An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

NASA Astrophysics Data System (ADS)

Yu, Hua-Gen

2016-08-01

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH4 and H2CO are given, together with a comparison with previous results.

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

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

Yu, Hua-Gen, E-mail: hgy@bnl.gov

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using amore » multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH{sub 4} and H{sub 2}CO are given, together with a comparison with previous results.« less

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

Filinov, A.V.; Golubnychiy, V.O.; Bonitz, M.

Extending our previous work [A.V. Filinov et al., J. Phys. A 36, 5957 (2003)], we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: (i) the diagonal Kelbg potential, (ii) the off-diagonal Kelbg potential, (iii) the improved diagonal Kelbg potential, (iv) an effective potential obtained with the Feynman-Kleinert variational principle, and (v) the 'exact' quantum pair potential derived from the two-particle density matrix. For the improved diagonal Kelbg potential, a simple temperature-dependent fit is derived which accurately reproduces the 'exact' pair potential in the whole temperature range. The derivedmore » pseudopotentials are then used in path integral Monte Carlo and molecular-dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about 60 000 K. Finally, we point out an interesting relationship between the quantum potentials and the effective potentials used in density-functional theory.« less

Ground State and Finite Temperature Lanczos Methods

NASA Astrophysics Data System (ADS)

Prelovšek, P.; Bonča, J.

The present review will focus on recent development of exact- diagonalization (ED) methods that use Lanczos algorithm to transform large sparse matrices onto the tridiagonal form. We begin with a review of basic principles of the Lanczos method for computing ground-state static as well as dynamical properties. Next, generalization to finite-temperatures in the form of well established finite-temperature Lanczos method is described. The latter allows for the evaluation of temperatures T>0 static and dynamic quantities within various correlated models. Several extensions and modification of the latter method introduced more recently are analysed. In particular, the low-temperature Lanczos method and the microcanonical Lanczos method, especially applicable within the high-T regime. In order to overcome the problems of exponentially growing Hilbert spaces that prevent ED calculations on larger lattices, different approaches based on Lanczos diagonalization within the reduced basis have been developed. In this context, recently developed method based on ED within a limited functional space is reviewed. Finally, we briefly discuss the real-time evolution of correlated systems far from equilibrium, which can be simulated using the ED and Lanczos-based methods, as well as approaches based on the diagonalization in a reduced basis.

Comparison of νμ->νe Oscillation calculations with matter effects

NASA Astrophysics Data System (ADS)

Gordon, Michael; Toki, Walter

2013-04-01

An introduction to neutrino oscillations in vacuum is presented, followed by a survey of various techniques for obtaining either exact or approximate expressions for νμ->νe oscillations in matter. The method devised by Mann, Kafka, Schneps, and Altinok produces an exact expression for the oscillation by determining explicitely the evolution operator. The method used by Freund yields an approximate oscillation probability by diagonalizing the Hamiltonian, finding the eigenvalues and eigenvectors, and then using those to find modified mixing angles with the matter effect taken into account. The method developed by Arafune, Koike, and Sato uses an alternate method to find an approximation of the evolution operator. These methods are compared to each other using parameters from both the T2K and LBNE experiments.

Theoretical study of the dependence of single impurity Anderson model on various parameters within distributional exact diagonalization method

NASA Astrophysics Data System (ADS)

Syaina, L. P.; Majidi, M. A.

2018-04-01

Single impurity Anderson model describes a system consisting of non-interacting conduction electrons coupled with a localized orbital having strongly interacting electrons at a particular site. This model has been proven successful to explain the phenomenon of metal-insulator transition through Anderson localization. Despite the well-understood behaviors of the model, little has been explored theoretically on how the model properties gradually evolve as functions of hybridization parameter, interaction energy, impurity concentration, and temperature. Here, we propose to do a theoretical study on those aspects of a single impurity Anderson model using the distributional exact diagonalization method. We solve the model Hamiltonian by randomly generating sampling distribution of some conducting electron energy levels with various number of occupying electrons. The resulting eigenvalues and eigenstates are then used to define the local single-particle Green function for each sampled electron energy distribution using Lehmann representation. Later, we extract the corresponding self-energy of each distribution, then average over all the distributions and construct the local Green function of the system to calculate the density of states. We repeat this procedure for various values of those controllable parameters, and discuss our results in connection with the criteria of the occurrence of metal-insulator transition in this system.

Efficient implementation of one- and two-component analytical energy gradients in exact two-component theory

NASA Astrophysics Data System (ADS)

Franzke, Yannick J.; Middendorf, Nils; Weigend, Florian

2018-03-01

We present an efficient algorithm for one- and two-component analytical energy gradients with respect to nuclear displacements in the exact two-component decoupling approach to the one-electron Dirac equation (X2C). Our approach is a generalization of the spin-free ansatz by Cheng and Gauss [J. Chem. Phys. 135, 084114 (2011)], where the perturbed one-electron Hamiltonian is calculated by solving a first-order response equation. Computational costs are drastically reduced by applying the diagonal local approximation to the unitary decoupling transformation (DLU) [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to the X2C Hamiltonian. The introduced error is found to be almost negligible as the mean absolute error of the optimized structures amounts to only 0.01 pm. Our implementation in TURBOMOLE is also available within the finite nucleus model based on a Gaussian charge distribution. For a X2C/DLU gradient calculation, computational effort scales cubically with the molecular size, while storage increases quadratically. The efficiency is demonstrated in calculations of large silver clusters and organometallic iridium complexes.

Time-dependent mean-field theory for x-ray near-edge spectroscopy

NASA Astrophysics Data System (ADS)

Bertsch, G. F.; Lee, A. J.

2014-02-01

We derive equations of motion for calculating the near-edge x-ray absorption spectrum in molecules and condensed matter, based on a two-determinant approximation and Dirac's variational principle. The theory provides an exact solution for the linear response when the Hamiltonian or energy functional has only diagonal interactions in some basis. We numerically solve the equations to compare with the Mahan-Nozières-De Dominicis theory of the edge singularity in metallic conductors. Our extracted power-law exponents are similar to those of the analytic theory, but are not in quantitative agreement. The calculational method can be readily generalized to treat Kohn-Sham Hamiltonians with electron-electron interactions derived from correlation-exchange potentials.

Dynamical spin structure factors of α-RuCl3

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi; Suga, Sei-ichiro

2018-03-01

Honeycomb-lattice magnet α-RuCl3 is considered to be a potential candidate of realizing Kitaev spin liquid, although this material undergoes a phase transition to the zigzag magnetically ordered state at T N ∼ 7 K. Quite recently, inelastic neutron-scattering experiments using single crystal α-RuCl3 have unveiled characteristic dynamical properties. We calculate dynamical spin structure factors of three ab-initio models for α-RuCl3 with an exact numerical diagonalization method. We also calculate temperature dependences of the specific heat by employing thermal pure quantum states. We compare our numerical results with the experiments and discuss characteristics obtained by using three ab-initio models.

Quantum Monte Carlo calculations of two neutrons in finite volume

DOE PAGES

Klos, P.; Lynn, J. E.; Tews, I.; ...

2016-11-18

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial formore » determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.« less

Exact solution of the XXX Gaudin model with generic open boundaries

NASA Astrophysics Data System (ADS)

Hao, Kun; Cao, Junpeng; Yang, Tao; Yang, Wen-Li

2015-03-01

The XXX Gaudin model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices is studied. Besides the inhomogeneous parameters, the associated Gaudin operators have six free parameters which break the U(1) -symmetry. With the help of the off-diagonal Bethe ansatz, we successfully obtained the eigenvalues of these Gaudin operators and the corresponding Bethe ansatz equations.

Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study.

PubMed

Goli, V M L Durga Prasad; Sahoo, Shaon; Ramasesha, S; Sen, Diptiman

2013-03-27

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J2) and dimerization (δ). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J2-δ plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

Investigating decoherence in a simple system

NASA Technical Reports Server (NTRS)

Albrecht, Andreas

1991-01-01

The results of some simple calculations designed to study quantum decoherence are presented. The physics of quantum decoherence are briefly reviewed, and a very simple 'toy' model is analyzed. Exact solutions are found using numerical techniques. The type of incoherence exhibited by the model can be changed by varying a coupling strength. The author explains why the conventional approach to studying decoherence by checking the diagonality of the density matrix is not always adequate. Two other approaches, the decoherence functional and the Schmidt paths approach, are applied to the toy model and contrasted to each other. Possible problems with each are discussed.

Wigner molecules in carbon-nanotube quantum dots

NASA Astrophysics Data System (ADS)

Secchi, Andrea; Rontani, Massimo

2010-07-01

We demonstrate that electrons in quantum dots defined by electrostatic gates in semiconductor nanotubes freeze orderly in space realizing a “Wigner molecule.” Our exact diagonalization calculations uncover the features of the electron molecule, which may be accessed by tunneling spectroscopy—indeed some of them have already been observed by Deshpande and Bockrath [Nat. Phys. 4, 314 (2008)]10.1038/nphys895. We show that numerical results are satisfactorily reproduced by a simple ansatz vibrational wave function: electrons have localized wave functions, like nuclei in an ordinary molecule, whereas low-energy excitations are collective vibrations of electrons around their equilibrium positions.

Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit

NASA Astrophysics Data System (ADS)

Mallayya, Krishnanand; Rigol, Marcos

2018-02-01

We implement numerical linked cluster expansions (NLCEs) to study dynamics of lattice systems following quantum quenches, and focus on a hard-core boson model in one-dimensional lattices. We find that, in the nonintegrable regime and within the accessible times, local observables exhibit exponential relaxation. We determine the relaxation rate as one departs from the integrable point and show that it scales quadratically with the strength of the integrability breaking perturbation. We compare the NLCE results with those from exact diagonalization calculations on finite chains with periodic boundary conditions, and show that NLCEs are far more accurate.

Role of heat equation in lap joint for welding process

NASA Astrophysics Data System (ADS)

Kumar, P.; Rohit, Sooraj

2017-07-01

Welding is predominantly used in industrial purposes and growth in their industry, which gives exact welding and more efficient. The major advantage of using this welding technique at initial stage it takes very low heat to weld the portion and gives a good result of low distortion in modules. In this context, two dissimilar metals copper and nickel are chosen for analysis in tungsten inert gas welding (TIG) in which length is 300 mm and breadth is 100 mm thickness 15 mm welded at room temperature a welded portion zone is formed simulation analysis has done on CATIA® and ANSYS®and MATLAB® code is generated for calculating temperatures at each node to calculate temperature at each node a new technique is used tri-diagonal matrix algorithm is used (TDMA) Steady state one dimension heat is calculated results compared between simulation analysis and analytical analysis temperature at each node is calculated both the temperatures are equal with error.

An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach

DOE PAGES

Yu, Hua-Gen

2002-01-01

We present a full dimensional variational algorithm to calculate vibrational energies of penta-atomic molecules. The quantum mechanical Hamiltonian of the system for J=0 is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame without any dynamical approximation. Moreover, the vibrational Hamiltonian has been obtained in an explicitly Hermitian form. Variational calculations are performed in a direct product discrete variable representation basis set. The sine functions are used for the radial coordinates, whereas the Legendre polynomials are employed for the polar angles. For the azimuthal angles, the symmetrically adapted Fourier–Chebyshev basis functions are utilized. The eigenvalue problem ismore » solved by a Lanczos iterative diagonalization algorithm. The preliminary application to methane is given. Ultimately, we made a comparison with previous results.« less

Generalized approximate spin projection calculations of effective exchange integrals of the CaMn4O5 cluster in the S1 and S3 states of the oxygen evolving complex of photosystem II.

PubMed

Isobe, H; Shoji, M; Yamanaka, S; Mino, H; Umena, Y; Kawakami, K; Kamiya, N; Shen, J-R; Yamaguchi, K

2014-06-28

Full geometry optimizations followed by the vibrational analysis were performed for eight spin configurations of the CaMn4O4X(H2O)3Y (X = O, OH; Y = H2O, OH) cluster in the S1 and S3 states of the oxygen evolution complex (OEC) of photosystem II (PSII). The energy gaps among these configurations obtained by vertical, adiabatic and adiabatic plus zero-point-energy (ZPE) correction procedures have been used for computation of the effective exchange integrals (J) in the spin Hamiltonian model. The J values are calculated by the (1) analytical method and the (2) generalized approximate spin projection (AP) method that eliminates the spin contamination errors of UB3LYP solutions. Using J values derived from these methods, exact diagonalization of the spin Hamiltonian matrix was carried out, yielding excitation energies and spin densities of the ground and lower-excited states of the cluster. The obtained results for the right (R)- and left (L)-opened structures in the S1 and S3 states are found to be consistent with available optical and magnetic experimental results. Implications of the computational results are discussed in relation to (a) the necessity of the exact diagonalization for computations of reliable energy levels, (b) magneto-structural correlations in the CaMn4O5 cluster of the OEC of PSII, (c) structural symmetry breaking in the S1 and S3 states, and (d) the right- and left-handed scenarios for the O-O bond formation for water oxidation.

Static holes in the geometrically frustrated bow-tie ladder

NASA Astrophysics Data System (ADS)

Martins, George B.; Brenig, Wolfram

2008-10-01

We investigate the doping of a geometrically frustrated spin ladder with static holes by a complementary approach using exact diagonalization and quantum dimers. Results for thermodynamic properties, the singlet density of states, the hole-binding energy and the spin correlations will be presented. For the undoped systems the ground state is non-degenerate, with translationally invariant nearest-neighbor spin correlations. For the doped case, we find that static holes polarize their vicinity through a localization of singlets, reducing the frustration. This polarization induces short range repulsive forces between two holes and an oscillatory behavior of the long range two-hole energy. For most quantities investigated, we find very good agreement between the quantum dimer approach and the results from exact diagonalization.

Angular-momentum couplings in ultra-long-range giant dipole molecules

NASA Astrophysics Data System (ADS)

Stielow, Thomas; Scheel, Stefan; Kurz, Markus

2018-02-01

In this article we extend the theory of ultra-long-range giant dipole molecules, formed by an atom in a giant dipole state and a ground-state alkali-metal atom, by angular-momentum couplings known from recent works on Rydberg molecules. In addition to s -wave scattering, the next higher order of p -wave scattering in the Fermi pseudopotential describing the binding mechanism is considered. Furthermore, the singlet and triplet channels of the scattering interaction as well as angular-momentum couplings such as hyperfine interaction and Zeeman interactions are included. Within the framework of Born-Oppenheimer theory, potential energy surfaces are calculated in both first-order perturbation theory and exact diagonalization. Besides the known pure triplet states, mixed-spin character states are obtained, opening up a whole new landscape of molecular potentials. We determine exact binding energies and wave functions of the nuclear rotational and vibrational motion numerically from the various potential energy surfaces.

Accurate collision-induced line-coupling parameters for the fundamental band of CO in He - Close coupling and coupled states scattering calculations

NASA Technical Reports Server (NTRS)

Green, Sheldon; Boissoles, J.; Boulet, C.

1988-01-01

The first accurate theoretical values for off-diagonal (i.e., line-coupling) pressure-broadening cross sections are presented. Calculations were done for CO perturbed by He at thermal collision energies using an accurate ab initio potential energy surface. Converged close coupling, i.e., numerically exact values, were obtained for coupling to the R(0) and R(2) lines. These were used to test the coupled states (CS) and infinite order sudden (IOS) approximate scattering methods. CS was found to be of quantitative accuracy (a few percent) and has been used to obtain coupling values for lines to R(10). IOS values are less accurate, but, owing to their simplicity, may nonetheless prove useful as has been recently demonstrated.

Electronic States and Persistent Currents in Nanowire Quantum Ring

NASA Astrophysics Data System (ADS)

Kokurin, I. A.

2018-04-01

The new model of a quantum ring (QR) defined inside a nanowire (NW) is proposed. The one-particle Hamiltonian for electron in [111]-oriented NW QR is constructed taking into account both Rashba and Dresselhaus spin-orbit coupling (SOC). The energy levels as a function of magnetic field are found using the exact numerical diagonalization. The persistent currents (both charge and spin) are calculated. The specificity of SOC and arising anticrossings in energy spectrum lead to unusual features in persistent current behavior. The variation of magnetic field or carrier concentration by means of gate can lead to pure spin persistent current with the charge current being zero.

Sparse polynomial space approach to dissipative quantum systems: application to the sub-ohmic spin-boson model.

PubMed

Alvermann, A; Fehske, H

2009-04-17

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral, and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behavior, and dissipative spin dynamics in the spin-boson model.

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

Mazzarella, G.; Toigo, F.; Salasnich, L.

We consider a bosonic Josephson junction made of N ultracold and dilute atoms confined by a quasi-one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schroedinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information F, the coherence by means of the visibilitymore » {alpha} of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy S. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for F and {alpha} to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.« less

Unveiling magnetic interactions of ruthenium trichloride via constraining direction of orbital moments: Potential routes to realize a quantum spin liquid

NASA Astrophysics Data System (ADS)

Hou, Y. S.; Xiang, H. J.; Gong, X. G.

2017-08-01

Recent experiments reveal that the honeycomb ruthenium trichloride α -RuC l3 is a prime candidate of the Kitaev quantum spin liquid (QSL). However, there is no theoretical model which can properly describe its experimental dynamical response due to the lack of a full understanding of its magnetic interactions. Here, we propose a general scheme to calculate the magnetic interactions in systems (e.g., α -RuC l3 ) with nonnegligible orbital moments by constraining the directions of orbital moments. With this scheme, we put forward a minimal J1-K1-Γ1-J3-K3 model for α -RuC l3 and find that: (I) The third nearest neighbor (NN) antiferromagnetic Heisenberg interaction J3 stabilizes the zigzag antiferromagnetic order; (II) The NN symmetric off-diagonal exchange Γ1 plays a pivotal role in determining the preferred direction of magnetic moments and generating the spin wave gap. An exact diagonalization study on this model shows that the Kitaev QSL can be realized by suppressing the NN symmetric off-diagonal exchange Γ1 and the third NN Heisenberg interaction J3. Thus, we not only propose a powerful general scheme for investigating the intriguing magnetism of Jeff=1 /2 magnets, but also point out future directions for realizing the Kitaev QSL in the honeycomb ruthenium trichloride α -RuC l3 .

Towards an exact theory of linear absorbance and circular dichroism of pigment-protein complexes: Importance of non-secular contributions

NASA Astrophysics Data System (ADS)

Dinh, Thanh-Chung; Renger, Thomas

2015-01-01

A challenge for the theory of optical spectra of pigment-protein complexes is the equal strength of the pigment-pigment and the pigment-protein couplings. Treating both on an equal footing so far can only be managed by numerically costly approaches. Here, we exploit recent results on a normal mode analysis derived spectral density that revealed the dominance of the diagonal matrix elements of the exciton-vibrational coupling in the exciton state representation. We use a cumulant expansion technique that treats the diagonal parts exactly, includes an infinite summation of the off-diagonal parts in secular and Markov approximations, and provides a systematic perturbative way to include non-secular and non-Markov corrections. The theory is applied to a model dimer and to chlorophyll (Chl) a and Chl b homodimers of the reconstituted water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The model calculations reveal that the non-secular/non-Markov effects redistribute oscillator strength from the strong to the weak exciton transition in absorbance and they diminish the rotational strength of the exciton transitions in circular dichroism. The magnitude of these corrections is in a few percent range of the overall signal, providing a quantitative explanation of the success of time-local convolution-less density matrix theory applied earlier. A close examination of the optical spectra of Chl a and Chl b homodimers in WSCP suggests that the opening angle between Qy transition dipole moments in Chl b homodimers is larger by about 9∘ than for Chl a homodimers for which a crystal structure of a related WSCP complex exists. It remains to be investigated whether this change is due to a different mutual geometry of the pigments or due to the different electronic structures of Chl a and Chl b.

