut G.

The minimization of an Ising spin-glass Hamiltonian is an NP-hard problem. Because many problems across disciplines can be mapped onto this class of Hamiltonian, novel efficient computing techniques are highly sought after. The recent development of quantum annealing machines promises to minimize these difficult problems more efficiently. However, the inherent noise found in these analog devices makes the minimization procedure difficult. While the machine might be working correctly, it might be minimizing a different Hamiltonian due to the inherent noise. This means that, in general, the ground-state configuration that correctly minimizes a noisy Hamiltonian might not minimize the noise-less Hamiltonian. Inspired by rigorous results that the energy of the noise-less ground-state configuration is equal to the expectation value of the energy of the noisy Hamiltonian at the (nonzero) Nishimori temperature [J. Phys. Soc. Jpn., 62, 40132930 (1993)], we numerically study the decoding probability of the original noise-less ground state with noisy Hamiltonians in two space dimensions, as well as the D-Wave Inc. Chimera topology. Our results suggest that thermal fluctuations might be beneficial during the optimization process in analog quantum annealing machines.

An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1994-01-01

The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.

Design and Analysis of an X-Ray Mirror Assembly Using the Meta-Shell Approach

NASA Technical Reports Server (NTRS)

McClelland, Ryan S.; Bonafede, Joseph; Saha, Timo T.; Solly, Peter M.; Zhang, William W.

2016-01-01

Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low sensitivity to thermal gradients.

Deformation of compound shells under action of internal shock wave loading

NASA Astrophysics Data System (ADS)

Chernobryvko, Marina; Kruszka, Leopold; Avramov, Konstantin

2015-09-01

The compound shells under the action of internal shock wave loading are considered. The compound shell consists of a thin cylindrical shell and two thin parabolic shells at the edges. The boundary conditions in the shells joints satisfy the equality of displacements. The internal shock wave loading is modelled as the surplus pressure surface. This pressure is a function of the shell coordinates and time. The strain rate deformation of compound shell takes place in both the elastic and in plastic stages. In the elastic stage the equations of the structure motions are obtained by the assumed-modes method, which uses the kinetic and potential energies of the cylindrical and two parabolic shells. The dynamic behaviour of compound shells is treated. In local plastic zones the 3-D thermo-elastic-plastic model is used. The deformations are described by nonlinear model. The stress tensor elements are determined using dynamic deformation theory. The deformation properties of materials are influenced by the strain rate behaviour, the influence of temperature parameters, and the elastic-plastic properties of materials. The dynamic yield point of materials and Pisarenko-Lebedev's criterion of destruction are used. The modified adaptive finite differences method of numerical analysis is suggested for those simulations. The accuracy of the numerical simulation is verified on each temporal step of calculation and in the case of large deformation gradients.

On the nature of a supposed water model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heckmann, Lotta, E-mail: lotta@fkp.tu-darmstadt.de; Drossel, Barbara

2014-08-15

A cell model that has been proposed by Stanley and Franzese in 2002 for modeling water is based on Potts variables that represent the possible orientations of bonds between water molecules. We show that in the liquid phase, where all cells are occupied by a molecule, the Hamiltonian of the cell model can be rewritten as a Hamiltonian of a conventional Potts model, albeit with two types of coupling constants. We argue that such a model, while having a first-order phase transition, cannot display the critical end point that is postulated for the phase transition between a high- and low-densitymore » liquid. A closer look at the mean-field calculations that claim to find such an end point in the cell model reveals that the mean-field theory is constructed such that the symmetry constraints on the order parameter are violated. This is equivalent to introducing an external field. The introduction of such a field can be given a physical justification due to the fact that water does not have the type of long-range order occurring in the Potts model.« less

Explicit methods in extended phase space for inseparable Hamiltonian problems

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2015-03-01

We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator.

Fragmentation of protostars dust shells at the Hayashi stage

NASA Astrophysics Data System (ADS)

Abdulmyanov, T. R.

2017-09-01

The aim of this study is to determine the density variations of a protostars dust shells at the Hayashi stage. The simplified model of the density wave perturbations are obtained on the base hydrodynamic equations. According to this model, the fragmentation of dust shells may occur at the stage of slow compression of protostar. Using the solution of the wave equation, the 3-D profiles of the density of the dust shell are defined.

Effective Simulation of Delamination in Aeronautical Structures Using Shells and Cohesive Elements

NASA Technical Reports Server (NTRS)

Davila, Carlos G.; Camanho, Pedro P.; Turon, Albert

2007-01-01

A cohesive element for shell analysis is presented. The element can be used to simulate the initiation and growth of delaminations between stacked, non-coincident layers of shell elements. The procedure to construct the element accounts for the thickness offset by applying the kinematic relations of shell deformation to transform the stiffness and internal force of a zero-thickness cohesive element such that interfacial continuity between the layers is enforced. The procedure is demonstrated by simulating the response and failure of the Mixed Mode Bending test and a skin-stiffener debond specimen. In addition, it is shown that stacks of shell elements can be used to create effective models to predict the inplane and delamination failure modes of thick components. The results indicate that simple shell models can retain many of the necessary predictive attributes of much more complex 3D models while providing the computational efficiency that is necessary for design.

Cohesive Elements for Shells

NASA Technical Reports Server (NTRS)

Davila, Carlos G.; Camanho, Pedro P.; Turon, Albert

2007-01-01

A cohesive element for shell analysis is presented. The element can be used to simulate the initiation and growth of delaminations between stacked, non-coincident layers of shell elements. The procedure to construct the element accounts for the thickness offset by applying the kinematic relations of shell deformation to transform the stiffness and internal force of a zero-thickness cohesive element such that interfacial continuity between the layers is enforced. The procedure is demonstrated by simulating the response and failure of the Mixed Mode Bending test and a skin-stiffener debond specimen. In addition, it is shown that stacks of shell elements can be used to create effective models to predict the inplane and delamination failure modes of thick components. The results indicate that simple shell models can retain many of the necessary predictive attributes of much more complex 3D models while providing the computational efficiency that is necessary for design.

Alternative bi-Hamiltonian structures for WDVV equations of associativity

NASA Astrophysics Data System (ADS)

Kalayci, J.; Nutku, Y.

1998-01-01

The WDVV equations of associativity in two-dimensional topological field theory are completely integrable third-order Monge-Ampère equations which admit bi-Hamiltonian structure. The time variable plays a distinguished role in the discussion of Hamiltonian structure, whereas in the theory of WDVV equations none of the independent variables merits such a distinction. WDVV equations admit very different alternative Hamiltonian structures under different possible choices of the time variable, but all these various Hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure. They can be identified as different components of the covariant Witten-Zuckerman symplectic 2-form current density where a variational formulation of the WDVV equation that leads to the Hamiltonian operator through the Dirac bracket is available.

Separate spatial Holographic-Hamiltonian soliton pairs and solitons interaction in an unbiased series photorefractive crystal circuit.

PubMed

Cai, Xin; Liu, Jinsong; Wang, Shenglie

2009-02-16

This paper presents calculations for an idea in photorefractive spatial soliton, namely, a dissipative holographic soliton and a Hamiltonian soliton in one dimension form in an unbiased series photorefractive crystal circuit consisting of two photorefractive crystals of which at least one must be photovoltaic. The two solitons are known collectively as a separate Holographic-Hamiltonian spatial soliton pair and there are two types: dark-dark and bright-dark if only one crystal of the circuit is photovoltaic. The numerical results show that the Hamiltonian soliton in a soliton pair can affect the holographic one by the light-induced current whereas the effect of the holographic soliton on the Hamiltonian soliton is too weak to be ignored, i.e., the holographic soliton cannot affect the Hamiltonian one.

Regime of validity of the pairing Hamiltonian in the study of Fermi gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, S. Y.; Pandharipande, V. R.