QCD dipole model and k T factorization

NASA Astrophysics Data System (ADS)

Bialas, A.; Navelet, H.; Peschanski, R.

2001-01-01

It is shown that the colour dipole approach to hard scattering at high energy is fully compatible with k T factorization at the leading logarithm approximation (in - logx Bj). The relations between the dipole amplitudes and unintegrated diagonal and non-diagonal gluon distributions are given. It is also shown that including the exact gluon kinematics in the k T factorization formula destroys the conservation of transverse position vectors and thus is incompatible with the dipole model for both elastic and diffractive amplitudes.

Theoretical treatment of the spin-orbit coupling in the rare gas oxides NeO, ArO, KrO, and XeO

NASA Technical Reports Server (NTRS)

Langhoff, S. R.

1980-01-01

Off-diagonal spin-orbit matrix elements are calculated as a function of internuclear distance for the rare gas oxides NeO, ArO, KrO, and XeO using the full microscopic spin-orbit Hamiltonian, including all one- and two-electron integrals, and POL-CI wave functions comparable to those of Dunning and Hay (1977). A good agreement was found when comparing these results in detail with the calculations of Cohen, Wadt and Hay (1979) that utilize an effective one-electron one-center spin-orbit operator. For the rare gas oxide molecules, it is suggested that the numerical results are a more sensitive test of the wave functions (particularly to the extent of charge transfer) than the exact evaluation of all terms in the full spin-orbit operator.

J dependence in the LSDA+U treatment of noncollinear magnets

NASA Astrophysics Data System (ADS)

Bousquet, Eric; Spaldin, Nicola

2010-12-01

We re-examine the commonly used density-functional theory plus Hubbard U (DFT+U) method for the case of noncollinear magnets. While many studies neglect to explicitly include the exchange-correction parameter J , or consider its exact value to be unimportant, here we show that in the case of noncollinear magnetism calculations the J parameter can strongly affect the magnetic ground state. We illustrate the strong J dependence of magnetic canting and magnetocrystalline anisotropy by calculating trends in the magnetic lithium orthophosphate family LiMPO4 ( M=Fe and Ni) and difluorite family MF2 ( M=Mn , Fe, Co, and Ni). Our results can be readily understood by expanding the usual DFT+U equations within the spinor scheme, in which the J parameter acts directly on the off-diagonal components which determine the spin canting.

Hole pairing and thermodynamic properties of the two dimensional frustrated t-J model

NASA Astrophysics Data System (ADS)

Roy, K.; Pal, P.; Nath, S.; Ghosh, N. K.

2018-04-01

The frustrated t-J model is investigated by using the exact-diagonalization (ED) method on an 8-site cluster. The effect on next-nearest-neighbor (NNN) exchange interaction J' (frustration) on the hole pairing and the thermodynamic properties of the system is considered. Two holes initially remain unbound at smaller value of J'/t, but tend to bind at larger value. The maximum possibility of pair formation has been observed to be at NNN sites. Entropy calculation shows that the system goes to more disordered state with J'. The specific heat curves show a single peak structure. A decrease in effective exchange energy is observed due to the frustration.

Optical coefficients in a semiconductor quantum ring: Electric field and donor impurity effects

NASA Astrophysics Data System (ADS)

Duque, C. M.; Acosta, Ruben E.; Morales, A. L.; Mora-Ramos, M. E.; Restrepo, R. L.; Ojeda, J. H.; Kasapoglu, E.; Duque, C. A.

2016-10-01

The electron states in a two-dimensional quantum dot ring are calculated in the presence of a donor impurity atom under the effective mass and parabolic band approximations. The effect of an externally applied electric field is also taken into account. The wavefunctions are obtained via the exact diagonalization of the problem Hamiltonian using a 2D expansion within the adiabatic approximation. The impurity-related optical response is analyzed via the optical absorption, relative refractive index change and the second harmonics generation. The dependencies of the electron states and these optical coefficients with the changes in the configuration of the quantum ring system are discussed in detail.

Comparative DMFT study of the eg-orbital Hubbard model in thin films

NASA Astrophysics Data System (ADS)

Rüegg, Andreas; Hung, Hsiang-Hsuan; Gull, Emanuel; Fiete, Gregory A.

2014-02-01

Heterostructures of transition-metal oxides have emerged as a new route to engineer electronic systems with desired functionalities. Motivated by these developments, we study a two-orbital Hubbard model in a thin-film geometry confined along the cubic [001] direction using the dynamical mean-field theory. We contrast the results of two approximate impurity solvers (exact diagonalization and one-crossing approximation) to the results of the numerically exact continuous-time quantum Monte Carlo solver. Consistent with earlier studies, we find that the one-crossing approximation performs well in the insulating regime, while the advantage of the exact-diagonalization-based solver is more pronounced in the metallic regime. We then investigate various aspects of strongly correlated eg-orbital systems in thin-film geometries. In particular, we show how the interfacial orbital polarization dies off quickly a few layers from the interface and how the film thickness affects the location of the interaction-driven Mott transition. In addition, we explore the changes in the electronic structure with varying carrier concentration and identify large variations of the orbital polarization in the strongly correlated regime.

A theoretical study of the dissociative recombination of SH+ with electrons through the 2Π states of SH.

PubMed

Kashinski, D O; Talbi, D; Hickman, A P; Di Nallo, O E; Colboc, F; Chakrabarti, K; Schneider, I F; Mezei, J Zs

2017-05-28

A quantitative theoretical study of the dissociative recombination of SH + with electrons has been carried out. Multireference, configuration interaction calculations were used to determine accurate potential energy curves for SH + and SH. The block diagonalization method was used to disentangle strongly interacting SH valence and Rydberg states and to construct a diabatic Hamiltonian whose diagonal matrix elements provide the diabatic potential energy curves. The off-diagonal elements are related to the electronic valence-Rydberg couplings. Cross sections and rate coefficients for the dissociative recombination reaction were calculated with a stepwise version of the multichannel quantum defect theory, using the molecular data provided by the block diagonalization method. The calculated rates are compared with the most recent measurements performed on the ion Test Storage Ring (TSR) in Heidelberg, Germany.

Bayesian block-diagonal variable selection and model averaging

PubMed Central

Papaspiliopoulos, O.; Rossell, D.

2018-01-01

Summary We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf. PMID:29861501

A new family of high-order compact upwind difference schemes with good spectral resolution

NASA Astrophysics Data System (ADS)

Zhou, Qiang; Yao, Zhaohui; He, Feng; Shen, M. Y.

2007-12-01

This paper presents a new family of high-order compact upwind difference schemes. Unknowns included in the proposed schemes are not only the values of the function but also those of its first and higher derivatives. Derivative terms in the schemes appear only on the upwind side of the stencil. One can calculate all the first derivatives exactly as one solves explicit schemes when the boundary conditions of the problem are non-periodic. When the proposed schemes are applied to periodic problems, only periodic bi-diagonal matrix inversions or periodic block-bi-diagonal matrix inversions are required. Resolution optimization is used to enhance the spectral representation of the first derivative, and this produces a scheme with the highest spectral accuracy among all known compact schemes. For non-periodic boundary conditions, boundary schemes constructed in virtue of the assistant scheme make the schemes not only possess stability for any selective length scale on every point in the computational domain but also satisfy the principle of optimal resolution. Also, an improved shock-capturing method is developed. Finally, both the effectiveness of the new hybrid method and the accuracy of the proposed schemes are verified by executing four benchmark test cases.

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order.

PubMed

Reiher, Markus; Wolf, Alexander

2004-12-08

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented. (c) 2004 American Institute of Physics.

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

Ma, Xiaoyao; Hall, Randall W.; Löffler, Frank

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methodsmore » and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.« less

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

NASA Astrophysics Data System (ADS)

Sadurní, E.; Torres, J. M.; Seligman, T. H.

2010-07-01

The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of a solution is given by recasting the known solution of the Dirac oscillator into matrix form; there one notes that a block-diagonal form arises in a Hamiltonian formulation. The blocks are two dimensional. Choosing couplings that do not affect the block structure, these blow up the 2 × 2 matrices to 4 × 4 matrices, thus conserving solvability. The result can be cast again in covariant form. By way of an example we apply this exact solution to calculate the evolution of entanglement.

Spin-state transition in LaCoO3 by variational cluster approximation

NASA Astrophysics Data System (ADS)

Eder, R.

2010-01-01

The variational cluster approximation (VCA) is applied to the calculation of thermodynamical quantities and single-particle spectra of LaCoO3 . Trial self-energies and the numerical value of the Luttinger-Ward functional are obtained by exact diagonalization of a CoO6 cluster. The VCA correctly predicts LaCoO3 as a paramagnetic insulator, and a gradual and relatively smooth increase in the occupation of high-spin Co3+ ions causes the temperature dependence of entropy and magnetic susceptibility. The single-particle spectral function agrees well with experiment; the experimentally observed temperature dependence of photoelectron spectra is reproduced satisfactorily. Remaining discrepancies with experiment highlight the importance of spin-orbit coupling and local lattice relaxation.

Competing orders in the Hofstadter t -J model

NASA Astrophysics Data System (ADS)

Tu, Wei-Lin; Schindler, Frank; Neupert, Titus; Poilblanc, Didier

2018-01-01

The Hofstadter model describes noninteracting fermions on a lattice in the presence of an external magnetic field. Motivated by the plethora of solid-state phases emerging from electron interactions, we consider an interacting version of the Hofstadter model, including a Hubbard repulsion U . We investigate this model in the large-U limit corresponding to a t -J Hamiltonian with an external (orbital) magnetic field. By using renormalized mean-field theory supplemented by exact diagonalization calculations of small clusters, we find evidence for competing symmetry-breaking phases, exhibiting (possibly coexisting) charge, bond, and superconducting orders. Topological properties of the states are also investigated, and some of our results are compared to related experiments involving ultracold atoms loaded on optical lattices in the presence of a synthetic gauge field.

Strong spin-orbit effects in transition metal oxides with tetrahedral coordination

NASA Astrophysics Data System (ADS)

Forte, Filomena; Guerra, Delia; Autieri, Carmine; Romano, Alfonso; Noce, Canio; Avella, Adolfo

2018-05-01

To prove that spin-orbit coupling can play a relevant role in determining the magnetic structure of transition metal oxides with tetrahedral coordination, we investigate the d1 Mott insulator KOsO4, combining density functional theory calculations and the exact diagonalization approach. We find that the interplay between crystal field, strong spin-orbit coupling, electronic correlations and structural distortions brings the system towards an antiferromagnetic phase, characterized by a non-vanishing orbital angular momentum and anisotropy among the in-plane and the out-of-plane antiferromagnetic correlations. We also show that, due to the peculiar interplay between spin-orbit coupling, Hund's coupling and hopping connectivity the system is on the verge of developing short range ferromagnetic correlations marked by strong directionality.

Current collapse in tunneling transport through benzene.

PubMed

Hettler, M H; Wenzel, W; Wegewijs, M R; Schoeller, H

2003-02-21

We investigate the electrical transport through a system of benzene coupled to metal electrodes by electron tunneling. Using electronic structure calculations, a semiquantitative model for the pi electrons of the benzene is derived that includes general two-body interactions. After exact diagonalization of the benzene model the transport is computed using perturbation theory for weak electrode-benzene coupling (golden rule approximation). We include the effect of an applied electric field on the molecular states, as well as radiative relaxation. We predict a current collapse and strong negative differential conductance due to a "blocking" state when the electrode is coupled to the para-position of benzene. In contrast, for coupling to the meta-position, a series of steps in the I-V curve is found.

Line mixing effects in isotropic Raman spectra of pure N{sub 2}: A classical trajectory study

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

Ivanov, Sergey V., E-mail: serg.vict.ivanov@gmail.com; Boulet, Christian; Buzykin, Oleg G.

2014-11-14

Line mixing effects in the Q branch of pure N{sub 2} isotropic Raman scattering are studied at room temperature using a classical trajectory method. It is the first study using an extended modified version of Gordon's classical theory of impact broadening and shift of rovibrational lines. The whole relaxation matrix is calculated using an exact 3D classical trajectory method for binary collisions of rigid N{sub 2} molecules employing the most up-to-date intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve off-diagonal cross-sections to make them obeying exactly the principle of detailed balance. The adequacy of themore » results is confirmed by the sum rule. The comparison is made with available experimental data as well as with benchmark fully quantum close coupling [F. Thibault, C. Boulet, and Q. Ma, J. Chem. Phys. 140, 044303 (2014)] and refined semi-classical Robert-Bonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semi-classical) were made using the same PES. The agreement between classical and quantum relaxation matrices is excellent, opening the way to the analysis of more complex molecular systems.« less

Static Holes in Geometrically Frustrated Bow Tie Ladder

NASA Astrophysics Data System (ADS)

Martins, George; Brenig, Wolfram

2007-03-01

Doping of the geometrically frustrated bow-tie spin ladder with static holes is investigated by a complementary approach using exact diagonalization and hard-core quantum dimers. Results for the thermodynamics in the undoped case, the singlet density of states, the hole-binding energy, and the spin correlations will be presented. We find that the static holes polarize their vicinity by a localization of singlets in order to reduce the frustration. As a consequence the singlet polarization cloud induces short range repulsive forces between the holes with oscillatory longer range behavior. For those systems we have studied, most results for the quantum dimer approach are found to be qualitatively if not quantitatively in agreement with exact diagonalization. The ground state of the undoped system is non-degenerate with translationally invariant nearest-neighbor spin correlations up to a few unit cells, which is consistent with a spin liquid state or a valence bond crystal with very large unit cell. C. Waldtmann, A. Kreutzmann, U. Schollwock, K. Maisinger, and H.-U. Everts, Phys. Rev. B 62, 9472 (2000).

Quantum Entanglement and the Topological Order of Fractional Hall States

NASA Astrophysics Data System (ADS)

Rezayi, Edward

2015-03-01

Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140.

Polaron dynamics with a multitude of Davydov D{sub 2} trial states

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

Zhou, Nengji; Department of Physics, Hangzhou Normal University, Hangzhou 310046; Huang, Zhongkai

2015-07-07

We propose an extension to the Davydov D{sub 2} Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the “multi-D{sub 2} Ansatz” is a linear combination of Davydov D{sub 2} trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schrödinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D{sub 1} and D{sub 2} Ansätze. With an increase in the number ofmore » the Davydov D{sub 2} trial states in the multi-D{sub 2} Ansatz, deviation from the exact Schrödinger dynamics is gradually diminished, leading to a numerically exact solution to the Schrödinger equation.« less

Confined One Dimensional Harmonic Oscillator as a Two-Mode System

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

Gueorguiev, V G; Rau, A P; Draayer, J P

2005-07-11

The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in anymore » other way. An alternative to casting the problem in terms of one or the other basis set consists of using an ''oblique'' basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful.« less

Rashba quantum wire: exact solution and ballistic transport.

PubMed

Perroni, C A; Bercioux, D; Ramaglia, V Marigliano; Cataudella, V

2007-05-08

The effect of Rashba spin-orbit interaction in quantum wires with hard-wall boundaries is discussed. The exact wavefunction and eigenvalue equation are worked out, pointing out the mixing between the spin and spatial parts. The spectral properties are also studied within perturbation theory with respect to the strength of the spin-orbit interaction and diagonalization procedure. A comparison is made with the results of a simple model, the two-band model, that takes account only of the first two sub-bands of the wire. Finally, the transport properties within the ballistic regime are analytically calculated for the two-band model and through a tight-binding Green function for the entire system. Single and double interfaces separating regions with different strengths of spin-orbit interaction are analysed by injecting carriers into the first and the second sub-band. It is shown that in the case of a single interface the spin polarization in the Rashba region is different from zero, and in the case of two interfaces the spin polarization shows oscillations due to spin-selective bound states.

Effective model with strong Kitaev interactions for α -RuCl3

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi; Suga, Sei-ichiro

2018-04-01

We use an exact numerical diagonalization method to calculate the dynamical spin structure factors of three ab initio models and one ab initio guided model for a honeycomb-lattice magnet α -RuCl3 . We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor spin-spin correlation function, and the static spin structure factor. From the results obtained from these four effective models, we find that, even when the magnetic order is stabilized at low temperature, the intensity at the Γ point in the dynamical spin structure factors increases with increasing nearest-neighbor spin correlation. In addition, we find that the four models fail to explain heat-capacity measurements whereas two of the four models succeed in explaining inelastic-neutron-scattering experiments. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function increases. However, the peak temperature in heat capacity is too low in comparison with that observed experimentally. To address these discrepancies, we propose an effective model that includes strong ferromagnetic Kitaev coupling, and we show that this model quantitatively reproduces both inelastic-neutron-scattering experiments and heat-capacity measurements. To further examine the adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra, which reproduces the experimental results: the spin-gapped excitation survives up to an onset field where the magnetic order disappears and the response in the high-field region is almost linear. Based on these numerical results, we argue that the low-energy magnetic excitation in α -RuCl3 is mainly characterized by interactions such as off-diagonal interactions and weak Heisenberg interactions between nearest-neighbor pairs, rather than by the strong Kitaev interactions.

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

Ma, Xiaoyao; Hall, Randall W.; Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H{sub 2}O, N{sub 2}, and F{sub 2} molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of othermore » quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.« less

Numerical study of the Kitaev-Heisenberg chain

NASA Astrophysics Data System (ADS)

Agrapidis, Cliò Efthimia; van den Brink, Jeroen; Nishimoto, Satoshi

2018-05-01

We study the one-dimensional Kitaev-Heisenberg model as a possible realization of magnetic degrees of freedom of the K-intercalated honeycomb-lattice ruthenium trichloride α-RuCl3, denoted as K0.5RuClm. First, we discuss the possible charge ordering pattern in K0.5RuClm, where half of the j =1/2 spins are replaced by nonmagnetic ions in the honeycomb layer. Next, we investigate the low-energy excitations of the 1D Kitaev-Heisenberg model by calculating the dynamical spin structure factor using the Lanczos exact-diagonalization method. In the vicinity of Kitaev limit, there exist two well-separated dispersions. The bandwidth of each dispersion depends on the Heisenberg and Kitaev terms. This result may be relevant to the low-lying magnetic excitations of K0.5RuClm.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison.

PubMed

Kumar, Santosh; Dietz, Barbara; Guhr, Thomas; Richter, Achim

2017-12-15

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

NASA Astrophysics Data System (ADS)

Kumar, Santosh; Dietz, Barbara; Guhr, Thomas; Richter, Achim

2017-12-01

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

Discrete Fourier Transform in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2015-01-01

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Entanglement in the Anisotropic Kondo Necklace Model

NASA Astrophysics Data System (ADS)

Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.

We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.

Hybrid Monte Carlo approach to the entanglement entropy of interacting fermions

NASA Astrophysics Data System (ADS)

Drut, Joaquín E.; Porter, William J.