2006-06-01

The ground state energy and pairing gap of the interacting Fermi gases calculated by the ab initio stochastic method are compared with those estimated from the Bardeen-Cooper-Schrieffer pairing Hamiltonian. We discuss the ingredients of this Hamiltonian in various regimes of interaction strength. In the weakly interacting (1/ak{sub F}<<0) regime the BCS Hamiltonian should describe Landau quasiparticle energies and interactions, on the other hand, in the strongly pairing regime, that is, 1/ak{sub F} > or approx. 0, it becomes part of the bare Hamiltonian. However, the bare BCS Hamiltonian is not adequate for describing atomic gases in the regime of weakmore » to moderate interaction strength -{infinity}<1/ak{sub F}<0 such as ak{sub F}{approx}-1.« less

Finite Element Analysis of Geodesically Stiffened Cylindrical Composite Shells Using a Layerwise Theory

NASA Technical Reports Server (NTRS)

Gerhard, Craig Steven; Gurdal, Zafer; Kapania, Rakesh K.

1996-01-01

Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.

Entanglement Hamiltonians for Chiral Fermions with Zero Modes.

PubMed

Klich, Israel; Vaman, Diana; Wong, Gabriel

2017-09-22

In this Letter, we study the effect of topological zero modes on entanglement Hamiltonians and the entropy of free chiral fermions in (1+1)D. We show how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain exact expressions for entanglement Hamiltonians. In the absence of the zero mode, the resulting entanglement Hamiltonians consist of local and bilocal terms. In the periodic sector, the presence of a zero mode leads to an additional nonlocal contribution to the entanglement Hamiltonian. We derive an exact expression for this term and for the resulting change in the entanglement entropy.

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

Covariant hamiltonian spin dynamics in curved space-time

NASA Astrophysics Data System (ADS)

d'Ambrosi, G.; Satish Kumar, S.; van Holten, J. W.

2015-04-01

The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.

{P}{T}-symmetric interpretation of the electromagnetic self-force

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Gianfreda, Mariagiovanna

2015-08-01

In 1980 Englert examined the classic problem of the electromagnetic self-force on an oscillating charged particle. His approach, which was based on an earlier idea of Bateman, was to introduce a time-reversed (charge-conjugate) particle and to show that the two-particle system is Hamiltonian. Unfortunately, Englert’s model did not solve the problem of runaway modes, and the corresponding quantum theory had ghost states. It is shown here that Englert’s Hamiltonian is {P}{T} symmetric, and that the problems with his model arise because the {P}{T} symmetry is broken at both the classical and the quantum level. However, by allowing the charged particles to interact and by adjusting the coupling parameters to put the model into an unbroken {P}{T}-symmetric region, one eliminates the classical nonrelativistic runaway modes and obtains a corresponding nonrelativistic quantum system that is in equilibrium and ghost free.

Human swallowing simulation based on videofluorography images using Hamiltonian MPS method

NASA Astrophysics Data System (ADS)

Kikuchi, Takahiro; Michiwaki, Yukihiro; Kamiya, Tetsu; Toyama, Yoshio; Tamai, Tasuku; Koshizuka, Seiichi

2015-09-01

In developed nations, swallowing disorders and aspiration pneumonia have become serious problems. We developed a method to simulate the behavior of the organs involved in swallowing to clarify the mechanisms of swallowing and aspiration. The shape model is based on anatomically realistic geometry, and the motion model utilizes forced displacements based on realistic dynamic images to reflect the mechanisms of human swallowing. The soft tissue organs are modeled as nonlinear elastic material using the Hamiltonian MPS method. This method allows for stable simulation of the complex swallowing movement. A penalty method using metaballs is employed to simulate contact between organ walls and smooth sliding along the walls. We performed four numerical simulations under different analysis conditions to represent four cases of swallowing, including a healthy volunteer and a patient with a swallowing disorder. The simulation results were compared to examine the epiglottic downfolding mechanism, which strongly influences the risk of aspiration.