2015-09-01

The Monte Carlo calculation of Rényi entanglement entropies Sn of interacting fermions suffers from a well-known signal-to-noise problem, even for a large number of situations in which the infamous sign problem is absent. A few methods have been proposed to overcome this issue, such as ensemble switching and the use of auxiliary partition-function ratios. Here, we present an approach that builds on the recently proposed free-fermion decomposition method; it incorporates entanglement in the probability measure in a natural way; it takes advantage of the hybrid Monte Carlo algorithm (an essential tool in lattice quantum chromodynamics and other gauge theories with dynamical fermions); and it does not suffer from noise problems. This method displays no sign problem for the same cases as other approaches and is therefore useful for a wide variety of systems. As a proof of principle, we calculate S2 for the one-dimensional, half-filled Hubbard model and compare with results from exact diagonalization and the free-fermion decomposition method.

Improving stochastic estimates with inference methods: calculating matrix diagonals.

PubMed

Selig, Marco; Oppermann, Niels; Ensslin, Torsten A

2012-02-01

Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image reconstruction and statistical inference. Here, methods of statistical inference are used to improve the accuracy or the computational costs of matrix probing methods to estimate matrix diagonals. In particular, the generalized Wiener filter methodology, as developed within information field theory, is shown to significantly improve estimates based on only a few sampling probes, in cases in which some form of continuity of the solution can be assumed. The strength, length scale, and precise functional form of the exploited autocorrelation function of the matrix diagonal is determined from the probes themselves. The developed algorithm is successfully applied to mock and real world problems. These performance tests show that, in situations where a matrix diagonal has to be calculated from only a small number of computationally expensive probes, a speedup by a factor of 2 to 10 is possible with the proposed method. © 2012 American Physical Society

Semiempirical evaluation of post-Hartree-Fock diagonal-Born-Oppenheimer corrections for organic molecules.

PubMed

Mohallem, José R

2008-04-14

Recent post-Hartree-Fock calculations of the diagonal-Born-Oppenheimer correction empirically show that it behaves quite similar to atomic nuclear mass corrections. An almost constant contribution per electron is identified, which converges with system size for specific series of organic molecules. This feature permits pocket-calculator evaluation of the corrections within thermochemical accuracy (10(-1) mhartree or kcal/mol).

Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases.

PubMed

Papenbrock, T; Reimann, S M; Kavoulakis, G M

2012-02-17

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consist of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.

Quantum Field Theory in Two Dimensions: Light-front Versus Space-like Solutions

NASA Astrophysics Data System (ADS)

Martinovic̆, L'ubomír

2017-07-01

A few non-perturbative topics of quantum field theory in D=1+1 are studied in both the conventional (SL) and light-front (LF) versions. First, we give a concise review of the recently proposed quantization of the two-dimensional massless LF fields. The LF version of bosonization follows in a simple and natural way including the bosonized form of the Thirring model. As a further application, we demonstrate the closeness of the 2D massless LF quantum fields to conformal field theory (CFT). We calculate several correlation functions including those between the components of the LF energy-momentum tensor and derive the LF version of the Virasoro algebra. Using the Euclidean time variable, we can immediately transform calculated quantities to the (anti)holomorphic form. The results found are in agreement with those from CFT. Finally, we show that the proposed framework provides us with the elements needed for an independent LF study of exactly solvable models. We compute the non-perturbative correlation functions from the exact operator solution of the LF Thirring model and compare it to the analogous results in the SL theory. While the vacuum effects are automatically taken into account in the LF case, the non-trivial vacuum structure has to be incorported by an explicit diagonalization of the SL Hamiltonians, to obtain the equivalently complete solution.

Isovector and flavor-diagonal charges of the nucleon

NASA Astrophysics Data System (ADS)

Gupta, Rajan; Bhattacharya, Tanmoy; Jang, Yong-Chull; Lin, Huey-Wen; Yoon, Boram

2018-03-01

We present an update on the status of the calculations of isovector and flavor-diagonal charges of the nucleon. The calculations of the isovector charges are being done using ten 2+1+1-flavor HISQ ensembles generated by the MILC collaboration covering the range of lattice spacings a ≈ 0.12, 0.09, 0.06 fm and pion masses Mπ ≈ 310, 220, 130 MeV. Excited-states contamination is controlled by using four-state fits to two-point correlators and three-states fits to the three-point correlators. The calculations of the disconnected diagrams needed to estimate flavor-diagonal charges are being done on a subset of six ensembles using the stocastic method. Final results are obtained using a simultaneous fit in M2π, the lattice spacing a and the finite volume parameter MπL keeping only the leading order corrections.

Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations

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

Cai, Yunfeng, E-mail: yfcai@math.pku.edu.cn; Department of Computer Science, University of California, Davis 95616; Bai, Zhaojun, E-mail: bai@cs.ucdavis.edu

2013-12-15

The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for ab initio electronic structure calculations. We propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative diagonalization of such eigenvalue problems. In partition-of-unity finite-element (PUFE) pseudopotential density-functional calculations, employing a nonorthogonal basis, we show that the hybrid preconditioned block steepest descent method is a cost-effective eigensolver, outperforming current state-of-the-art global preconditioning schemes, and comparably efficient for the ill-conditioned generalized eigenvalue problems produced by PUFE as the locally optimal blockmore » preconditioned conjugate-gradient method for the well-conditioned standard eigenvalue problems produced by planewave methods.« less

Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales

NASA Astrophysics Data System (ADS)

Winter, Stephen M.; Li, Ying; Jeschke, Harald O.; Valentí, Roser

2016-06-01

In this study, we reanalyze the magnetic interactions in the Kitaev spin-liquid candidate materials Na2IrO3,α -RuCl3 , and α -Li2IrO3 using nonperturbative exact diagonalization methods. These methods are more appropriate given the relatively itinerant nature of the systems suggested in previous works. We treat all interactions up to third neighbors on equal footing. The computed terms reveal significant long-range coupling, bond anisotropy, and/or off-diagonal couplings which we argue naturally explain the observed ordered phases in these systems. Given these observations, the potential for realizing the spin-liquid state in real materials is analyzed, and synthetic challenges are defined and explained.

Vaidya spacetime in the diagonal coordinates

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

Berezin, V. A., E-mail: berezin@inr.ac.ru; Dokuchaev, V. I., E-mail: dokuchaev@inr.ac.ru; Eroshenko, Yu. N., E-mail: eroshenko@inr.ac.ru

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric andmore » cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g{sub 00} = 0 or g{sub 00} = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.« less

Two Universality Classes for the Many-Body Localization Transition

NASA Astrophysics Data System (ADS)

Khemani, Vedika; Sheng, D. N.; Huse, David A.

2017-08-01

We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the first dominated by "intrinsic" intrasample randomness, and the second dominated by external intersample quenched randomness. We show that the effects of intersample quenched randomness are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the external-randomness-dominated universality class. Our results provide an explanation for why exact-diagonalization studies on random models see an apparent scaling near the transition while also obtaining finite-size scaling exponents that strongly violate Harris-Chayes bounds that apply to disorder-driven transitions. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects.

Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Pollet, Lode; Sorg, Stefan; Vidmar, Lev

2015-03-01

We study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. The same interaction quench was realized in a recent experiment. Using exact diagonalization and the density-matrix renormalization-group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis and we observe that the microcanonical ensemble describes the time averages of many observables reasonably well for small and intermediate interaction strength. Moreover, the diagonal and the canonical ensembles are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Supported by the DFG through FOR 801 and the Alexander von Humboldt foundation.

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

NASA Astrophysics Data System (ADS)

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris; Dagotto, Elbio

2015-06-01

Lattice spin-fermion models are important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the "spins," are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The "traveling cluster approximation" (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 103 sites. In this publication, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. This allows us to solve generic spin-fermion models easily on 104 lattice sites and with some effort on 105 lattice sites, representing the record lattice sizes studied for this family of models.

Raman Scattering from Higgs Mode Oscillations in the Two-Dimensional Antiferromagnet Ca_{2}RuO_{4}.

PubMed

Souliou, Sofia-Michaela; Chaloupka, Jiří; Khaliullin, Giniyat; Ryu, Gihun; Jain, Anil; Kim, B J; Le Tacon, Matthieu; Keimer, Bernhard

2017-08-11

We present and analyze Raman spectra of the Mott insulator Ca_{2}RuO_{4}, whose quasi-two-dimensional antiferromagnetic order has been described as a condensate of low-lying spin-orbit excitons with angular momentum J_{eff}=1. In the A_{g} polarization geometry, the amplitude (Higgs) mode of the spin-orbit condensate is directly probed in the scalar channel, thus avoiding infrared-singular magnon contributions. In the B_{1g} geometry, we observe a single-magnon peak as well as two-magnon and two-Higgs excitations. Model calculations using exact diagonalization quantitatively agree with the observations. Together with recent neutron scattering data, our study provides strong evidence for excitonic magnetism in Ca_{2}RuO_{4} and points out new perspectives for research on the Higgs mode in two dimensions.

Raman Scattering from Higgs Mode Oscillations in the Two-Dimensional Antiferromagnet Ca2RuO4

NASA Astrophysics Data System (ADS)

Souliou, Sofia-Michaela; Chaloupka, Jiří; Khaliullin, Giniyat; Ryu, Gihun; Jain, Anil; Kim, B. J.; Le Tacon, Matthieu; Keimer, Bernhard

2017-08-01

We present and analyze Raman spectra of the Mott insulator Ca2RuO4 , whose quasi-two-dimensional antiferromagnetic order has been described as a condensate of low-lying spin-orbit excitons with angular momentum Jeff=1 . In the Ag polarization geometry, the amplitude (Higgs) mode of the spin-orbit condensate is directly probed in the scalar channel, thus avoiding infrared-singular magnon contributions. In the B1 g geometry, we observe a single-magnon peak as well as two-magnon and two-Higgs excitations. Model calculations using exact diagonalization quantitatively agree with the observations. Together with recent neutron scattering data, our study provides strong evidence for excitonic magnetism in Ca2 RuO4 and points out new perspectives for research on the Higgs mode in two dimensions.

Quantum criticality and first-order transitions in the extended periodic Anderson model

NASA Astrophysics Data System (ADS)

Hagymási, I.; Itai, K.; Sólyom, J.

2013-03-01

We investigate the behavior of the periodic Anderson model in the presence of d-f Coulomb interaction (Udf) using mean-field theory, variational calculation, and exact diagonalization of finite chains. The variational approach based on the Gutzwiller trial wave function gives a critical value of Udf and two quantum critical points (QCPs), where the valence susceptibility diverges. We derive the critical exponent for the valence susceptibility and investigate how the position of the QCP depends on the other parameters of the Hamiltonian. For larger values of Udf, the Kondo regime is bounded by two first-order transitions. These first-order transitions merge into a triple point at a certain value of Udf. For even larger Udf valence skipping occurs. Although the other methods do not give a critical point, they support this scenario.

Analysis of solar spectra in the middle ultraviolet and visible for atmospheric trace constituents measurements. [hydroxyl radicals

NASA Technical Reports Server (NTRS)

Goldman, A.

1980-01-01

Individual spectral line parameters including line positions, strengths, and intensities were generated for the sq Alpha Sigma - sq Chi Pi (0,0) band of OH, applicable to atmospheric and high temperatures. Energy levels and transition frequencies are calculated by numerically diagonalizing the Hamiltonian. Line strengths are calculated using the dipole matrix and eigenvectors derived from energy matrix diagonalization. The line strengths are compared to those calculated from previously published algebraic line strength formulas. Tables of line parameters are presented for 240 K and 4600 K.

Fast, exact k-space sample density compensation for trajectories composed of rotationally symmetric segments, and the SNR-optimized image reconstruction from non-Cartesian samples.

PubMed

Mitsouras, Dimitris; Mulkern, Robert V; Rybicki, Frank J

2008-08-01

A recently developed method for exact density compensation of non uniformly arranged samples relies on the analytically known cross-correlations of Fourier basis functions corresponding to the traced k-space trajectory. This method produces a linear system whose solution represents compensated samples that normalize the contribution of each independent element of information that can be expressed by the underlying trajectory. Unfortunately, linear system-based density compensation approaches quickly become computationally demanding with increasing number of samples (i.e., image resolution). Here, it is shown that when a trajectory is composed of rotationally symmetric interleaves, such as spiral and PROPELLER trajectories, this cross-correlations method leads to a highly simplified system of equations. Specifically, it is shown that the system matrix is circulant block-Toeplitz so that the linear system is easily block-diagonalized. The method is described and demonstrated for 32-way interleaved spiral trajectories designed for 256 image matrices; samples are compensated non iteratively in a few seconds by solving the small independent block-diagonalized linear systems in parallel. Because the method is exact and considers all the interactions between all acquired samples, up to a 10% reduction in reconstruction error concurrently with an up to 30% increase in signal to noise ratio are achieved compared to standard density compensation methods. (c) 2008 Wiley-Liss, Inc.

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.

Robotic Compliant Motion Control for Aircraft Refueling Applications

DTIC Science & Technology

1988-12-01

J. DUVALL 29 SEP 88 C-26 SUBROUTINE IMPCONST(CONST,MINV, BMAT ) Abstract: This subroutine calculates the 25 constants used by the Fortran subroutine...mass with center of gravity along the joint 6 axis. The desired mass and the damping ( BMAT ) matrices are assumed to be diagonal. Joints angles 4,5...constants. MINV -- A 2x2 matrix containing the elements of the inverse desired mass matrix (diagonal). BMAT -- A 2x2 matrix of damping coefficents (diagonal

Gapless spin excitations in the S = 1 / 2 Kagome- and triangular-lattice Heisenberg antiferromagnets

NASA Astrophysics Data System (ADS)

Sakai, Tôru; Nakano, Hiroki

2018-05-01

The S = 1 / 2 kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.

Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations

NASA Technical Reports Server (NTRS)

Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.

1998-01-01

We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.

Nonequilibrium thermo-chemical calculations using a diagonal implicit scheme

NASA Technical Reports Server (NTRS)

Imlay, Scott T.; Roberts, Donald W.; Soetrisno, Moeljo; Eberhardt, Scott

1991-01-01

A recently developed computer program for hypersonic vehicle flow analysis is described. The program uses a diagonal implicit algorithm to solve the equations of viscous flow for a gas in thermochemical nonequilibrium. The diagonal scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The program uses multiple zones of grids patched together and includes radiation wall and rarefied gas boundary conditions. Solutions are presented for hypersonic flows of air and hydrogen air mixtures.

Transformation matrices between non-linear and linear differential equations

NASA Technical Reports Server (NTRS)

Sartain, R. L.

1983-01-01

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

N-H stretching modes of adenosine monomer in solution studied by ultrafast nonlinear infrared spectroscopy and ab initio calculations.

PubMed

Greve, Christian; Preketes, Nicholas K; Costard, Rene; Koeppe, Benjamin; Fidder, Henk; Nibbering, Erik T J; Temps, Friedrich; Mukamel, Shaul; Elsaesser, Thomas

2012-07-26

The N-H stretching vibrations of adenine, one of the building blocks of DNA, are studied by combining infrared absorption and nonlinear two-dimensional infrared spectroscopy with ab initio calculations. We determine diagonal and off-diagonal anharmonicities of N-H stretching vibrations in chemically modified adenosine monomer dissolved in chloroform. For the single-quantum excitation manifold, the normal mode picture with symmetric and asymmetric NH(2) stretching vibrations is fully appropriate. For the two-quantum excitation manifold, however, the interplay between intermode coupling and frequency shifts due to a large diagonal anharmonicity leads to a situation where strong mixing does not occur. We compare our findings with previously reported values obtained on overtone spectroscopy of coupled hydrogen stretching oscillators.

Wigner crystalline edges in ν<~1 quantum dots

NASA Astrophysics Data System (ADS)

Goldmann, Eyal; Renn, Scot R.

1999-12-01

We investigate the edge reconstruction phenomenon believed to occur in quantum dots in the quantum Hall regime when the filling fraction is ν<~1. Our approach involves the examination of large dots (<= 40 electrons) using a partial diagonalization technique in which the occupancies of the deep interior orbitals are frozen. To interpret the results of this calculation, we evaluate the overlap between the diagonalized ground state and a set of trial wave functions which we call projected necklace (PN) states. A PN state is simply the angular momentum projection of a maximum density droplet surrounded by a ring of localized electrons. Our calculations reveal that PN states have up to 99% overlap with the diagonalized ground states, and are lower in energy than the states identified in Chamon and Wen's study of the edge reconstruction.

Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model

NASA Astrophysics Data System (ADS)

Nishiyama, Yoshihiro

2018-04-01

The criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model was investigated numerically. The dynamical conductivity (associated with the O(3) symmetry) displays the inductor σ( ω) = ( iωL)-1 and capacitor iωC behaviors for the ordered and disordered phases, respectively. Both constants, C and L, have the same scaling dimension as that of the reciprocal paramagnetic gap Δ -1. Then, there arose a question to fix the set of critical amplitude ratios among them. So far, the O(2) case has been investigated in the context of the boson-vortex duality. In this paper, we employ the exact diagonalization method, which enables us to calculate the paramagnetic gap Δ directly. Thereby, the set of critical amplitude ratios as to C, L and Δ are estimated with the finite-size-scaling analysis for the cluster with N ≤ 34 spins.

Scrambling of quantum information in quantum many-body systems

NASA Astrophysics Data System (ADS)

Iyoda, Eiki; Sagawa, Takahiro

2018-04-01

We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is delocalized. We clarify that scrambling is an independent property of the integrability of Hamiltonians; TMI can be negative or positive for both integrable and nonintegrable systems. This implies that scrambling is a separate concept from conventional quantum chaos characterized by nonintegrability. Specifically, we argue that there are a few exceptional initial states that do not exhibit scrambling, and show that such exceptional initial states have small effective dimensions. Furthermore, we calculate TMI in the Sachdev-Ye-Kitaev (SYK) model, a fermionic toy model of quantum gravity. We find that disorder does not make scrambling slower but makes it smoother in the SYK model, in contrast to many-body localization in spin chains.

Effects of geometrical frustration on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice

NASA Astrophysics Data System (ADS)

Farkašovský, Pavol

2018-05-01

The small-cluster exact-diagonalization calculations and the projector quantum Monte Carlo method are used to examine the competing effects of geometrical frustration and interaction on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice. It is shown that the geometrical frustration stabilizes the ferromagnetic state at high electron concentrations ( n ≳ 7/4), where strong correlations between ferromagnetism and the shape of the noninteracting density of states are observed. In particular, it is found that ferromagnetism is stabilized for these values of frustration parameters, which lead to the single-peaked noninterating density of states at the band edge. Once, two or more peaks appear in the noninteracting density of states at the band edge the ferromagnetic state is suppressed. This opens a new route towards the understanding of ferromagnetism in strongly correlated systems.

Electronic excitations in γ -Li2IrO3

NASA Astrophysics Data System (ADS)

Li, Ying; Winter, Stephen M.; Jeschke, Harald O.; Valentí, Roser

2017-01-01

We investigate the electronic properties of the three-dimensional stripyhoneycomb γ -Li2IrO3 via relativistic density functional theory calculations as well as exact diagonalization of finite clusters and explore the details of the optical conductivity. Our analysis of this quantity reveals the microscopic origin of the experimentally observed (i) optical transitions and (ii) anisotropic behavior along the various polarization directions. In particular, we find that the optical excitations are overall dominated by transitions between jeff=1 /2 and 3/2 states and the weight of transitions between jeff=1 /2 states at low frequencies can be correlated to deviations from a pure Kitaev description. We furthermore reanalyze within this approach the electronic excitations in the known two-dimensional honeycomb systems α -Li2IrO3 and Na2IrO3 and discuss the results in comparison to γ -Li2IrO3 .

Electronic entanglement in late transition metal oxides.

PubMed

Thunström, Patrik; Di Marco, Igor; Eriksson, Olle

2012-11-02

We present a study of the entanglement in the electronic structure of the late transition metal monoxides--MnO, FeO, CoO, and NiO--obtained by means of density-functional theory in the local density approximation combined with dynamical mean-field theory. The impurity problem is solved through exact diagonalization, which grants full access to the thermally mixed many-body ground state density operator. The quality of the electronic structure is affirmed through a direct comparison between the calculated electronic excitation spectrum and photoemission experiments. Our treatment allows for a quantitative investigation of the entanglement in the electronic structure. Two main sources of entanglement are explicitly resolved through the use of a fidelity based geometrical entanglement measure, and additional information is gained from a complementary entropic entanglement measure. We show that the interplay of crystal field effects and Coulomb interaction causes the entanglement in CoO to take a particularly intricate form.

Topological gapped edge states in fractional quantum Hall-superconductor heterostructures

NASA Astrophysics Data System (ADS)

Cook, Ashley; Repellin, Cécile; Regnault, Nicolas; Neupert, Titus

We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. We focus on a time-reversal symmetric bilayer fractional quantum Hall system of Laughlin ν = 1 / 3 states. The fully gapped edges carry a topological parafermionic degree of freedom that can encode quantum information protected against local perturbations. We numerically simulate such a system using exact diagonalization by restricting the calculation to the Laughlin quasihole subspace. We study the quantization of the total charge on each edge and show that the ground states are permuted by spin flux insertion and the parafermionic Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The full affiliation for Author 3 is: Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

PubMed Central

Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581

Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?

NASA Astrophysics Data System (ADS)

Gandolfi, S.; Hammer, H.-W.; Klos, P.; Lynn, J. E.; Schwenk, A.

2017-06-01

We present quantum Monte Carlo calculations of few-neutron systems confined in external potentials based on local chiral interactions at next-to-next-to-leading order in chiral effective field theory. The energy and radial densities for these systems are calculated in different external Woods-Saxon potentials. We assume that their extrapolation to zero external-potential depth provides a quantitative estimate of three- and four-neutron resonances. The validity of this assumption is demonstrated by benchmarking with an exact diagonalization in the two-body case. We find that the extrapolated trineutron resonance, as well as the energy for shallow well depths, is lower than the tetraneutron resonance energy. This suggests that a three-neutron resonance exists below a four-neutron resonance in nature and is potentially measurable. To confirm that the relative ordering of three- and four-neutron resonances is not an artifact of the external confinement, we test that the odd-even staggering in the helium isotopic chain is reproduced within this approach. Finally, we discuss similarities between our results and ultracold Fermi gases.

Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?

DOE PAGES

Gandolfi, Stefano; Hammer, Hans -Werner; Klos, P.; ...

2017-06-08

Here, we present quantum Monte Carlo calculations of few-neutron systems confined in external potentials based on local chiral interactions at next-to-next-to-leading order in chiral effective field theory. The energy and radial densities for these systems are calculated in different external Woods-Saxon potentials. We assume that their extrapolation to zero external-potential depth provides a quantitative estimate of three- and four-neutron resonances. The validity of this assumption is demonstrated by benchmarking with an exact diagonalization in the two-body case. We find that the extrapolated trineutron resonance, as well as the energy for shallow well depths, is lower than the tetraneutron resonance energy.more » This suggests that a three-neutron resonance exists below a four-neutron resonance in nature and is potentially measurable. To confirm that the relative ordering of three- and four-neutron resonances is not an artifact of the external confinement, we test that the odd-even staggering in the helium isotopic chain is reproduced within this approach. Finally, we discuss similarities between our results and ultracold Fermi gases.« less

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order

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

Reiher, Markus; Wolf, Alexander

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exactmore » decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented.« less

Spectral Quadrature method for accurate O ( N ) electronic structure calculations of metals and insulators

DOE PAGES

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

2015-12-02

We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order tomore » exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N 3) planewave results. In conclusion, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.« less

Deforming black hole and cosmological solutions by quasiperiodic and/or pattern forming structures in modified and Einstein gravity

NASA Astrophysics Data System (ADS)

Bubuianu, Laurenţiu; Vacaru, Sergiu I.

2018-05-01

We elaborate on the anholonomic frame deformation method, AFDM, for constructing exact solutions with quasiperiodic structure in modified gravity theories, MGTs, and general relativity, GR. Such solutions are described by generic off-diagonal metrics, nonlinear and linear connections and (effective) matter sources with coefficients depending on all spacetime coordinates via corresponding classes of generation and integration functions and (effective) matter sources. There are studied effective free energy functionals and nonlinear evolution equations for generating off-diagonal quasiperiodic deformations of black hole and/or homogeneous cosmological metrics. The physical data for such functionals are stated by different values of constants and prescribed symmetries for defining quasiperiodic structures at cosmological scales, or astrophysical objects in nontrivial gravitational backgrounds some similar forms as in condensed matter physics. It is shown how quasiperiodic structures determined by general nonlinear, or additive, functionals for generating functions and (effective) sources may transform black hole like configurations into cosmological metrics and inversely. We speculate on possible implications of quasiperiodic solutions in dark energy and dark matter physics. Finally, it is concluded that geometric methods for constructing exact solutions consist an important alternative tool to numerical relativity for investigating nonlinear effects in astrophysics and cosmology.

Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order

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

Thingna, Juzar; Wang, Jian-Sheng; Haenggi, Peter

A novel scheme for the steady state solution of the standard Redfield quantum master equation is developed which yields agreement with the exact result for the corresponding reduced density matrix up to second order in the system-bath coupling strength. We achieve this objective by use of an analytic continuation of the off-diagonal matrix elements of the Redfield solution towards its diagonal limit. Notably, our scheme does not require the provision of yet higher order relaxation tensors. Testing this modified method for a heat bath consisting of a collection of harmonic oscillators we assess that the system relaxes towards its correctmore » coupling-dependent, generalized quantum Gibbs state in second order. We numerically compare our formulation for a damped quantum harmonic system with the nonequilibrium Green's function formalism: we find good agreement at low temperatures for coupling strengths that are even larger than expected from the very regime of validity of the second-order Redfield quantum master equation. Yet another advantage of our method is that it markedly reduces the numerical complexity of the problem; thus, allowing to study efficiently large-sized system Hilbert spaces.« less

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

DOE PAGES

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris; ...

2015-06-08

Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA)more » is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10 3 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10 4 lattice sites and with some effort on 10 5 lattice sites, representing the record lattice sizes studied for this family of models.« less

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

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

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris

Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA)more » is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10 3 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10 4 lattice sites and with some effort on 10 5 lattice sites, representing the record lattice sizes studied for this family of models.« less

Magneto-transport properties of a two-dimensional electron gas under lateral periodic modulation

NASA Astrophysics Data System (ADS)

Shi, Qinwei

Several physical systems related to two-dimensional electron gas (2DEG) subjected to an electric or a magnetic modulation at various strength have been theoretically studied. In Chapter 3, a quantum transport theory is developed for the calculation of magnetoresistance rhoxx in a 2DEG subjected to strong one-dimensional periodic potential and at low uniform magnetic field (the Weiss oscillations regime). The theory is based on the exact diagonalization of the Hamiltonian and the constant relaxation time approximation. The theoretical predictions are in good agreement with the experimental results. The discrepancy between the classical calculation and the experiment is removed in our quantum treatment. In particular, the quenching of the Weiss oscillations is understood in this framework. In Chapter 4, the non-perturbative method for electric modulated system (EMS) is used to calculate the magnetoresistance rhoxx for a magnetic modulated system (MMS), which is a 2DEG subjected to strong one-dimensional periodic magnetic modulation and at low uniform magnetic field. As the amplitude of magnetic modulation increases we first find a quenching of the low fields oscillations. This is similar to the quenching of the Weiss oscillations in the EMS case. As the strength of the magnetic modulation increases further, a new series of oscillations appears in our calculation. The temperature dependence of these new oscillations shows that the basic mechanism of these oscillations is similar to Weiss oscillations, and the origin can be identified with the extra term in the Hamiltonian for the MMS case. In Chapter 5, a self-consistent quantum transport theory is developed to calculate magnetocoductivities in a 2DEG subjected to strong one-dimensional periodic potential and at high uniform magnetic field (SdH oscillation regime). The theory is based on the self-consistent Born approximation (SCBA) for the randomly distributed short-range impurities together with an exact diagonalization of the Hamiltonian. Quantum oscillations of magneto conductivities as a function of the amplitude of electric modulation are calculated and the basic mechanism behind these oscillations is discussed. In chapter 6, a tight-binding model is used to discuss the energy spectrum of 2DEG subjected to a strong two-dimensional magnetic modulation and a uniform magnetic field corresponding to a rational value of magnetic flux per unit cell f=pqf0. Some symmetries broken in the case of one-dimensional magnetic modulation are recovered in the two-dimensional case. Furthermore, when q is even, the magnetic Bloch band is broken into q subbands; while for odd q, the magnetic Bloch band is broken into 2 q subbands. This has interesting implication on the magnetotransport properties as one changes f . Our energy spectrum is similar but more complex than the Hofstadter's butterfly. Some suggestions to observe the new fractal energy spectrum are made.

Teaching the "Diagonalization Concept" in Linear Algebra with Technology: A Case Study at Galatasaray University

ERIC Educational Resources Information Center

Yildiz Ulus, Aysegul

2013-01-01

This paper examines experimental and algorithmic contributions of advanced calculators (graphing and computer algebra system, CAS) in teaching the concept of "diagonalization," one of the key topics in Linear Algebra courses taught at the undergraduate level. Specifically, the proposed hypothesis of this study is to assess the effective…

Exact Fundamental Limits of the First and Second Hyperpolarizabilities

NASA Astrophysics Data System (ADS)

Lytel, Rick; Mossman, Sean; Crowell, Ethan; Kuzyk, Mark G.

2017-08-01

Nonlinear optical interactions of light with materials originate in the microscopic response of the molecular constituents to excitation by an optical field, and are expressed by the first (β ) and second (γ ) hyperpolarizabilities. Upper bounds to these quantities were derived seventeen years ago using approximate, truncated state models that violated completeness and unitarity, and far exceed those achieved by potential optimization of analytical systems. This Letter determines the fundamental limits of the first and second hyperpolarizability tensors using Monte Carlo sampling of energy spectra and transition moments constrained by the diagonal Thomas-Reiche-Kuhn (TRK) sum rules and filtered by the off-diagonal TRK sum rules. The upper bounds of β and γ are determined from these quantities by applying error-refined extrapolation to perfect compliance with the sum rules. The method yields the largest diagonal component of the hyperpolarizabilities for an arbitrary number of interacting electrons in any number of dimensions. The new method provides design insight to the synthetic chemist and nanophysicist for approaching the limits. This analysis also reveals that the special cases which lead to divergent nonlinearities in the many-state catastrophe are not physically realizable.

Diagonalizing the Hamiltonian of λϕ4 theory in 2 space-time dimensions

NASA Astrophysics Data System (ADS)

Christensen, Neil

2018-01-01

We propose a new non-perturbative technique for calculating the scattering amplitudes of field-theory directly from the eigenstates of the Hamiltonian. Our method involves a discretized momentum space and a momentum cutoff, thereby truncating the Hilbert space and making numerical diagonalization of the Hamiltonian achievable. We show how to do this in the context of a simplified λϕ4 theory in two space-time dimensions. We present the results of our diagonalization, its dependence on time, its dependence on the parameters of the theory and its renormalization.

Fingering patterns in magnetic fluids: Perturbative solutions and the stability of exact stationary shapes

NASA Astrophysics Data System (ADS)

Anjos, Pedro H. A.; Lira, Sérgio A.; Miranda, José A.

2018-04-01

We examine the formation of interfacial patterns when a magnetic liquid droplet (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. By using a vortex-sheet formalism, we find exact stationary solutions for the fluid-fluid interface in the form of n -fold polygonal shapes. A weakly nonlinear, mode-coupling method is then utilized to find time-evolving perturbative solutions for the interfacial patterns. The stability of such nonzero surface tension exact solutions is checked and discussed, by trying to systematically approach the exact stationary shapes through perturbative solutions containing an increasingly larger number of participating Fourier modes. Our results indicate that the exact stationary solutions of the problem are stable, and that a good matching between exact and perturbative shape solutions is achieved just by using a few Fourier modes. The stability of such solutions is substantiated by a linearization process close to the stationary shape, where a system of mode-coupling equations is diagonalized, determining the eigenvalues which dictate the stability of a fixed point.

Analytical effective tensor for flow-through composites

DOEpatents

Sviercoski, Rosangela De Fatima [Los Alamos, NM

2012-06-19

A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.

A parallel algorithm for Hamiltonian matrix construction in electron-molecule collision calculations: MPI-SCATCI

NASA Astrophysics Data System (ADS)

Al-Refaie, Ahmed F.; Tennyson, Jonathan

2017-12-01

Construction and diagonalization of the Hamiltonian matrix is the rate-limiting step in most low-energy electron - molecule collision calculations. Tennyson (1996) implemented a novel algorithm for Hamiltonian construction which took advantage of the structure of the wavefunction in such calculations. This algorithm is re-engineered to make use of modern computer architectures and the use of appropriate diagonalizers is considered. Test calculations demonstrate that significant speed-ups can be gained using multiple CPUs. This opens the way to calculations which consider higher collision energies, larger molecules and / or more target states. The methodology, which is implemented as part of the UK molecular R-matrix codes (UKRMol and UKRMol+) can also be used for studies of bound molecular Rydberg states, photoionization and positron-molecule collisions.

A new fast direct solver for the boundary element method

NASA Astrophysics Data System (ADS)

Huang, S.; Liu, Y. J.

2017-09-01

A new fast direct linear equation solver for the boundary element method (BEM) is presented in this paper. The idea of the new fast direct solver stems from the concept of the hierarchical off-diagonal low-rank matrix. The hierarchical off-diagonal low-rank matrix can be decomposed into the multiplication of several diagonal block matrices. The inverse of the hierarchical off-diagonal low-rank matrix can be calculated efficiently with the Sherman-Morrison-Woodbury formula. In this paper, a more general and efficient approach to approximate the coefficient matrix of the BEM with the hierarchical off-diagonal low-rank matrix is proposed. Compared to the current fast direct solver based on the hierarchical off-diagonal low-rank matrix, the proposed method is suitable for solving general 3-D boundary element models. Several numerical examples of 3-D potential problems with the total number of unknowns up to above 200,000 are presented. The results show that the new fast direct solver can be applied to solve large 3-D BEM models accurately and with better efficiency compared with the conventional BEM.

US Army Research Laboratory Power-Line UAV Modeling and Simulation (ARL-PLUMS Ver 2.x) Software Tool: User Manual and Technical Report

DTIC Science & Technology

2015-09-01

shown have units of pF/m. This is the capacitance matrix for the 115-kV 3-phase circuit seen in Fig. 24.....................................24 Fig. 29...The window that appears when one clicks “Calculate Lambdas ”. These are the linear charge densities for the 115-kV 3-phase circuit seen in Fig. 24...calculate the capacitance matrix (Fig. 28). The diagonal entries are called the coefficients of capacitance, and the non-diagonal entries are called

The calculated rovibronic spectrum of scandium hydride, ScH

NASA Astrophysics Data System (ADS)

Lodi, Lorenzo; Yurchenko, Sergei N.; Tennyson, Jonathan

2015-07-01

The electronic structure of six low-lying electronic states of scandium hydride, X 1Σ+, a 3Δ, b 3Π, A 1Δ, c 3Σ+ and B 1Π, is studied using multi-reference configuration interaction as a function of bond length. Diagonal and off-diagonal dipole moment, spin-orbit coupling and electronic angular momentum curves are also computed. The results are benchmarked against experimental measurements and calculations on atomic scandium. The resulting curves are used to compute a line list of molecular rovibronic transitions for 45ScH.

A Note on Parameters of Random Substitutions by γ-Diagonal Matrices

NASA Astrophysics Data System (ADS)

Kang, Ju-Sung

Random substitutions are very useful and practical method for privacy-preserving schemes. In this paper we obtain the exact relationship between the estimation errors and three parameters used in the random substitutions, namely the privacy assurance metric γ, the total number n of data records, and the size N of transition matrix. We also demonstrate some simulations concerning the theoretical result.

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.

Quantum entanglement and criticality of the antiferromagnetic Heisenberg model in an external field.

PubMed

Liu, Guang-Hua; Li, Ruo-Yan; Tian, Guang-Shan

2012-06-27

By Lanczos exact diagonalization and the infinite time-evolving block decimation (iTEBD) technique, the two-site entanglement as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization in the antiferromagnetic Heisenberg (AFH) model under an external field are investigated. With increasing external field, the small size system shows some distinct upward magnetization stairsteps, accompanied synchronously with some downward two-site entanglement stairsteps. In the thermodynamic limit, the two-site entanglement, as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization are calculated, and the critical magnetic field h(c) = 2.0 is determined exactly. Our numerical results show that the quantum entanglement is sensitive to the subtle changing of the ground state, and can be used to describe the magnetization and quantum phase transition. Based on the discontinuous behavior of the first-order derivative of the entanglement entropy and fidelity per site, we think that the quantum phase transition in this model should belong to the second-order category. Furthermore, in the magnon existence region (h < 2.0), a logarithmically divergent behavior of block entanglement which can be described by a free bosonic field theory is observed, and the central charge c is determined to be 1.

Excited state correlations of the finite Heisenberg chain

NASA Astrophysics Data System (ADS)

Pozsgay, Balázs

2017-02-01

We consider short range correlations in excited states of the finite XXZ and XXX Heisenberg spin chains. We conjecture that the known results for the factorized ground state correlations can be applied to the excited states too, if the so-called physical part of the construction is changed appropriately. For the ground state we derive simple algebraic expressions for the physical part; the formulas only use the ground state Bethe roots as an input. We conjecture that the same formulas can be applied to the excited states as well, if the exact Bethe roots of the excited states are used instead. In the XXZ chain the results are expected to be valid for all states (except certain singular cases where regularization is needed), whereas in the XXX case they only apply to singlet states or group invariant operators. Our conjectures are tested against numerical data from exact diagonalization and coordinate Bethe Ansatz calculations, and perfect agreement is found in all cases. In the XXX case we also derive a new result for the nearest-neighbour correlator < σ 1zσ 2z> , which is valid for non-singlet states as well. Our results build a bridge between the known theory of factorized correlations, and the recently conjectured TBA-like description for the building blocks of the construction.

Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model

NASA Astrophysics Data System (ADS)

Dorfner, F.; Vidmar, L.; Brockt, C.; Jeckelmann, E.; Heidrich-Meisner, F.

2015-03-01

We study the real-time dynamics of a highly excited charge carrier coupled to quantum phonons via a Holstein-type electron-phonon coupling. This is a prototypical example for the nonequilibrium dynamics in an interacting many-body system where excess energy is transferred from electronic to phononic degrees of freedom. We use diagonalization in a limited functional space (LFS) to study the nonequilibrium dynamics on a finite one-dimensional chain. This method agrees with exact diagonalization and the time-evolving block-decimation method, in both the relaxation regime and the long-time stationary state, and among these three methods it is the most efficient and versatile one for this problem. We perform a comprehensive analysis of the time evolution by calculating the electron, phonon and electron-phonon coupling energies, and the electronic momentum distribution function. The numerical results are compared to analytical solutions for short times, for a small hopping amplitude and for a weak electron-phonon coupling. In the latter case, the relaxation dynamics obtained from the Boltzmann equation agrees very well with the LFS data. We also study the time dependence of the eigenstates of the single-site reduced density matrix, which defines the so-called optimal phonon modes. We discuss their structure in nonequilibrium and the distribution of their weights. Our analysis shows that the structure of optimal phonon modes contains very useful information for the interpretation of the numerical data.