Quantum phase transition and quench dynamics in the anisotropic Rabi model

NASA Astrophysics Data System (ADS)

Shen, Li-Tuo; Yang, Zhen-Biao; Wu, Huai-Zhi; Zheng, Shi-Biao

2017-01-01

We investigate the quantum phase transition (QPT) and quench dynamics in the anisotropic Rabi model when the ratio of the qubit transition frequency to the oscillator frequency approaches infinity. Based on the Schrieffer-Wolff transformation, we find an anti-Hermitian operator that maps the original Hamiltonian into a one-dimensional oscillator Hamiltonian within the spin-down subspace. We analytically derive the eigenenergy and eigenstate of the normal and superradiant phases and demonstrate that the system undergoes a second-order quantum phase transition at a critical border. The critical border is a straight line in a two-dimensional parameter space which essentially extends the dimensionality of QPT in the Rabi model. By combining the Kibble-Zurek mechanism and the adiabatic dynamics method, we find that the residual energy vanishes as the quench time tends to zero, which is a sharp contrast to the universal scaling where the residual energy diverges in the same limit.

Metric versus observable operator representation, higher spin models

NASA Astrophysics Data System (ADS)

Fring, Andreas; Frith, Thomas

2018-02-01

We elaborate further on the metric representation that is obtained by transferring the time-dependence from a Hermitian Hamiltonian to the metric operator in a related non-Hermitian system. We provide further insight into the procedure on how to employ the time-dependent Dyson relation and the quasi-Hermiticity relation to solve time-dependent Hermitian Hamiltonian systems. By solving both equations separately we argue here that it is in general easier to solve the former. We solve the mutually related time-dependent Schrödinger equation for a Hermitian and non-Hermitian spin 1/2, 1 and 3/2 model with time-independent and time-dependent metric, respectively. In all models the overdetermined coupled system of equations for the Dyson map can be decoupled algebraic manipulations and reduces to simple linear differential equations and an equation that can be converted into the non-linear Ermakov-Pinney equation.

Spin-splitting calculation for zincblende semiconductors using an atomic bond-orbital model.

PubMed

Kao, Hsiu-Fen; Lo, Ikai; Chiang, Jih-Chen; Chen, Chun-Nan; Wang, Wan-Tsang; Hsu, Yu-Chi; Ren, Chung-Yuan; Lee, Meng-En; Wu, Chieh-Lung; Gau, Ming-Hong

2012-10-17

We develop a 16-band atomic bond-orbital model (16ABOM) to compute the spin splitting induced by bulk inversion asymmetry in zincblende materials. This model is derived from the linear combination of atomic-orbital (LCAO) scheme such that the characteristics of the real atomic orbitals can be preserved to calculate the spin splitting. The Hamiltonian of 16ABOM is based on a similarity transformation performed on the nearest-neighbor LCAO Hamiltonian with a second-order Taylor expansion k at the Γ point. The spin-splitting energies in bulk zincblende semiconductors, GaAs and InSb, are calculated, and the results agree with the LCAO and first-principles calculations. However, we find that the spin-orbit coupling between bonding and antibonding p-like states, evaluated by the 16ABOM, dominates the spin splitting of the lowest conduction bands in the zincblende materials.

Exact expression of the t-J model in terms of local spin and fermionic holon operators

NASA Astrophysics Data System (ADS)

Wang, Y. R.; Rice, M. J.

1994-02-01

An exact expression for the Hamiltonian H of the t-J model in terms of local spin (Si) and fermionic holon (ei) operators is derived which requires no constraint between these operators. The result for the Hamiltonian H is H=-t tsumijeie°j(1/2+2Si.Sj)+(J/2)t smij(1-e°iei)(Si.Sj-1/4)(1-e°je The number of electrons at site i is given by ni=1-e°iei, and the true spin operator S~i, is related to the local spin operator by S~i=(1-e°iei)Si. The expression correctly produces the Nagaoka theorem in the limit J-->0, and preserves the time-reversal symmetry of the original model. For a bipartite lattice, H describes a competition between ferromagnetism, favored by the hopping term, and antiferromagnetism, favored by the Heisenberg term.