Higher-order gravitational lensing reconstruction using Feynman diagrams

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

Jenkins, Elizabeth E.; Manohar, Aneesh V.; Yadav, Amit P.S.

2014-09-01

We develop a method for calculating the correlation structure of the Cosmic Microwave Background (CMB) using Feynman diagrams, when the CMB has been modified by gravitational lensing, Faraday rotation, patchy reionization, or other distorting effects. This method is used to calculate the bias of the Hu-Okamoto quadratic estimator in reconstructing the lensing power spectrum up to  O (φ{sup 4}) in the lensing potential φ. We consider both the diagonal noise TT TT, EB EB, etc. and, for the first time, the off-diagonal noise TT TE, TB EB, etc. The previously noted large  O (φ{sup 4}) term in the second order noise ismore » identified to come from a particular class of diagrams. It can be significantly reduced by a reorganization of the φ expansion. These improved estimators have almost no bias for the off-diagonal case involving only one B component of the CMB, such as EE EB.« less

Implementation of the diagonalization-free algorithm in the self-consistent field procedure within the four-component relativistic scheme.

PubMed

Hrdá, Marcela; Kulich, Tomáš; Repiský, Michal; Noga, Jozef; Malkina, Olga L; Malkin, Vladimir G

2014-09-05

A recently developed Thouless-expansion-based diagonalization-free approach for improving the efficiency of self-consistent field (SCF) methods (Noga and Šimunek, J. Chem. Theory Comput. 2010, 6, 2706) has been adapted to the four-component relativistic scheme and implemented within the program package ReSpect. In addition to the implementation, the method has been thoroughly analyzed, particularly with respect to cases for which it is difficult or computationally expensive to find a good initial guess. Based on this analysis, several modifications of the original algorithm, refining its stability and efficiency, are proposed. To demonstrate the robustness and efficiency of the improved algorithm, we present the results of four-component diagonalization-free SCF calculations on several heavy-metal complexes, the largest of which contains more than 80 atoms (about 6000 4-spinor basis functions). The diagonalization-free procedure is about twice as fast as the corresponding diagonalization. Copyright © 2014 Wiley Periodicals, Inc.

Hidden symmetries for ellipsoid-solitonic deformations of Kerr-Sen black holes and quantum anomalies

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2013-02-01

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and we study hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.

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

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order tomore » exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N 3) planewave results. In conclusion, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.« less

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

Can nonstandard interactions jeopardize the hierarchy sensitivity of DUNE?

NASA Astrophysics Data System (ADS)

Deepthi, K. N.; Goswami, Srubabati; Nath, Newton

2017-10-01

We study the effect of nonstandard interactions (NSIs) on the propagation of neutrinos through the Earth's matter and how it affects the hierarchy sensitivity of the DUNE experiment. We emphasize the special case when the diagonal NSI parameter ɛe e=-1 , nullifying the standard matter effect. We show that if, in addition, C P violation is maximal then this gives rise to an exact intrinsic hierarchy degeneracy in the appearance channel, irrespective of the baseline and energy. Introduction of the off diagonal NSI parameter, ɛe τ, shifts the position of this degeneracy to a different ɛe e. Moreover the unknown magnitude and phases of the off diagonal NSI parameters can give rise to additional degeneracies. Overall, given the current model independent limits on NSI parameters, the hierarchy sensitivity of DUNE can get seriously impacted. However, a more precise knowledge of the NSI parameters, especially ɛe e, can give rise to an improved sensitivity. Alternatively, if a NSI exists in nature, and still DUNE shows hierarchy sensitivity, certain ranges of the NSI parameters can be excluded. Additionally, we briefly discuss the implications of ɛe e=-1 (in the Earth) on the Mikheyev-Smirnov-Wolfenstein effect in the Sun.

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

NASA Astrophysics Data System (ADS)

Jahromi, Saeed S.; Orús, Román; Kargarian, Mehdi; Langari, Abdollah

2018-03-01

The infinite projected entangled-pair state (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the corner transfer matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground-state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground-state fidelity, and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.

Probing α -RuCl3 Beyond Magnetic Order: Effects of Temperature and Magnetic Field

NASA Astrophysics Data System (ADS)

Winter, Stephen M.; Riedl, Kira; Kaib, David; Coldea, Radu; Valentí, Roser

2018-02-01

Recent studies have brought α -RuCl3 to the forefront of experimental searches for materials realizing Kitaev spin-liquid physics. This material exhibits strongly anisotropic exchange interactions afforded by the spin-orbit coupling of the 4 d Ru centers. We investigate the dynamical response at finite temperature and magnetic field for a realistic model of the magnetic interactions in α -RuCl3 . These regimes are thought to host unconventional paramagnetic states that emerge from the suppression of magnetic order. Using exact diagonalization calculations of the quantum model complemented by semiclassical analysis, we find a very rich evolution of the spin dynamics as the applied field suppresses the zigzag order and stabilizes a quantum paramagnetic state that is adiabatically connected to the fully polarized state at high fields. At finite temperature, we observe large redistributions of spectral weight that can be attributed to the anisotropic frustration of the model. These results are compared to recent experiments and provide a road map for further studies of these regimes.

Raman and fluorescence characteristics of resonant inelastic X-ray scattering from doped superconducting cuprates

DOE PAGES

Huang, H. Y.; Jia, C. J.; Chen, Z. Y.; ...

2016-01-22

Measurements of spin excitations are essential for an understanding of spin-mediated pairing for superconductivity; and resonant inelastic X-ray scattering (RIXS) provides a considerable opportunity to probe high-energy spin excitations. However, whether RIXS correctly measures the collective spin excitations of doped superconducting cuprates remains under debate. Here we demonstrate distinct Raman- and fluorescence-like RIXS excitations of Bi1.5Pb0.6Sr1.54CaCu2O8+δ. Combining photon-energy and momentum dependent RIXS measurements with theoretical calculations using exact diagonalization provides conclusive evidence that the Raman-like RIXS excitations correspond to collective spin excitations, which are magnons in the undoped Mott insulators and evolve into paramagnons in doped superconducting compounds. In contrast,more » the fluorescence-like shifts are due primarily to the continuum of particle-hole excitations in the charge channel. Our results show that under the proper experimental conditions RIXS indeed can be used to probe paramagnons in doped high-Tc cuprate superconductors.« less

Markov-modulated Markov chains and the covarion process of molecular evolution.

PubMed

Galtier, N; Jean-Marie, A

2004-01-01

The covarion (or site specific rate variation, SSRV) process of biological sequence evolution is a process by which the evolutionary rate of a nucleotide/amino acid/codon position can change in time. In this paper, we introduce time-continuous, space-discrete, Markov-modulated Markov chains as a model for representing SSRV processes, generalizing existing theory to any model of rate change. We propose a fast algorithm for diagonalizing the generator matrix of relevant Markov-modulated Markov processes. This algorithm makes phylogeny likelihood calculation tractable even for a large number of rate classes and a large number of states, so that SSRV models become applicable to amino acid or codon sequence datasets. Using this algorithm, we investigate the accuracy of the discrete approximation to the Gamma distribution of evolutionary rates, widely used in molecular phylogeny. We show that a relatively large number of classes is required to achieve accurate approximation of the exact likelihood when the number of analyzed sequences exceeds 20, both under the SSRV and among site rate variation (ASRV) models.

Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures

NASA Astrophysics Data System (ADS)

Repellin, Cécile; Cook, Ashley M.; Neupert, Titus; Regnault, Nicolas

2018-03-01

Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole-subspace of a (time-reversal symmetric) bilayer fractional quantum Hall system of Laughlin ν = 1/3 states. We show that the edge ground states are permuted by spin-dependent flux insertion and demonstrate their fractional 6π Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The versatility and efficiency of our setup make it a well suited method to tackle wider questions of edge phases and phase transitions in fractional quantum Hall systems.

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

Graduate Student Support for Quantum Computing With Superconducting Charge States

DTIC Science & Technology

2005-08-31

cavity resonance frequency ωr, the atomic transition frequency Ω, and the strength of the atom- photon coupling g appearing in the Jaynes - Cummings ...the atom through the cavity. In the absence of damping, exact diagonalization of the Jaynes - Cumming Hamiltonian yields the excited eigen- states...cillating terms and omitting damping for the moment, 5 Eq. (16) reduces to the Jaynes - Cummings Hamiltonian (1) with Ω = EJ/~ and the vacuum Rabi frequency

Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

NASA Astrophysics Data System (ADS)

Seiler, Christian; Evers, Ferdinand

2016-10-01

A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.

Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

NASA Astrophysics Data System (ADS)

Weinstein, Marvin; Chandra, Ravi; Auerbach, Assa

2012-02-01

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements. In contrast to variational approaches and most implementations of DMRG, Lanczos rotations towards the ground state do not involve incremental minimizations, (e.g. sweeping procedures) which may get stuck in false local minima. The lattice of size N is partitioned into two subclusters. At each iteration the rotating Lanczos vector is compressed into two sets of nsvd small subcluster vectors using singular value decomposition. For low entanglement entropy See, (satisfied by short range Hamiltonians), the truncation error is bounded by (-nsvd^1/See). Convergence is tested for the Heisenberg model on Kagom'e clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given. Reference: arXiv:1105.0007

Time-dependent generalized Gibbs ensembles in open quantum systems

NASA Astrophysics Data System (ADS)

Lange, Florian; Lenarčič, Zala; Rosch, Achim

2018-04-01

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

The relation between the quantum discord and quantum teleportation: The physical interpretation of the transition point between different quantum discord decay regimes

NASA Astrophysics Data System (ADS)

Roszak, K.; Cywiński, Ł.

2015-10-01

We study quantum teleportation via Bell-diagonal mixed states of two qubits in the context of the intrinsic properties of the quantum discord. We show that when the quantum-correlated state of the two qubits is used for quantum teleportation, the character of the teleportation efficiency changes substantially depending on the Bell-diagonal-state parameters, which can be seen when the worst-case-scenario or best-case-scenario fidelity is studied. Depending on the parameter range, one of two types of single-qubit states is hardest/easiest to teleport. The transition between these two parameter ranges coincides exactly with the transition between the range of classical correlation decay and quantum correlation decay characteristic for the evolution of the quantum discord. The correspondence provides a physical interpretation for the prominent feature of the decay of the quantum discord.

Block-diagonalization as a tool for the robust diabatization of high-dimensional potential energy surfaces

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

Venghaus, Florian; Eisfeld, Wolfgang, E-mail: wolfgang.eisfeld@uni-bielefeld.de

2016-03-21

Robust diabatization techniques are key for the development of high-dimensional coupled potential energy surfaces (PESs) to be used in multi-state quantum dynamics simulations. In the present study we demonstrate that, besides the actual diabatization technique, common problems with the underlying electronic structure calculations can be the reason why a diabatization fails. After giving a short review of the theoretical background of diabatization, we propose a method based on the block-diagonalization to analyse the electronic structure data. This analysis tool can be used in three different ways: First, it allows to detect issues with the ab initio reference data and ismore » used to optimize the setup of the electronic structure calculations. Second, the data from the block-diagonalization are utilized for the development of optimal parametrized diabatic model matrices by identifying the most significant couplings. Third, the block-diagonalization data are used to fit the parameters of the diabatic model, which yields an optimal initial guess for the non-linear fitting required by standard or more advanced energy based diabatization methods. The new approach is demonstrated by the diabatization of 9 electronic states of the propargyl radical, yielding fully coupled full-dimensional (12D) PESs in closed form.« less

Molecular origin of differences in hole and electron mobility in amorphous Alq3--a multiscale simulation study.

PubMed

Fuchs, Andreas; Steinbrecher, Thomas; Mommer, Mario S; Nagata, Yuki; Elstner, Marcus; Lennartz, Christian

2012-03-28

In order to determine the molecular origin of the difference in electron and hole mobilities of amorphous thin films of Alq(3) (meridional Alq(3) (tris(8-hydroxyquinoline) aluminium)) we performed multiscale simulations covering quantum mechanics, molecular mechanics and lattice models. The study includes realistic disordered morphologies, polarized site energies to describe diagonal disorder, quantum chemically calculated transfer integrals for the off-diagonal disorder, inner sphere reorganization energies and an approximative scheme for outer sphere reorganization energies. Intermolecular transfer rates were calculated via Marcus-theory and mobilities were simulated via kinetic Monte Carlo simulations and by a Master Equation approach. The difference in electron and hole mobility originates from the different localization of charge density in the radical anion (more delocalized) compared to the radical cation (more confined). This results in higher diagonal disorder for holes and less favourable overlap properties for the hole transfer integrals leading to an overall higher electron mobility.

The g Factors of Ground State of Ruby and Their Pressure-Induced Shifts

NASA Astrophysics Data System (ADS)

Ma, Dongping; Zhang, Hongmei; Chen, Jurong; Liu, Yanyun

1998-12-01

By using the theory of pressure-induced shifts and the eigenfunctions at normal and various pressures obtained from the diagonalization of the complete d3 energy matrix adopting C3v symmetry, g factors of the ground state of ruby and their pressure-induced shifts have been calculated. The results are in very good agreement with the experimental data. For the precise calculation of properties of the ground skate, it is necessary to take into account the effects of all the excited states by the diagonalization of the complete energy matrix. The project (Grant No. 19744001) supported by National Natural Science Foundation of China

Rapid calculation method for Frenkel-type two-exciton states in one to three dimensions

NASA Astrophysics Data System (ADS)

Ajiki, Hiroshi

2014-07-01

Biexciton and two-exciton dissociated states of Frenkel-type excitons are well described by a tight-binding model with a nearest-neighbor approximation. Such two-exciton states in a finite-size lattice are usually calculated by numerical diagonalization of the Hamiltonian, which requires an increasing amount of computational time and memory as the lattice size increases. I develop here a rapid, memory-saving method to calculate the energies and wave functions of two-exciton states by employing a bisection method. In addition, an attractive interaction between two excitons in the tight-binding model can be obtained directly so that the biexciton energy agrees with the observed energy, without the need for the trial-and-error procedure implemented in the numerical diagonalization method.

Gyrokinetic modelling of the quasilinear particle flux for plasmas with neutral-beam fuelling

NASA Astrophysics Data System (ADS)

Narita, E.; Honda, M.; Nakata, M.; Yoshida, M.; Takenaga, H.; Hayashi, N.

2018-02-01

A quasilinear particle flux is modelled based on gyrokinetic calculations. The particle flux is estimated by determining factors, namely, coefficients of off-diagonal terms and a particle diffusivity. In this paper, the methodology to estimate the factors is presented using a subset of JT-60U plasmas. First, the coefficients of off-diagonal terms are estimated by linear gyrokinetic calculations. Next, to obtain the particle diffusivity, a semi-empirical approach is taken. Most experimental analyses for particle transport have assumed that turbulent particle fluxes are zero in the core region. On the other hand, even in the stationary state, the plasmas in question have a finite turbulent particle flux due to neutral-beam fuelling. By combining estimates of the experimental turbulent particle flux and the coefficients of off-diagonal terms calculated earlier, the particle diffusivity is obtained. The particle diffusivity should reflect a saturation amplitude of instabilities. The particle diffusivity is investigated in terms of the effects of the linear instability and linear zonal flow response, and it is found that a formula including these effects roughly reproduces the particle diffusivity. The developed framework for prediction of the particle flux is flexible to add terms neglected in the current model. The methodology to estimate the quasilinear particle flux requires so low computational cost that a database consisting of the resultant coefficients of off-diagonal terms and particle diffusivity can be constructed to train a neural network. The development of the methodology is the first step towards a neural-network-based particle transport model for fast prediction of the particle flux.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

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

Meek, Garrett A.; Levine, Benjamin G., E-mail: levine@chemistry.msu.edu

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplingsmore » at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.« less

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-05-01

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

PubMed

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

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).

Measurement of the Spectroscopic Quadrupole Moment for the 2+1 State in 10Be:. Testing AB Initio Calculations

NASA Astrophysics Data System (ADS)

Orce, J. N.; Djongolov, M.; Navratil, P.; Ball, G.; Garnsworthy, A. B.; Hackman, G.; Lassen, J.; Meissner, J.; Pearson, C. J.; Li, R.; Milovanovic, L.; Sjue, S. K. L.; Teigelhoefer, A.; Triambak, S.; Williams, S. J.; Falou, H. Al; Drake, T. E.; Andreoiu, C.; Cross, D.; Kshetri, R.; Finlay, P.; Garrett, P. E.; Leach, K. G.; Rand, E. T.; Sumithrarachchi, C. S.; Svensson, C. E.; Tardiff, E. R.; Wong, J.; Forssen, C.; Hayes, A. B.; Sarazin, F.; Stoyer, M. A.; Wu, C. Y.

2013-03-01

The highly efficient and segmented TIGRESS HPGe γ-ray array at TRIUMF has been used to perform a reorientation effect Coulomb excitation study of the 2+1 state at 3.368 MeV in 10Be. This is the first Coulomb excitation measurement that provides information on diagonal matrix elements for such a high lying first excited state from μ-ray data. With the availability of accurate lifetime data, a restriction on the diagonal < 2+1|M({E}2)|2+1> matrix element is determined. This result is compared to a no core shell model calculation with the CD-Bonn 2000 two nucleon potential.

Bethe states of the trigonometric SU(3) spin chain with generic open boundaries

NASA Astrophysics Data System (ADS)

Sun, Pei; Xin, Zhirong; Qiao, Yi; Wen, Fakai; Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Tao; Yang, Wen-Li; Shi, Kangjie

2018-06-01

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU (3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T - Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe-type eigenstates which have well-defined homogeneous limit. This exact solution provides a basis for further analyzing the thermodynamic properties and correlation functions of the anisotropic models associated with higher rank algebras.

Exchange interactions in a dinuclear manganese (II) complex with cyanopyridine-N-oxide bridging ligands

NASA Astrophysics Data System (ADS)

Markosyan, A. S.; Gaidukova, I. Yu.; Ruchkin, A. V.; Anokhin, A. O.; Irkhin, V. Yu.; Ryazanov, M. V.; Kuz'mina, N. P.; Nikiforov, V. N.

2014-01-01

The magnetic properties of dinuclear manganese(II) complex [Mn(hfa)2cpo]2 (where hfa is hexafluoroacetylacetonate anion and cpo is 4-cyanopyridine-N-oxide) are presented. The non-monotonous dependence of magnetic susceptibility is explained in terms of the hierarchy of exchange parameters by using exact diagonalization. The thermodynamic behavior of pure cpo and [Mn(hfa)2(cpo)]2 is simulated numerically by an extrapolation to spin S=5/2. The Mn-Mn exchange integral is evaluated.

Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field

NASA Astrophysics Data System (ADS)

Krokhmalskii, Taras; Baliha, Vasyl; Derzhko, Oleg; Schulenburg, Jörg; Richter, Johannes

2018-05-01

Frustrated bilayer quantum magnets have attracted attention as flat-band spin systems with unconventional thermodynamic properties. We study the low-temperature properties of a frustrated honeycomb-lattice bilayer spin-1/2 isotropic (XXX) Heisenberg antiferromagnet in a magnetic field by means of an effective low-energy theory using exact diagonalizations and quantum Monte Carlo simulations. Our main focus is on the magnetization curve and the temperature dependence of the specific heat indicating a finite-temperature phase transition in high magnetic fields.

High-Tc superconductivity: The t-J-V model and its applications

NASA Astrophysics Data System (ADS)

Roy, K.; Pal, P.; Nath, S.; Ghosh, N. K.

2017-05-01

We present numerical results of the t-J-V model in an 8-site tilted square cluster using exact diagonalization (ED) method with periodic boundary conditions. Effective hopping amplitude initially increases with inter-site Coulomb repulsion (V), but decreases at larger V's. The hole-hole correlation decreases with inter-site distances at smaller V. With the increase of Coulomb repulsion, the system becomes ordered. The specific heat curves confirm the non-Fermi liquid behavior of the system under t-J-V model.

Spectral function of few electrons in quantum wires and carbon nanotubes as a signature of Wigner localization

NASA Astrophysics Data System (ADS)

Secchi, Andrea; Rontani, Massimo

2012-03-01

We demonstrate that the profile of the space-resolved spectral function at finite temperature provides a signature of Wigner localization for electrons in quantum wires and semiconducting carbon nanotubes. Our numerical evidence is based on the exact diagonalization of the microscopic Hamiltonian of few particles interacting in gate-defined quantum dots. The minimal temperature required to suppress residual exchange effects in the spectral function image of (nanotubes) quantum wires lies in the (sub)kelvin range.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE PAGES

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin; ...

2017-11-08

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime.

PubMed

Tsiper, E V

2006-08-18

The concept of fractional charge is central to the theory of the fractional quantum Hall effect. Here I use exact diagonalization as well as configuration space renormalization to study finite clusters which are large enough to contain two independent edges. I analyze the conditions of resonant tunneling between the two edges. The "computer experiment" reveals a periodic sequence of resonant tunneling events consistent with the experimentally observed fractional quantization of electric charge in units of e/3 and e/5.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

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

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Baryon interactions from lattice QCD with physical masses — strangeness S = -1 sector —

NASA Astrophysics Data System (ADS)

Nemura, Hidekatsu; Aoki, Sinya; Doi, Takumi; Gongyo, Shinya; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Iritani, Takumi; Ishii, Noriyoshi; Miyamoto, Takaya; Sasaki, Kenji

2018-03-01

We present our recent results of baryon interactions with strangeness S = -1 based on Nambu-Bethe-Salpeter (NBS) correlation functions calculated fromlattice QCD with almost physical quark masses corresponding to (mk,mk) ≈ (146, 525) MeV and large volume (La)4 ≈ (96a)4 ≈ (8.1 fm)4. In order to perform a comprehensive study of baryon interactions, a large number of NBS correlation functions from NN to ΞΞ are calculated simultaneously by using large scale computer resources. In this contribution, we focus on the strangeness S = -1 channels of the hyperon interactions by means of HAL QCD method. Four sets of three potentials (the 3S1 - 3 D1 central, 3S1 - 3 D1 tensor, and the 1S0 central potentials) are presented for the ∑N - ∑N (the isospin I = 3/2) diagonal, the ∧N - ∧N diagonal, the ∧N → ∑N transition, and the ∑N - ∑N (I = 1/2) diagonal interactions. Scattering phase shifts for ∑N (I = 3/2) system are presented.

Tunneling splitting in double-proton transfer: direct diagonalization results for porphycene.

PubMed

Smedarchina, Zorka; Siebrand, Willem; Fernández-Ramos, Antonio

2014-11-07

Zero-point and excited level splittings due to double-proton tunneling are calculated for porphycene and the results are compared with experiment. The calculation makes use of a multidimensional imaginary-mode Hamiltonian, diagonalized directly by an effective reduction of its dimensionality. Porphycene has a complex potential energy surface with nine stationary configurations that allow a variety of tunneling paths, many of which include classically accessible regions. A symmetry-based approach is used to show that the zero-point level, although located above the cis minimum, corresponds to concerted tunneling along a direct trans - trans path; a corresponding cis - cis path is predicted at higher energy. This supports the conclusion of a previous paper [Z. Smedarchina, W. Siebrand, and A. Fernández-Ramos, J. Chem. Phys. 127, 174513 (2007)] based on the instanton approach to a model Hamiltonian of correlated double-proton transfer. A multidimensional tunneling Hamiltonian is then generated, based on a double-minimum potential along the coordinate of concerted proton motion, which is newly evaluated at the RI-CC2/cc-pVTZ level of theory. To make it suitable for diagonalization, its dimensionality is reduced by treating fast weakly coupled modes in the adiabatic approximation. This results in a coordinate-dependent mass of tunneling, which is included in a unique Hermitian form into the kinetic energy operator. The reduced Hamiltonian contains three symmetric and one antisymmetric mode coupled to the tunneling mode and is diagonalized by a modified Jacobi-Davidson algorithm implemented in the Jadamilu software for sparse matrices. The results are in satisfactory agreement with the observed splitting of the zero-point level and several vibrational fundamentals after a partial reassignment, imposed by recently derived selection rules. They also agree well with instanton calculations based on the same Hamiltonian.

Exact finite volume expectation values of local operators in excited states

NASA Astrophysics Data System (ADS)

Pozsgay, B.; Szécsényi, I. M.; Takács, G.

2015-04-01

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

Construction of exact constants of motion and effective models for many-body localized systems

NASA Astrophysics Data System (ADS)

Goihl, M.; Gluza, M.; Krumnow, C.; Eisert, J.

2018-04-01

One of the defining features of many-body localization is the presence of many quasilocal conserved quantities. These constants of motion constitute a cornerstone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasilocal unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately, thus restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish an alternative approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-z operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder.

Pressure effects on band structures in dense lithium

NASA Astrophysics Data System (ADS)

Goto, Naoyuki; Nagara, Hitose

2012-07-01

We studied the change of the band structures in some structures of Li predicted at high pressures, using GGA and GW calculations. The width of the 1s band coming from the 1s electron of Li shows broadening by the pressurization, which is the normal behavior of bands at high pressure. The width of the band just below the Fermi level decreases by the pressurization, which is an opposite behavior to the normal bands. The character of this narrowing band is mostly p-like with a little s-like portion. The band gaps in some structures are really observed even by the GGA calculations. The gaps by the GW calculations increase to about 1.5 times the GGA values. Generally the one-shot GW calculation (diagonal only calculations) gives more reliable values than the GGA, but it may fail to predict band gaps for the case where band dispersion shows complex crossing near the Fermi level. There remains some structures for which GW calculations with off-diagonal elements taken into account are needed to identify the phase to be metallic or semiconducting.

An Efficient numerical method to calculate the conductivity tensor for disordered topological matter

NASA Astrophysics Data System (ADS)

Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.

2015-03-01

We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

FOB-SH: Fragment orbital-based surface hopping for charge carrier transport in organic and biological molecules and materials

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

Spencer, J.; Gajdos, F.; Blumberger, J., E-mail: j.blumberger@ucl.ac.uk

2016-08-14

We introduce a fragment orbital-based fewest switches surface hopping method, FOB-SH, designed to efficiently simulate charge carrier transport in strongly fluctuating condensed phase systems such as organic semiconductors and biomolecules. The charge carrier wavefunction is expanded and the electronic Hamiltonian constructed in a set of singly occupied molecular orbitals of the molecular sites that mediate the charge transfer. Diagonal elements of the electronic Hamiltonian (site energies) are obtained from a force field, whereas the off-diagonal or electronic coupling matrix elements are obtained using our recently developed analytic overlap method. We derive a general expression for the exact forces on themore » adiabatic ground and excited electronic state surfaces from the nuclear gradients of the charge localized electronic states. Applications to electron hole transfer in a model ethylene dimer and through a chain of ten model ethylenes validate our implementation and demonstrate its computational efficiency. On the larger system, we calculate the qualitative behaviour of charge mobility with change in temperature T for different regimes of the intermolecular electronic coupling. For small couplings, FOB-SH predicts a crossover from a thermally activated regime at low temperatures to a band-like transport regime at higher temperatures. For higher electronic couplings, the thermally activated regime disappears and the mobility decreases according to a power law. This is interpreted by a gradual loss in probability for resonance between the sites as the temperature increases. The polaron hopping model solved for the same system gives a qualitatively different result and underestimates the mobility decay at higher temperatures. Taken together, the FOB-SH methodology introduced here shows promise for a realistic investigation of charge carrier transport in complex organic, aqueous, and biological systems.« less

FOB-SH: Fragment orbital-based surface hopping for charge carrier transport in organic and biological molecules and materials

NASA Astrophysics Data System (ADS)

Spencer, J.; Gajdos, F.; Blumberger, J.

2016-08-01

We introduce a fragment orbital-based fewest switches surface hopping method, FOB-SH, designed to efficiently simulate charge carrier transport in strongly fluctuating condensed phase systems such as organic semiconductors and biomolecules. The charge carrier wavefunction is expanded and the electronic Hamiltonian constructed in a set of singly occupied molecular orbitals of the molecular sites that mediate the charge transfer. Diagonal elements of the electronic Hamiltonian (site energies) are obtained from a force field, whereas the off-diagonal or electronic coupling matrix elements are obtained using our recently developed analytic overlap method. We derive a general expression for the exact forces on the adiabatic ground and excited electronic state surfaces from the nuclear gradients of the charge localized electronic states. Applications to electron hole transfer in a model ethylene dimer and through a chain of ten model ethylenes validate our implementation and demonstrate its computational efficiency. On the larger system, we calculate the qualitative behaviour of charge mobility with change in temperature T for different regimes of the intermolecular electronic coupling. For small couplings, FOB-SH predicts a crossover from a thermally activated regime at low temperatures to a band-like transport regime at higher temperatures. For higher electronic couplings, the thermally activated regime disappears and the mobility decreases according to a power law. This is interpreted by a gradual loss in probability for resonance between the sites as the temperature increases. The polaron hopping model solved for the same system gives a qualitatively different result and underestimates the mobility decay at higher temperatures. Taken together, the FOB-SH methodology introduced here shows promise for a realistic investigation of charge carrier transport in complex organic, aqueous, and biological systems.

Two-Dimensional Collective Hamiltonian for Chiral and Wobbling Modes

DOE PAGES

Chen, Q. B.; Zhang, S. Q.; Zhao, P. W.; ...

2016-10-03

Here, a two-dimensional collective Hamiltonian (2DCH) on both azimuth and polar motions in triaxial nuclei is proposed to investigate the chiral and wobbling modes. In the 2DCH, the collective potential and the mass parameters are determined from three-dimensional tilted axis cranking (TAC) calculations. The broken chiral and signature symmetries in the TAC solutions are restored by the 2DCH. The validity of the 2DCH is illustrated with a triaxial rotor (γ= -30°) coupling to one h 11/2 proton particle and one h 11/2 neutron hole. By diagonalizing the 2DCH, the angular momenta and energy spectra are obtained. These results agree withmore » the exact solutions of the particle rotor model (PRM) at high rotational frequencies. However, at low frequencies, the energies given by the 2DCH are larger than those by the PRM due to the underestimation of the mass parameters. In addition, with increasing angular momentum, the transitions from the chiral vibration to chiral rotation and further to longitudinal wobbling motion have been presented in the 2DCH.« less

Simulation of Quantum Many-Body Dynamics for Generic Strongly-Interacting Systems

NASA Astrophysics Data System (ADS)

Meyer, Gregory; Machado, Francisco; Yao, Norman

2017-04-01

Recent experimental advances have enabled the bottom-up assembly of complex, strongly interacting quantum many-body systems from individual atoms, ions, molecules and photons. These advances open the door to studying dynamics in isolated quantum systems as well as the possibility of realizing novel out-of-equilibrium phases of matter. Numerical studies provide insight into these systems; however, computational time and memory usage limit common numerical methods such as exact diagonalization to relatively small Hilbert spaces of dimension 215 . Here we present progress toward a new software package for dynamical time evolution of large generic quantum systems on massively parallel computing architectures. By projecting large sparse Hamiltonians into a much smaller Krylov subspace, we are able to compute the evolution of strongly interacting systems with Hilbert space dimension nearing 230. We discuss and benchmark different design implementations, such as matrix-free methods and GPU based calculations, using both pre-thermal time crystals and the Sachdev-Ye-Kitaev model as examples. We also include a simple symbolic language to describe generic Hamiltonians, allowing simulation of diverse quantum systems without any modification of the underlying C and Fortran code.

Inverse participation ratios in the XX spin chain

NASA Astrophysics Data System (ADS)

Tsukerman, Emmanuel

2017-03-01

We continue the study of the inverse participation ratios (IPRs) of the XXZ Heisenberg spin chain initiated by Stéphan, Furukawa, Misguich, and Pasquier (2009) and continued by Misguich, Pasquier, and Luck (2016) by focusing on the case of the XX Heisenberg spin chain. For the ground state, Stéphan et al. note that calculating the IPR is equivalent to Dyson's constant term ex-conjecture. We express the IPRs of excited states as an apparently new "discrete" Hall inner product. We analyze this inner product using the theory of symmetric functions (Jack polynomials, Schur polynomials, the standard Hall inner product, and ωq ,t) to determine some exact expressions and asymptotics for IPRs. We show that IPRs can be indexed by partitions, and asymptotically the IPR of a partition is equal to that of the conjugate partition. We relate the IPRs to two other models from physics, namely, the circular symplectic ensemble of Dyson and the Dyson-Gaudin two-dimensional Coulomb lattice gas. Finally, we provide a description of the IPRs in terms of a signed count of diagonals of permutohedra.

Two-Dimensional Collective Hamiltonian for Chiral and Wobbling Modes

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

Chen, Q. B.; Zhang, S. Q.; Zhao, P. W.

Here, a two-dimensional collective Hamiltonian (2DCH) on both azimuth and polar motions in triaxial nuclei is proposed to investigate the chiral and wobbling modes. In the 2DCH, the collective potential and the mass parameters are determined from three-dimensional tilted axis cranking (TAC) calculations. The broken chiral and signature symmetries in the TAC solutions are restored by the 2DCH. The validity of the 2DCH is illustrated with a triaxial rotor (γ= -30°) coupling to one h 11/2 proton particle and one h 11/2 neutron hole. By diagonalizing the 2DCH, the angular momenta and energy spectra are obtained. These results agree withmore » the exact solutions of the particle rotor model (PRM) at high rotational frequencies. However, at low frequencies, the energies given by the 2DCH are larger than those by the PRM due to the underestimation of the mass parameters. In addition, with increasing angular momentum, the transitions from the chiral vibration to chiral rotation and further to longitudinal wobbling motion have been presented in the 2DCH.« less

Strain distribution and band structure of InAs/GaAs quantum ring superlattice

NASA Astrophysics Data System (ADS)

Mughnetsyan, Vram; Kirakosyan, Albert

2017-12-01

The elastic strain distribution and the band structure of InAs/GaAs one-layer quantum ring superlattice with square symmetry has been considered in this work. The Green's function formalism based on the method of inclusions has been implied to calculate the components of the strain tensor, while the combination of Green's function method with the Fourier transformation to momentum space in Pikus-Bir Hamiltonian has been used for obtaining the miniband energy dispersion surfaces via the exact diagonalization procedure. The dependencies of the strain tensor components on spatial coordinates are compared with ones for single quantum ring and are in good agreement with previously obtained results for cylindrical quantum disks. It is shown that strain significantly affects the miniband structure of the superlattice and has contribution to the degeneracy lifting effect due to heavy hole-light hole coupling. The demonstrated method is simple and provides reasonable results for comparatively small Hamiltonian matrix. The obtained results may be useful for further investigation and construction of novel devices based on quantum ring superlattices.

A real-frequency solver for the Anderson impurity model based on bath optimization and cluster perturbation theory

NASA Astrophysics Data System (ADS)

Zingl, Manuel; Nuss, Martin; Bauernfeind, Daniel; Aichhorn, Markus

2018-05-01

Recently solvers for the Anderson impurity model (AIM) working directly on the real-frequency axis have gained much interest. A simple and yet frequently used impurity solver is exact diagonalization (ED), which is based on a discretization of the AIM bath degrees of freedom. Usually, the bath parameters cannot be obtained directly on the real-frequency axis, but have to be determined by a fit procedure on the Matsubara axis. In this work we present an approach where the bath degrees of freedom are first discretized directly on the real-frequency axis using a large number of bath sites (≈ 50). Then, the bath is optimized by unitary transformations such that it separates into two parts that are weakly coupled. One part contains the impurity site and its interacting Green's functions can be determined with ED. The other (larger) part is a non-interacting system containing all the remaining bath sites. Finally, the Green's function of the full AIM is calculated via coupling these two parts with cluster perturbation theory.

Charged excitons in a dilute two-dimensional electron gas in a high magnetic field

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

Wojs, Arkadiusz; Institute of Physics, Wroclaw University of Technology, Wroclaw 50-370,; Quinn, John J.

2000-08-15

A theory of charged excitons X{sup -} in a dilute two-dimensional (2D) electron gas in a high-magnetic field is presented. In contrast to previous calculations, three bound X{sup -} states (one singlet and two triplets) are found in a narrow and symmetric GaAs quantum well. The singlet and a ''bright'' triplet are the two optically active states observed in experiments. The bright triplet has the binding energy of about 1 meV, smaller than the singlet and a ''dark'' triplet. The interaction of bound X{sup -}'s with a dilute 2D electron gas is investigated using exact diagonalization techniques. It is foundmore » that the short-range character of the e-X{sup -} interactions effectively isolates bound X{sup -} states from a dilute e-h plasma. This results in the insensitivity of the photoluminescence spectrum to the filling factor {nu}, and a rapid decrease of the oscillator strength of the dark triplet X{sup -} as a function of {nu}{sup -1}. (c) 2000 The American Physical Society.« less

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

Bezák, Viktor, E-mail: bezak@fmph.uniba.sk

Quantum theory of the non-harmonic oscillator defined by the energy operator proposed by Yurke and Buks (2006) is presented. Although these authors considered a specific problem related to a model of transmission lines in a Kerr medium, our ambition is not to discuss the physical substantiation of their model. Instead, we consider the problem from an abstract, logically deductive, viewpoint. Using the Yurke–Buks energy operator, we focus attention on the imaginary-time propagator. We derive it as a functional of the Mehler kernel and, alternatively, as an exact series involving Hermite polynomials. For a statistical ensemble of identical oscillators defined bymore » the Yurke–Buks energy operator, we calculate the partition function, average energy, free energy and entropy. Using the diagonal element of the canonical density matrix of this ensemble in the coordinate representation, we define a probability density, which appears to be a deformed Gaussian distribution. A peculiarity of this probability density is that it may reveal, when plotted as a function of the position variable, a shape with two peaks located symmetrically with respect to the central point.« less

Nonlocal torque operators in ab initio theory of the Gilbert damping in random ferromagnetic alloys

NASA Astrophysics Data System (ADS)

Turek, I.; Kudrnovský, J.; Drchal, V.

2015-12-01

We present an ab initio theory of the Gilbert damping in substitutionally disordered ferromagnetic alloys. The theory rests on introduced nonlocal torques which replace traditional local torque operators in the well-known torque-correlation formula and which can be formulated within the atomic-sphere approximation. The formalism is sketched in a simple tight-binding model and worked out in detail in the relativistic tight-binding linear muffin-tin orbital method and the coherent potential approximation (CPA). The resulting nonlocal torques are represented by nonrandom, non-site-diagonal, and spin-independent matrices, which simplifies the configuration averaging. The CPA-vertex corrections play a crucial role for the internal consistency of the theory and for its exact equivalence to other first-principles approaches based on the random local torques. This equivalence is also illustrated by the calculated Gilbert damping parameters for binary NiFe and FeCo random alloys, for pure iron with a model atomic-level disorder, and for stoichiometric FePt alloys with a varying degree of L 10 atomic long-range order.