Complete Hamiltonian analysis of cosmological perturbations at all orders

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nandi, Debottam; Shankaranarayanan, S., E-mail: debottam@iisertvm.ac.in, E-mail: shanki@iisertvm.ac.in

2016-06-01

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the 'gauge-fixing' issues and extend the analysis to scalar field models and show that our approach can be applied to any order of perturbation for any first order derivative fields. In the case of Galilean scalar fields, our procedure can extract constrained relations at all orders in perturbations leading to the fact that there is no extra degrees of freedom due to the presence of higher time derivatives of the field in themore » Lagrangian. We compare and contrast our approach to the Lagrangian approach (Chen et al. [2006]) for extracting higher order correlations and show that our approach is efficient and robust and can be applied to any model of gravity and matter fields without invoking slow-roll approximation.« less

Signatures of the A2 term in ultrastrongly coupled oscillators

NASA Astrophysics Data System (ADS)

Tufarelli, Tommaso; McEnery, K. R.; Maier, S. A.; Kim, M. S.

2015-06-01

We study a bosonic matter excitation coupled to a single-mode cavity field via electric dipole. Counter-rotating and A2 terms are included in the interaction model, A being the vector potential of the cavity field. In the ultrastrong coupling regime the vacuum of the bare modes is no longer the ground state of the Hamiltonian and contains a nonzero population of polaritons, the true normal modes of the system. If the parameters of the model satisfy the Thomas-Reiche-Kuhn sum rule, we find that the two polaritons are always equally populated. We show how this prediction could be tested in a quenching experiment, by rapidly switching on the coupling and analyzing the radiation emitted by the cavity. A refinement of the model based on a microscopic minimal coupling Hamiltonian is also provided, and its consequences on our results are characterized analytically.

Shell models of magnetohydrodynamic turbulence

NASA Astrophysics Data System (ADS)

Plunian, Franck; Stepanov, Rodion; Frick, Peter

2013-02-01

Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accurate dissipation rate. Using modern computers it is difficult to attain an inertial range of three decades with direct numerical simulations, whereas eight are possible using shell models. In this review we set up a general mathematical framework allowing the description of any MHD shell model. The variety of the latter, with their advantages and weaknesses, is introduced. Finally we consider a number of applications, dealing with free-decaying MHD turbulence, dynamo action, Alfvén waves and the Hall effect.

Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core

NASA Astrophysics Data System (ADS)

Fazzolari, Fiorenzo A.; Carrera, Erasmo

2014-02-01

In this paper, the Ritz minimum energy method, based on the use of the Principle of Virtual Displacements (PVD), is combined with refined Equivalent Single Layer (ESL) and Zig Zag (ZZ) shell models hierarchically generated by exploiting the use of Carrera's Unified Formulation (CUF), in order to engender the Hierarchical Trigonometric Ritz Formulation (HTRF). The HTRF is then employed to carry out the free vibration analysis of doubly curved shallow and deep functionally graded material (FGM) shells. The PVD is further used in conjunction with the Gauss theorem to derive the governing differential equations and related natural boundary conditions. Donnell-Mushtari's shallow shell-type equations are given as a particular case. Doubly curved FGM shells and doubly curved sandwich shells made up of isotropic face sheets and FGM core are investigated. The proposed shell models are widely assessed by comparison with the literature results. Two benchmarks are provided and the effects of significant parameters such as stacking sequence, boundary conditions, length-to-thickness ratio, radius-to-length ratio and volume fraction index on the circular frequency parameters and modal displacements are discussed.

Modeling Optical Spectra of Large Organic Systems Using Real-Time Propagation of Semiempirical Effective Hamiltonians

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Soumen; Andersen, Amity; Gagliardi, Laura

2017-08-16

We present an implementation of a time-dependent semiempirical method (INDO/S) in NWChem using real-time (RT) propagation to address, in principle, the entire spectrum of valence electronic excitations. Adopting this model, we study the UV-visible spectra of medium-sized systems like P3B2, f-coronene, and in addition much larger systems like ubiquitin in the gas phase and the betanin chromophore in the presence of two explicit solvents (water and methanol). RT-INDO/S provides qualitatively and indeed often quantitatively accurate results when compared with RT- TDDFT or experimental spectra. While demonstrated here for INDO/S in particular, our implementation provides a framework for performing electron dynamicsmore » in large systems using semiempirical Hartree-Fock (HF) Hamiltonians in general.« less

Time-invariant PT product and phase locking in PT -symmetric lattice models

NASA Astrophysics Data System (ADS)

Joglekar, Yogesh N.; Onanga, Franck Assogba; Harter, Andrew K.