Electronic state and optical response in a hydrogen-bonded molecular conductor

NASA Astrophysics Data System (ADS)

Naka, Makoto; Ishihara, Sumio

2018-06-01

Motivated by recent experimental studies of hydrogen-bonded molecular conductors κ -X 3(Cat-EDT-TTF) 2[X =H , D], interplays of protons and correlated electrons, and their effects on magnetic, dielectric, and optical properties, are studied theoretically. We introduce a model Hamiltonian for κ -X 3(Cat-EDT-TTF) 2, in which molecular dimers are connected by hydrogen bonds. Ground-state phase diagram and optical conductivity spectra are examined by using the mean-field approximation and the exact diagonalization method in finite-size cluster. Three types of the competing electronic and protonic phases, charge density wave phase, polar charge-ordered phase, and antiferromagnetic dimer-Mott insulating phase are found. Observed softening of the interdimer excitation due to the electron-proton coupling implies reduction of the effective electron-electron repulsion, i.e., "Hubbard U ," due to the quantum proton motion. Contrastingly, the intradimer charge excitation is hardened due to the proton-electron coupling. Implications of the theoretical calculations to the recent experimental results in κ -X 3(Cat-EDT-TTF) 2 are discussed.

Studying relaxation phenomena via effective master equations

NASA Astrophysics Data System (ADS)

Chan, David; Wan, Jones T. K.; Chu, L. L.; Yu, K. W.

2000-04-01

The real-time dynamics of various relaxation phenomena can be conveniently formulated by a master equation with the enumeration of transition rates between given classes of conformations. To study the relaxation time towards equilibrium, it suffices to solve for the second largest eigenvalue of the resulting eigenvalue equation. Generally speaking, there is no analytic solution for the dynamic equation. Mean-field approaches generally yield misleading results while the presumably exact Monte-Carlo methods require prohibitive time steps in most real systems. In this work, we propose an exact decimation procedure for reducing the number of conformations significantly, while there is no loss of information, i.e., the reduced (or effective) equation is an exact transformed version of the original one. However, we have to pay the price: the initial Markovianity of the evolution equation is lost and the reduced equation contains memory terms in the transition rates. Since the transformed equation has significantly reduced number of degrees of freedom, the systems can readily be diagonalized by iterative means, to obtain the exact second largest eigenvalue and hence the relaxation time. The decimation method has been applied to various relaxation equations with generally desirable results. The advantages and limitations of the method will be discussed.

On the consistency of the Oppenheimer-Snyder solution for a dust star. Reply to Marshall's criticism

NASA Astrophysics Data System (ADS)

Zakir, Zahid

2018-02-01

The recent alternative to the Oppenheimer-Snyder (OS) solution for a dust star proposed by Marshall in the paper "Gravitational collapse without black holes" (Astrophys. Space Sci. 342:329, 2012) is analyzed. It is shown that this proposal leads to a non-diagonal metric, with which the Einstein equations become practically unsolvable. Any ansatz proposed as their exact solution turns out to be arbitrary and may be unlimited number of the such solutions. This is due to the fact that an auxiliary function y(R,r), introduced by OS as t=M(y), is unambiguously fixed by the diagonality condition and the matching on the surface, and thus in the non-diagonal case it remains arbitrary. It is also shown that the OS solution, as a description in terms of the Schwarzschild coordinates, leads to a frozen star (or frozar) picture not only for the surface, asymptotically freezing outside the gravitational radius, but for interior layers too which also freeze near their own asymptotes. At most of the inner region these asymptotes are located almost equidistantly and only for layers initially close to the surface they become denser. The reason for the such densifying is not "a gravitational repulsion", but their later freezing and higher spatial contractions, while they remain be uniform and free falling in the comoving frames.

Overlaps with arbitrary two-site states in the XXZ spin chain

NASA Astrophysics Data System (ADS)

Pozsgay, B.

2018-05-01

We present a conjectured exact formula for overlaps between the Bethe states of the spin-1/2 XXZ chain and generic two-site states. The result takes the same form as in the previously known cases: it involves the same ratio of two Gaudin-like determinants, and a product of single-particle overlap functions, which can be fixed using a combination of the quench action and quantum transfer matrix methods. Our conjecture is confirmed by numerical data from exact diagonalization. For one-site states, the formula is found to be correct even in chains with odd length. It is also pointed out that the ratio of the Gaudin-like determinants plays a crucial role in the overlap sum rule: it guarantees that in the thermodynamic limit there remains no term in the quench action.

Trial wave functions for a composite Fermi liquid on a torus

NASA Astrophysics Data System (ADS)

Fremling, M.; Moran, N.; Slingerland, J. K.; Simon, S. H.

2018-01-01

We study the two-dimensional electron gas in a magnetic field at filling fraction ν =1/2 . At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.

Weak interaction probes of light nuclei

NASA Astrophysics Data System (ADS)

Towner, I. S.

1986-03-01

Experimental evidence for pion enhancement in axial charge transitions as predicted by softpion theorems is reviewed. Corrections from non-soft-pion terms seem to be limited. For transitions involving the space part of the axial-vector current, soft-pion theorems are powerless. Meson-exchange currents then involve a complicated interplay among competing process. Explicit calculations in the hard-pion model for closed-shell-plus (or minus)-one nuclei, A=15 and A= =17, are in reasonable agreement with experiment. Quenching in the off-diagonal spin-flip matrix element is larger than in the diagonal matrix element.

Off-diagonal series expansion for quantum partition functions

NASA Astrophysics Data System (ADS)

Hen, Itay

2018-05-01

We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the classical component of the Hamiltonian with the expansion parameter being the strength of the off-diagonal, or quantum, portion. To demonstrate the usefulness of the technique we analytically compute to third order the partition functions of the 1D Ising model with longitudinal and transverse fields, and the quantum 1D Heisenberg model.

Numerical Aspects of Atomic Physics: Helium Basis Sets and Matrix Diagonalization

NASA Astrophysics Data System (ADS)

Jentschura, Ulrich; Noble, Jonathan

2014-03-01

We present a matrix diagonalization algorithm for complex symmetric matrices, which can be used in order to determine the resonance energies of auto-ionizing states of comparatively simple quantum many-body systems such as helium. The algorithm is based in multi-precision arithmetic and proceeds via a tridiagonalization of the complex symmetric (not necessarily Hermitian) input matrix using generalized Householder transformations. Example calculations involving so-called PT-symmetric quantum systems lead to reference values which pertain to the imaginary cubic perturbation (the imaginary cubic anharmonic oscillator). We then proceed to novel basis sets for the helium atom and present results for Bethe logarithms in hydrogen and helium, obtained using the enhanced numerical techniques. Some intricacies of ``canned'' algorithms such as those used in LAPACK will be discussed. Our algorithm, for complex symmetric matrices such as those describing cubic resonances after complex scaling, is faster than LAPACK's built-in routines, for specific classes of input matrices. It also offer flexibility in terms of the calculation of the so-called implicit shift, which is used in order to ``pivot'' the system toward the convergence to diagonal form. We conclude with a wider overview.

Useful lower limits to polarization contributions to intermolecular interactions using a minimal basis of localized orthogonal orbitals: theory and analysis of the water dimer.

PubMed

Azar, R Julian; Horn, Paul Richard; Sundstrom, Eric Jon; Head-Gordon, Martin

2013-02-28

The problem of describing the energy-lowering associated with polarization of interacting molecules is considered in the overlapping regime for self-consistent field wavefunctions. The existing approach of solving for absolutely localized molecular orbital (ALMO) coefficients that are block-diagonal in the fragments is shown based on formal grounds and practical calculations to often overestimate the strength of polarization effects. A new approach using a minimal basis of polarized orthogonal local MOs (polMOs) is developed as an alternative. The polMO basis is minimal in the sense that one polarization function is provided for each unpolarized orbital that is occupied; such an approach is exact in second-order perturbation theory. Based on formal grounds and practical calculations, the polMO approach is shown to underestimate the strength of polarization effects. In contrast to the ALMO method, however, the polMO approach yields results that are very stable to improvements in the underlying AO basis expansion. Combining the ALMO and polMO approaches allows an estimate of the range of energy-lowering due to polarization. Extensive numerical calculations on the water dimer using a large range of basis sets with Hartree-Fock theory and a variety of different density functionals illustrate the key considerations. Results are also presented for the polarization-dominated Na(+)CH4 complex. Implications for energy decomposition analysis of intermolecular interactions are discussed.

Discrete disorder models for many-body localization

NASA Astrophysics Data System (ADS)

Janarek, Jakub; Delande, Dominique; Zakrzewski, Jakub

2018-04-01

Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time nonergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.

Quantum dimer model for the pseudogap metal

PubMed Central

Punk, Matthias; Allais, Andrea; Sachdev, Subir

2015-01-01

We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S=1/2, charge +e fermionic dimers. The model realizes a “fractionalized Fermi liquid” with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8×8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments. PMID:26195771

Relaxation Matrix for Symmetric Tops with Inversion Symmetry: Line Coupling and Line Mixing Effects on NH3 Lines in the V4 Band

NASA Technical Reports Server (NTRS)

Ma, Q.; Boulet, C.; Tipping, R. H.

2017-01-01

Line shape parameters including the half-widths and the off-diagonal elements of the relaxation matrix have been calculated for self-broadened NH3 lines in the perpendicular v4 band. As in the pure rotational and the parallel v1 bands, the small inversion splitting in this band causes a complete failure of the isolated line approximation. As a result, one has to use formalisms not relying on this approximation. However, due to differences between parallel and perpendicular bands of NH3, the applicability of the formalism used in our previous studies of the v1 band and other parallel bands must be carefully verified. We have found that, as long as potential models only contain components with K1 equals K2 equals 0, whose matrix elements require the selection rule delta k equals 0, the formalism is applicable for the v4 band with some minor adjustments. Based on both theoretical considerations and results from numerical calculations, the non-diagonality of the relaxation matrices in all the PP, RP, PQ, RQ, PR, and RR branches is discussed. Theoretically calculated self-broadened half-widths are compared with measurements and the values listed in HITRAN 2012. With respect to line coupling effects, we have compared our calculated intra-doublet off-diagonal elements of the relaxation matrix with reliable measurements carried out in the PP branch where the spectral environment is favorable. The agreement is rather good since our results do well reproduce the observed k and j dependences of these elements, thus validating our formalism.

Mechanisms of Diagonal-Shear Failure in Reinforced Concrete Beams analyzed by AE-SiGMA

NASA Astrophysics Data System (ADS)

Ohno, Kentaro; Shimozono, Shinichiro; Sawada, Yosuke; Ohtsu, Masayasu

Serious shear failures in reinforced concrete (RC) structures were reported in the Hanshin-Awaji Earthquake. In particular, it was demonstrated that a diagonal-shear failure could lead to disastrous damage. However, mechanisms of the diagonal-shear failure in RC beams have not been completely clarified yet. In this study, the diagonal-shear failure in RC beams is investigated, applying acoustic emission (AE) method. To identify source mechanisms of AE signals, SiGMA (Simplified Green's functions for Moment tensor Analysis) procedure was applied. Prior to four-point bending tests of RC beams, theoretical waveforms were calculated to determine the optimal arrangement of AE sensors. Then, cracking mechanisms in experiments were investigated by applying the SiGMA procedure to AE waveforms. From results of the SiGMA analysis, dominant motions of micro-cracks are found to be of shear crack in all the loading stages. As the load increased, the number of tensile cracks increased and eventually the diagonal-shear failure occurred in the shear span. Prior to final failure, AE cluster of micro-cracks was intensely observed in the shear span. To classify AE sources into tensile and shear cracks, AE parameter analysis was also applied. As a result, most of AE hits are classified into tensile cracks. The difference between results obtained by the AE parameter analysis and by the SiGMA analysis is investigated and discussed.

Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules

NASA Technical Reports Server (NTRS)

Ma, Q.; Boulet, C.; Tipping, R. H.

2014-01-01

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

Wavelets in electronic structure calculations

NASA Astrophysics Data System (ADS)

Modisette, Jason Perry

1997-09-01

Ab initio calculations of the electronic structure of bulk materials and large clusters are not possible on today's computers using current techniques. The storage and diagonalization of the Hamiltonian matrix are the limiting factors in both memory and execution time. The scaling of both quantities with problem size can be reduced by using approximate diagonalization or direct minimization of the total energy with respect to the density matrix in conjunction with a localized basis. Wavelet basis members are much more localized than conventional bases such as Gaussians or numerical atomic orbitals. This localization leads to sparse matrices of the operators that arise in SCF multi-electron calculations. We have investigated the construction of the one-electron Hamiltonian, and also the effective one- electron Hamiltonians that appear in density-functional and Hartree-Fock theories. We develop efficient methods for the generation of the kinetic energy and potential matrices, the Hartree and exchange potentials, and the local exchange-correlation potential of the LDA. Test calculations are performed on one-electron problems with a variety of potentials in one and three dimensions.

Quantum transport in antidot arrays in magnetic fields

NASA Astrophysics Data System (ADS)

Ishizaka, Satoshi; Nihey, Fumiyuki; Nakamura, Kazuo; Sone, Jun' Ichi; Ando, Tsuneya

1995-04-01

Transport in antidot arrays in magnetic fields is studied numerically. We calculate the density of states and conductivity tensor by the self-consistent Born approximation. Although peak positions of the density of states agree well with the quantization condition for several short periodic orbits, the behavior of the conductivity tensor is very complicated. Coupling among the periodic orbits causes an oscillation in the Hall conductivity in magnetic fields around the localized peak. In low magnetic fields, the skipping orbit, which runs from an antidot to its neighboring antidot, plays a crucial role for diagonal conductivity, and its coupling with the periodic orbits causes an oscillation in the diagonal conductivity. The resulting magnetoresistance oscillates with a period near one magnetic flux quantum as observed in recent experiments. Furthermore, the oscillation due to the manifestation of Hofstadter's butterfly is present in both the diagonal conductivity and the Hall conductivity.

Theoretical Studies of Spectroscopic Line Mixing in Remote Sensing Applications

NASA Astrophysics Data System (ADS)

Ma, Q.

2015-12-01

The phenomenon of collisional transfer of intensity due to line mixing has an increasing importance for atmospheric monitoring. From a theoretical point of view, all relevant information about the collisional processes is contained in the relaxation matrix where the diagonal elements give half-widths and shifts, and the off-diagonal elements correspond to line interferences. For simple systems such as those consisting of diatom-atom or diatom-diatom, accurate fully quantum calculations based on interaction potentials are feasible. However, fully quantum calculations become unrealistic for more complex systems. On the other hand, the semi-classical Robert-Bonamy (RB) formalism, which has been widely used to calculate half-widths and shifts for decades, fails in calculating the off-diagonal matrix elements. As a result, in order to simulate atmospheric spectra where the effects from line mixing are important, semi-empirical fitting or scaling laws such as the ECS and IOS models are commonly used. Recently, while scrutinizing the development of the RB formalism, we have found that these authors applied the isolated line approximation in their evaluating matrix elements of the Liouville scattering operator given in exponential form. Since the criterion of this assumption is so stringent, it is not valid for many systems of interest in atmospheric applications. Furthermore, it is this assumption that blocks the possibility to calculate the whole relaxation matrix at all. By eliminating this unjustified application, and accurately evaluating matrix elements of the exponential operators, we have developed a more capable formalism. With this new formalism, we are now able not only to reduce uncertainties for calculated half-widths and shifts, but also to remove a once insurmountable obstacle to calculate the whole relaxation matrix. This implies that we can address the line mixing with the semi-classical theory based on interaction potentials between molecular absorber and molecular perturber. We have applied this formalism to address the line mixing for Raman and infrared spectra of molecules such as N2, C2H2, CO2, NH3, and H2O. By carrying out rigorous calculations, our calculated relaxation matrices are in good agreement with both experimental data and results derived from the ECS model.

Log-Linear Modeling of Agreement among Expert Exposure Assessors

PubMed Central

Hunt, Phillip R.; Friesen, Melissa C.; Sama, Susan; Ryan, Louise; Milton, Donald

2015-01-01

Background: Evaluation of expert assessment of exposure depends, in the absence of a validation measurement, upon measures of agreement among the expert raters. Agreement is typically measured using Cohen’s Kappa statistic, however, there are some well-known limitations to this approach. We demonstrate an alternate method that uses log-linear models designed to model agreement. These models contain parameters that distinguish between exact agreement (diagonals of agreement matrix) and non-exact associations (off-diagonals). In addition, they can incorporate covariates to examine whether agreement differs across strata. Methods: We applied these models to evaluate agreement among expert ratings of exposure to sensitizers (none, likely, high) in a study of occupational asthma. Results: Traditional analyses using weighted kappa suggested potential differences in agreement by blue/white collar jobs and office/non-office jobs, but not case/control status. However, the evaluation of the covariates and their interaction terms in log-linear models found no differences in agreement with these covariates and provided evidence that the differences observed using kappa were the result of marginal differences in the distribution of ratings rather than differences in agreement. Differences in agreement were predicted across the exposure scale, with the likely moderately exposed category more difficult for the experts to differentiate from the highly exposed category than from the unexposed category. Conclusions: The log-linear models provided valuable information about patterns of agreement and the structure of the data that were not revealed in analyses using kappa. The models’ lack of dependence on marginal distributions and the ease of evaluating covariates allow reliable detection of observational bias in exposure data. PMID:25748517

Towards first-principles calculation of electronic excitations in the ring of the protein-bound bacteriochlorophylls

NASA Astrophysics Data System (ADS)

Polyakov, Igor V.; Khrenova, Maria G.; Moskovsky, Alexander A.; Shabanov, Boris M.; Nemukhin, Alexander V.

2018-04-01

Modeling electronic excitation of bacteriochlorophyll (BChl) molecules in light-harvesting (LH) antennae from photosynthetic centers presents a challenge for the quantum theory. We report on a quantum chemical study of the ring of 32 BChl molecules from the bacterial core complex LH1-RC. Diagonal and off-diagonal elements of the excitonic Hamiltonian matrices are estimated in quantum chemical calculations of relevant fragments using the TD-DFT and CIS approaches. The deviation of the computed excitation energy of this BChl system from the experimental data related to the Qy band maximum of this LH1-RC complex is about 0.2 eV. We demonstrate that corrections due to improvement in modeling of an individual BChl molecule and due to contributions from the protein environment are in the range of the obtained discrepancy between theory and experiment. Differences between results of the excitonic model and direct quantum chemical calculations of BChl aggregates fall in the same range.

Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems

NASA Astrophysics Data System (ADS)

Liu, Zhao; Bhatt, R. N.

2015-09-01

Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, density-matrix-renormalization-group (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrix-product-state (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the many-body Hamiltonian as a matrix-product-operator (MPO) and using single-site update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.