2018-01-01

Over the past decade, non-Hermitian, PT -symmetric Hamiltonians have been investigated as candidates for both a fundamental, unitary, quantum theory and open systems with a nonunitary time evolution. In this paper, we investigate the implications of the former approach in the context of the latter. Motivated by the invariance of the PT (inner) product under time evolution, we discuss the dynamics of wave-function phases in a wide range of PT -symmetric lattice models. In particular, we numerically show that, starting with a random initial state, a universal, gain-site location dependent locking between wave-function phases at adjacent sites occurs in the PT -symmetry-broken region. Our results pave the way towards understanding the physically observable implications of time invariants in the nonunitary dynamics produced by PT -symmetric Hamiltonians.

Hamiltonian mean-field model: effect of temporal perturbation in coupling matrix

NASA Astrophysics Data System (ADS)

Bhadra, Nivedita; Patra, Soumen K.

2018-05-01

The Hamiltonian mean-field (HMF) model is a system of fully coupled rotators which exhibits a second-order phase transition at some critical energy in its canonical ensemble. We investigate the case where the interaction between the rotors is governed by a time-dependent coupling matrix. Our numerical study reveals a shift in the critical point due to the temporal modulation. The shift in the critical point is shown to be independent of the modulation frequency above some threshold value, whereas the impact of the amplitude of modulation is dominant. In the microcanonical ensemble, the system with constant coupling reaches a quasi-stationary state (QSS) at an energy near the critical point. Our result indicates that the QSS subsists in presence of such temporal modulation of the coupling parameter.

On the Decay of Correlations in Non-Analytic SO(n)-Symmetric Models

NASA Astrophysics Data System (ADS)

Naddaf, Ali

We extend the method of complex translations which was originally employed by McBryan-Spencer [2] to obtain a decay rate for the two point function in two-dimensional SO(n)-symmetric models with non-analytic Hamiltonians for $.

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

NASA Astrophysics Data System (ADS)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

Two-nucleon high-spin states, the Bansal-French model and the crude shell model

NASA Astrophysics Data System (ADS)

Chan, Tsan Ung

1987-08-01

Recent data on two-nucleon stretched high-spin states agree well with the crude shell model predictions. For two-neutron high-spin states, the A and T linear dependence of B2n in the Bansal-French model can be deduced from the A and T linear dependence of Bn and the crude shell model. 7-2 states in some Zn and Ge even nuclei might be two-proton states. This hypothesis should be confirmed by two-proton transfer reaction.

Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states

PubMed Central

Bonet-Luz, Esther

2016-01-01

The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest’s theorem is shown to be Lie–Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie–Poisson structure associated with another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models that have previously appeared in the chemical physics literature. PMID:27279764

The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems

NASA Astrophysics Data System (ADS)

Koon, Wang Sang; Marsden, Jerrold E.

1997-08-01

This paper compares the Hamiltonian approach to systems with nonholonomic constraints (see [31, 2, 4, 29] and references therein) with the Lagrangian approach (see [16, 27, 9]). There are many differences in the approaches and each has its own advantages; some structures have been discovered on one side and their analogues on the other side are interesting to clarify. For example, the momentum equation and the reconstruction equation were first found on the Lagrangian side and are useful for the control theory of these systems, while the failure of the reduced two-form to be closed (i.e., the failure of the Poisson bracket to satisfy the Jacobi identity) was first noticed on the Hamiltonian side. Clarifying the relation between these approaches is important for the future development of the control theory and stability and bifurcation theory for such systems. In addition to this work, we treat, in this unified framework, a simplified model of the bicycle (see [12, 13]), which is an important underactuated (nonminimum phase) control system.

Space-time models based on random fields with local interactions

NASA Astrophysics Data System (ADS)

Hristopulos, Dionissios T.; Tsantili, Ivi C.

2016-08-01

The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-07-29

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N 2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less

Further Results in Bend-Buckling Analysis of Ring Stiffened Cylindrical Shells.

DTIC Science & Technology

1986-08-01

Submerged Shell Targets, NSWC TR 84-380, Dec 1984. 2. Moussouros, M., "Finite Element Modeling Techniques for Buckling Analysis of Cylindrical Shells...KCR, MBR , M0 , F0 , and I, R is the mean radius as given by R0 ) R0 - Mean radius of circular cylindrical shell (perfect shell or radius of

Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

NASA Astrophysics Data System (ADS)

Ferreira, L. A.; Miramontes, J. Luis; Guillén, Joaquín Sánchez

1995-02-01

We consider the Hamiltonian reduction of the "two-loop" Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra G. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of G, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.

Open quantum systems, effective Hamiltonians, and device characterization

NASA Astrophysics Data System (ADS)

Duffus, S. N. A.; Dwyer, V. M.; Everitt, M. J.

2017-10-01

High fidelity models, which are able to both support accurate device characterization and correctly account for environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity of the density matrix, one preferred model of open systems describes the dynamics with a master equation in Lindblad form. In practice, Linblad operators are rarely derived from first principles, and often a particular form of annihilator is assumed. This results in dynamical models that miss those additional terms which must generally be added for the master equation to assume the Lindblad form, together with the other concomitant terms that must be assimilated into an effective Hamiltonian to produce the correct free evolution. In first principles derivations, such additional terms are often canceled (or countered), frequently in a somewhat ad hoc manner, leading to a number of competing models. Whilst the implications of this paper are quite general, to illustrate the point we focus here on an example anharmonic system; specifically that of a superconducting quantum interference device (SQUID) coupled to an Ohmic bath. The resulting master equation implies that the environment has a significant impact on the system's energy; we discuss the prospect of keeping or canceling this impact and note that, for the SQUID, monitoring the magnetic susceptibility under control of the capacitive coupling strength and the externally applied flux results in experimentally measurable differences between a number of these models. In particular, one should be able to determine whether a squeezing term of the form X ̂P ̂+P ̂X ̂ should be present in the effective Hamiltonian or not. If model generation is not performed correctly, device characterization will be prone to systemic errors.

X-rays from Eta Carinae

NASA Technical Reports Server (NTRS)

Chlebowski, T.; Seward, F. D.; Swank, J.; Szymkowiak, A.

1984-01-01

X-ray observations of Eta Car obtained with the high-resolution imager and solid-state spectrometer of the Einstein observatory are reported and interpreted in terms of a two-shell model. A soft component with temperature 5 million K is located in the expanding outer shell, and the hard core component with temperature 80 million K is attributed to the interaction of a high-velocity stellar wind from the massive central object with the inner edge of a dust shell. Model calculations based on comparison with optical and IR data permit estimation of the mass of the outer shell (0.004 solar mass), the mass of the dust shell (3 solar mass), and the total shell expansion energy (less than 2 x 10 to the 49th ergs).

Centrifugal distortion coefficients of asymmetric-top molecules: Reduction of the octic terms of the rotational Hamiltonian

NASA Astrophysics Data System (ADS)

Ramachandra Rao, Ch. V. S.

1983-11-01

The rotational Hamiltonian of an asymmetric-top molecule in its standard form, containing terms up to eighth degree in the components of the total angular momentum, is transformed by a unitary transformation with parameters Spqr to a reduced Hamiltonian so as to avoid the indeterminacies inherent in fitting the complete Hamiltonian to observed energy levels. Expressions are given for the nine determinable combinations of octic constants Θ' i ( i = 1 to 9) which are invariant under the unitary transformation. A method of reduction suitable for energy calculations by matrix diagonalization is considered. The relations between the coefficients of the transformed Hamiltonian, for suitable choice of the parameters Spqr, and those of the reduced Hamiltonian are given. This enables the determination of the nine octic constants Θ' i in terms of the experimental constants.

Influence of an asymmetric ring on the modeling of an orthogonally stiffened cylindrical shell

NASA Technical Reports Server (NTRS)

Rastogi, Naveen; Johnson, Eric R.

1994-01-01

Structural models are examined for the influence of a ring with an asymmetrical cross section on the linear elastic response of an orthogonally stiffened cylindrical shell subjected to internal pressure. The first structural model employs classical theory for the shell and stiffeners. The second model employs transverse shear deformation theories for the shell and stringer and classical theory for the ring. Closed-end pressure vessel effects are included. Interacting line load intensities are computed in the stiffener-to-skin joints for an example problem having the dimensions of the fuselage of a large transport aircraft. Classical structural theory is found to exaggerate the asymmetric response compared to the transverse shear deformation theory.

Quasi-additive estimates on the Hamiltonian for the one-dimensional long range Ising model

NASA Astrophysics Data System (ADS)

Littin, Jorge; Picco, Pierre

2017-07-01

In this work, we study the problem of getting quasi-additive bounds for the Hamiltonian of the long range Ising model, when the two-body interaction term decays proportionally to 1/d2 -α , α ∈(0,1 ) . We revisit the paper by Cassandro et al. [J. Math. Phys. 46, 053305 (2005)] where they extend to the case α ∈[0 ,ln3/ln2 -1 ) the result of the existence of a phase transition by using a Peierls argument given by Fröhlich and Spencer [Commun. Math. Phys. 84, 87-101 (1982)] for α =0 . The main arguments of Cassandro et al. [J. Math. Phys. 46, 053305 (2005)] are based in a quasi-additive decomposition of the Hamiltonian in terms of hierarchical structures called triangles and contours, which are related to the original definition of contours introduced by Fröhlich and Spencer [Commun. Math. Phys. 84, 87-101 (1982)]. In this work, we study the existence of a quasi-additive decomposition of the Hamiltonian in terms of the contours defined in the work of Cassandro et al. [J. Math. Phys. 46, 053305 (2005)]. The most relevant result obtained is Theorem 4.3 where we show that there is a quasi-additive decomposition for the Hamiltonian in terms of contours when α ∈[0,1 ) but not in terms of triangles. The fact that it cannot be a quasi-additive bound in terms of triangles lead to a very interesting maximization problem whose maximizer is related to a discrete Cantor set. As a consequence of the quasi-additive bounds, we prove that we can generalise the [Cassandro et al., J. Math. Phys. 46, 053305 (2005)] result, that is, a Peierls argument, to the whole interval α ∈[0,1 ) . We also state here the result of Cassandro et al. [Commun. Math. Phys. 327, 951-991 (2014)] about cluster expansions which implies that Theorem 2.4 that concerns interfaces and Theorem 2.5 that concerns n point truncated correlation functions in Cassandro et al. [Commun. Math. Phys. 327, 951-991 (2014)] are valid for all α ∈[0,1 ) instead of only α ∈[0 ,ln3/ln2 -1 ) .

Meta-shell Approach for Constructing Lightweight and High Resolution X-Ray Optics

NASA Technical Reports Server (NTRS)

McClelland, Ryan S.

2016-01-01

Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low thermal distortion. Recent results are discussed including Structural Thermal Optical Performance (STOP) analysis as well as vibration and shock testing of prototype meta-shells.

Hamiltonian approach to slip-stacking dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, S. Y.; Ng, K. Y.

Hamiltonian dynamics has been applied to study the slip-stacking dynamics. The canonical-perturbation method is employed to obtain the second-harmonic correction term in the slip-stacking Hamiltonian. The Hamiltonian approach provides a clear optimal method for choosing the slip-stacking parameter and improving stacking efficiency. The dynamics are applied specifically to the Fermilab Booster-Recycler complex. As a result, the dynamics can also be applied to other accelerator complexes.

Hamiltonian approach to slip-stacking dynamics

DOE PAGES

Lee, S. Y.; Ng, K. Y.

2017-06-29

Hamiltonian dynamics has been applied to study the slip-stacking dynamics. The canonical-perturbation method is employed to obtain the second-harmonic correction term in the slip-stacking Hamiltonian. The Hamiltonian approach provides a clear optimal method for choosing the slip-stacking parameter and improving stacking efficiency. The dynamics are applied specifically to the Fermilab Booster-Recycler complex. As a result, the dynamics can also be applied to other accelerator complexes.

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.