(p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation

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

Ben Geloun, Joseph; Govaerts, Jan; Hounkonnou, M. Norbert

2007-03-15

Classes of (p,q) deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q) arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translatesmore » into (p,q) deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.« less

The difference between two random mixed quantum states: exact and asymptotic spectral analysis

NASA Astrophysics Data System (ADS)

Mejía, José; Zapata, Camilo; Botero, Alonso

2017-01-01

We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact joint eigenvalue probability density function for arbitrary dimensions can be obtained from the joint probability density function of the diagonal elements of the difference matrix, which is straightforward to compute. Subsequently, we use standard results from free probability theory to derive a relatively simple analytic expression for the asymptotic eigenvalue density (AED) of the difference matrix ensemble, and using Carlson’s theorem, we obtain an expression for its absolute moments. These results allow us to quantify the typical asymptotic distance between the two random mixed states using various distance measures; in particular, we obtain the almost sure asymptotic behavior of the operator norm distance and the trace distance.

Spatial correlations in driven-dissipative photonic lattices

NASA Astrophysics Data System (ADS)

Biondi, Matteo; Lienhard, Saskia; Blatter, Gianni; Türeci, Hakan E.; Schmidt, Sebastian

2017-12-01

We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose–Hubbard and spin-1/2 XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array (∼ 1/z) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) we show that the gas–liquid transition in the driven-dissipative Bose–Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching–bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon.

Calculating intensities using effective Hamiltonians in terms of Coriolis-adapted normal modes.

PubMed

Karthikeyan, S; Krishnan, Mangala Sunder; Carrington, Tucker

2005-01-15

The calculation of rovibrational transition energies and intensities is often hampered by the fact that vibrational states are strongly coupled by Coriolis terms. Because it invalidates the use of perturbation theory for the purpose of decoupling these states, the coupling makes it difficult to analyze spectra and to extract information from them. One either ignores the problem and hopes that the effect of the coupling is minimal or one is forced to diagonalize effective rovibrational matrices (rather than diagonalizing effective rotational matrices). In this paper we apply a procedure, based on a quantum mechanical canonical transformation for deriving decoupled effective rotational Hamiltonians. In previous papers we have used this technique to compute energy levels. In this paper we show that it can also be applied to determine intensities. The ideas are applied to the ethylene molecule.

On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials.

PubMed

Noel, Yves; D'arco, Philippe; Demichelis, Raffaella; Zicovich-Wilson, Claudio M; Dovesi, Roberto

2010-03-01

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two-dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono- and bi-electronic integrals that enter into the Fock (Kohn-Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M x 2M matrix. The efficiency and accuracy of the computational scheme is documented. (c) 2009 Wiley Periodicals, Inc.

Hole pairing and ground state properties of high-Tc superconductivity within the t-t'-J-V model

NASA Astrophysics Data System (ADS)

Roy, Krishanu; Pal, Papiya; Nath, Subhadip; Ghosh, Nanda Kumar

2018-04-01

The t-t'-J-V model, one of the realistic models for studying high-Tc cuprates, has been investigated to explore the hole pairing and other ground state properties using exact diagonalization (ED) technique with 2 holes in a small 8-site cluster. The role of next-nearest-neighbor (NNN) hopping and nearest-neighbor (NN) Coulomb repulsion has been considered. It appears that qualitative behavior of the ground state energies of an 8-site and 16- or 18-site cluster is similar. Results show that a small short-ranged antiferromagnetic (AF) correlation exists in the 2 hole case which is favored by large V/t. A superconducting phase emerges at 0 ≤ V/t ≤ 4J. Hole-hole correlation calculation also suggests that the two holes of the pair are either at |i - j| = 1 or √2. Negative t'/t suppresses the possibility of pairing of holes. Though s-wave pairing susceptibility is dominant, pairing correlation length calculation indicates that the long range pairing, which is suitable for superconductivity, is in the d-wave channel. Both s- and d-wave pairing susceptibility gets suppressed by V/t while d-(s-) wave susceptibility gets favored (suppressed) by t'/t. The charge gap shows a gapped behavior while a spin-gapless region exists at small V/t for finite t'/t.

Corner-corrected diagonal-norm summation-by-parts operators for the first derivative with increased order of accuracy

NASA Astrophysics Data System (ADS)

Del Rey Fernández, David C.; Boom, Pieter D.; Zingg, David W.

2017-02-01

Combined with simultaneous approximation terms, summation-by-parts (SBP) operators offer a versatile and efficient methodology that leads to consistent, conservative, and provably stable discretizations. However, diagonal-norm operators with a repeating interior-point operator that have thus far been constructed suffer from a loss of accuracy. While on the interior, these operators are of degree 2p, at a number of nodes near the boundaries, they are of degree p, and therefore of global degree p - meaning the highest degree monomial for which the operators are exact at all nodes. This implies that for hyperbolic problems and operators of degree greater than unity they lead to solutions with a global order of accuracy lower than the degree of the interior-point operator. In this paper, we develop a procedure to construct diagonal-norm first-derivative SBP operators that are of degree 2p at all nodes and therefore can lead to solutions of hyperbolic problems of order 2 p + 1. This is accomplished by adding nonzero entries in the upper-right and lower-left corners of SBP operator matrices with a repeating interior-point operator. This modification necessitates treating these new operators as elements, where mesh refinement is accomplished by increasing the number of elements in the mesh rather than increasing the number of nodes. The significant improvements in accuracy of this new family, for the same repeating interior-point operator, are demonstrated in the context of the linear convection equation.

Harnessing molecular excited states with Lanczos chains.

PubMed

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-24

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Harnessing molecular excited states with Lanczos chains

NASA Astrophysics Data System (ADS)

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O.; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-01

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Matrix-product-state method with local basis optimization for nonequilibrium electron-phonon systems

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Brockt, Christoph; Dorfner, Florian; Vidmar, Lev; Jeckelmann, Eric

We present a method for simulating the time evolution of quasi-one-dimensional correlated systems with strongly fluctuating bosonic degrees of freedom (e.g., phonons) using matrix product states. For this purpose we combine the time-evolving block decimation (TEBD) algorithm with a local basis optimization (LBO) approach. We discuss the performance of our approach in comparison to TEBD with a bare boson basis, exact diagonalization, and diagonalization in a limited functional space. TEBD with LBO can reduce the computational cost by orders of magnitude when boson fluctuations are large and thus it allows one to investigate problems that are out of reach of other approaches. First, we test our method on the non-equilibrium dynamics of a Holstein polaron and show that it allows us to study the regime of strong electron-phonon coupling. Second, the method is applied to the scattering of an electronic wave packet off a region with electron-phonon coupling. Our study reveals a rich physics including transient self-trapping and dissipation. Supported by Deutsche Forschungsgemeinschaft (DFG) via FOR 1807.

Coherent optical excitations in superconducting qubit chain

NASA Astrophysics Data System (ADS)

Ian, Hou; Liu, Yu-Xi

2012-06-01

In the recent years, the theories of quantum optics have been borrowed to study the flows of electron pairs and their interactions with the circuit photon in the superconducting qubit circuits. These studies bring about new theories of quantum optics, such as the tunable electromagnetically induced transparency effect, peculiar to the Cooper pairs in circuits. In this talk, we focus on a special type of superconducting qubit circuits: superconducting qubit chain (SQC), which comprises dozens of qubits linearly placed along a stripline resonator. Since the dimensions of the qubits and the stripline have made their interactions inhomogeneous, the SQC cannot be diagonalized using the usual Dicke model. We present a new theoretical method, the deformation-projection method, for the exact diagonalization of the collective excitations of the qubits. This method allows us to predict that these excitations emulate the behaviors of Wannier and Frenckel excitons in the solid-state systems. The spontaneous emissions from the individual qubits in SQC are relayed to their neighbors, eventually arriving at a coherent emission, known as superradiance. We present a quantum relay model, which is crucial to quantum information processing, based on this finding.

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

Volkas, R. R.; Foot, R.; He, X.

The universal QCD color theory is extended to an SU(3)/sub 1//direct product/SU(3)/sub 2//direct product/SU(3)/sub 3/ gauge theory, where quarks of the /ital i/th generation transform as triplets under SU(3)/sub /ital i// and singlets under the other two factors. The usual color group is then identified with the diagonal subgroup, which remains exact after symmetry breaking. The gauge bosons associated with the 16 broken generators then form two massive octets under ordinary color. The interactions between quarks and these heavy gluonlike particles are explicitly nonuniversal and thus an exploration of their physical implications allows us to shed light on the fundamentalmore » issue of strong-interaction universality. Nonuniversality and weak flavor mixing are shown to generate heavy-gluon-induced flavor-changing neutral currents. The phenomenology of these processes is studied, as they provide the major experimental constraint on the extended theory. Three symmetry-breaking scenarios are presented. The first has color breaking occurring at the weak scale, while the second and third divorce the two scales. The third model has the interesting feature of radiatively induced off-diagonal Kobayashi-Maskawa matrix elements.« less

A new algorithm for real-time optimal dispatch of active and reactive power generation retaining nonlinearity

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

Roy, L.; Rao, N.D.

1983-04-01

This paper presents a new method for optimal dispatch of real and reactive power generation which is based on cartesian coordinate formulation of economic dispatch problem and reclassification of state and control variables associated with generator buses. The voltage and power at these buses are classified as parametric and functional inequality constraints, and are handled by reduced gradient technique and penalty factor approach respectively. The advantage of this classification is the reduction in the size of the equality constraint model, leading to less storage requirement. The rectangular coordinate formulation results in an exact equality constraint model in which the coefficientmore » matrix is real, sparse, diagonally dominant, smaller in size and need be computed and factorized once only in each gradient step. In addition, Lagragian multipliers are calculated using a new efficient procedure. A natural outcome of these features is the solution of the economic dispatch problem, faster than other methods available to date in the literature. Rapid and reliable convergence is an additional desirable characteristic of the method. Digital simulation results are presented on several IEEE test systems to illustrate the range of application of the method visa-vis the popular Dommel-Tinney (DT) procedure. It is found that the proposed method is more reliable, 3-4 times faster and requires 20-30 percent less storage compared to the DT algorithm, while being just as general. Thus, owing to its exactness, robust mathematical model and less computational requirements, the method developed in the paper is shown to be a practically feasible algorithm for on-line optimal power dispatch.« less

Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models

NASA Astrophysics Data System (ADS)

Le Deunff, Jérémy; Mouchet, Amaury; Schlagheck, Peter

2013-10-01

Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit resonance island chain structures with accurately controlled sizes and positions of the islands. Using complex classical trajectories that evolve along suitably defined paths in the complex time domain, we construct a semiclassical theory of the resonance-assisted tunneling process. This semiclassical approach yields a compact analytical expression for tunnelling-induced level splittings which is found to be in very good agreement with the exact splittings obtained through numerical diagonalization.

Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates

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

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

We investigate the disorder-induced localization transition in Bose-Einstein condensates for the Anderson and Aubry-Andre models in the noninteracting limit using exact diagonalization. We show that, in addition to the standard superfluid fraction, other tools such as the entanglement and fidelity can provide clear signatures of the transition. Interestingly, the fidelity exhibits good sensitivity even for small lattices. Effects of the system size on these quantities are analyzed in detail, including the determination of a finite-size-scaling law for the critical disorder strength in the case of the Anderson model.

Bound States in Dimerized and Frustrated Heisenberg Chains

NASA Astrophysics Data System (ADS)

Bouzerar, G.; Sil, S.

Using the Bond-Operator Technique (BOT), we have studied the low energy excitation spectrum of a frustrated dimerized antiferromagnetic Heisenberg chain. In particular, we have compared our analytical results with previous Exact Diagonalization (ED) data. Qualitatively, the BOT results are in good agreement with the ED data. And even a very good quantitative agreement is obtained in some parameter region. It is clearly shown that there is only one elementary excitation branch (lowest triplet branch) and that the two other well defined excitations which appear below the continuum, one singlet and one triplet, are bound states of two elementary triplets.

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3

NASA Astrophysics Data System (ADS)

Yadav, Ravi; Bogdanov, Nikolay A.; Katukuri, Vamshi M.; Nishimoto, Satoshi; van den Brink, Jeroen; Hozoi, Liviu

2016-11-01

Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d5 honeycomb halide α-RuCl3. From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d5 halides and oxides in general.

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3.

PubMed

Yadav, Ravi; Bogdanov, Nikolay A; Katukuri, Vamshi M; Nishimoto, Satoshi; van den Brink, Jeroen; Hozoi, Liviu

2016-11-30

Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d 5 honeycomb halide α-RuCl 3 . From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d 5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d 5 halides and oxides in general.

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3

PubMed Central

Yadav, Ravi; Bogdanov, Nikolay A.; Katukuri, Vamshi M.; Nishimoto, Satoshi; van den Brink, Jeroen; Hozoi, Liviu

2016-01-01

Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d5 honeycomb halide α-RuCl3. From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d5 halides and oxides in general. PMID:27901091

Universality and tails of long-range interactions in one dimension

NASA Astrophysics Data System (ADS)

Valiente, Manuel; Öhberg, Patrik

2017-07-01

Long-range interactions and, in particular, two-body potentials with power-law long-distance tails are ubiquitous in nature. For two bosons or fermions in one spatial dimension, the latter case being formally equivalent to three-dimensional s -wave scattering, we show how generic asymptotic interaction tails can be accounted for in the long-distance limit of scattering wave functions. This is made possible by introducing a generalization of the collisional phase shifts to include space dependence. We show that this distance dependence is universal, in that it does not depend on short-distance details of the interaction. The energy dependence is also universal, and is fully determined by the asymptotic tails of the two-body potential. As an important application of our findings, we describe how to eliminate finite-size effects with long-range potentials in the calculation of scattering phase shifts from exact diagonalization. We show that even with moderately small system sizes it is possible to accurately extract phase shifts that would otherwise be plagued with finite-size errors. We also consider multichannel scattering, focusing on the estimation of open channel asymptotic interaction strengths via finite-size analysis.

Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering

NASA Astrophysics Data System (ADS)

Atalay, Bora; Berker, A. Nihat

2018-05-01

Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states q =3 ,4 in d dimensions. We use renormalization-group theory that is exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all d >1 and all noninfinite temperatures, the system eventually renormalizes to a random single state, thus signaling q ×q degenerate ordering. Note that this is the maximally degenerate ordering. For high-temperature initial conditions, the system crosses over to this highly degenerate ordering only after spending many renormalization-group iterations near the disordered (infinite-temperature) fixed point. Thus, a temperature range of short-range disorder in the presence of long-range order is identified, as previously seen in underfrustrated Ising spin-glass systems. The entropy is calculated for all temperatures, behaves similarly for ferromagnetic and antiferromagnetic interactions, and shows a derivative maximum at the short-range disordering temperature. With a sharp immediate contrast of infinitesimally higher dimension 1 +ɛ , the system is as expected disordered at all temperatures for d =1 .

Evidence for W=0 pairing in repulsive Hubbard square and hexagonal geometries

NASA Astrophysics Data System (ADS)

Perfetto, Enrico; Stefanucci, Gianluca; Callegari, Agnese; Cini, Michele

2004-08-01

Square and hexagonal lattices with purely repulsive on-site interactions on all sites and appropriate fillings show W=0 pairing, and the effective attractive interaction is due to a symmetry driven correlation effect; the W=0 pairs are two-body singlet eigenstates of the Hamiltonian with vanishing on-site repulsion. We can set up gedanken experiments with these bound pairs. Chains of CuO 4 units connected by weak links provide a test case which displays bound pair hopping and superconducting flux quantization (SFQ). Focusing on the low-energy sector, one obtains an accurate description in terms of an effective hard-core boson Hamiltonian which naturally describes itinerant pairs and SFQ in mesoscopic rings. For the numerical calculations, we take advantage of a recently proposed exact spin-disentangled diagonalization technique which can be generally applied to many-fermion problems and drastically reduces the size of the matrices to be handled. Remarkably, the very same pairing mechanism also works neatly with the wrapped honeycomb lattice, suitable for armchair carbon nanotubes; the binding energy of W=0 pairs depends strongly on the filling and decreases towards a small but non-zero value in the graphite limit.

Phase transition and field effect topological quantum transistor made of monolayer MoS2

NASA Astrophysics Data System (ADS)

Simchi, H.; Simchi, M.; Fardmanesh, M.; Peeters, F. M.

2018-06-01

We study topological phase transitions and topological quantum field effect transistor in monolayer molybdenum disulfide (MoS2) using a two-band Hamiltonian model. Without considering the quadratic (q 2) diagonal term in the Hamiltonian, we show that the phase diagram includes quantum anomalous Hall effect, quantum spin Hall effect, and spin quantum anomalous Hall effect regions such that the topological Kirchhoff law is satisfied in the plane. By considering the q 2 diagonal term and including one valley, it is shown that MoS2 has a non-trivial topology, and the valley Chern number is non-zero for each spin. We show that the wave function is (is not) localized at the edges when the q 2 diagonal term is added (deleted) to (from) the spin-valley Dirac mass equation. We calculate the quantum conductance of zigzag MoS2 nanoribbons by using the nonequilibrium Green function method and show how this device works as a field effect topological quantum transistor.

On the interpretation of kernels - Computer simulation of responses to impulse pairs

NASA Technical Reports Server (NTRS)

Hung, G.; Stark, L.; Eykhoff, P.

1983-01-01

A method is presented for the use of a unit impulse response and responses to impulse pairs of variable separation in the calculation of the second-degree kernels of a quadratic system. A quadratic system may be built from simple linear terms of known dynamics and a multiplier. Computer simulation results on quadratic systems with building elements of various time constants indicate reasonably that the larger time constant term before multiplication dominates in the envelope of the off-diagonal kernel curves as these move perpendicular to and away from the main diagonal. The smaller time constant term before multiplication combines with the effect of the time constant after multiplication to dominate in the kernel curves in the direction of the second-degree impulse response, i.e., parallel to the main diagonal. Such types of insight may be helpful in recognizing essential aspects of (second-degree) kernels; they may be used in simplifying the model structure and, perhaps, add to the physical/physiological understanding of the underlying processes.

Multigrid calculation of three-dimensional turbomachinery flows

NASA Technical Reports Server (NTRS)

Caughey, David A.

1989-01-01

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

Damage Evaluation in Shear-Critical Reinforced Concrete Beam using Piezoelectric Transducers as Smart Aggregates

NASA Astrophysics Data System (ADS)

Chalioris, Constantin E.; Papadopoulos, Nikos A.; Angeli, Georgia M.; Karayannis, Chris G.; Liolios, Asterios A.; Providakis, Costas P.

2015-10-01

Damage detection at early cracking stages in shear-critical reinforced concrete beams, before further deterioration and their inevitable brittle shear failure is crucial for structural safety and integrity. The effectiveness of a structural health monitoring technique using the admittance measurements of piezoelectric transducers mounted on a reinforced concrete beam without shear reinforcement is experimentally investigated. Embedded "smart aggregate" transducers and externally bonded piezoelectric patches have been placed in arrays at both shear spans of the beam. Beam were tested till total shear failure and monitored at three different states; healthy, flexural cracking and diagonal cracking. Test results showed that transducers close to the critical diagonal crack provided sound and graduated discrepancies between the admittance responses at the healthy state and thedamage levels.Damage assessment using statistical indices calculated from the measurements of all transducers was also attempted. Rational changes of the index values were obtained with respect to the increase of the damage. Admittance responses and index values of the transducers located on the shear span where the critical diagonal crack formed provided cogent evidence of damage. On the contrary, negligible indication of damage was yielded by the responses of the transducers located on the other shear span, where no diagonal cracking occurred.

Quench action and Rényi entropies in integrable systems

NASA Astrophysics Data System (ADS)

Alba, Vincenzo; Calabrese, Pasquale

2017-09-01

Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the nonequilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary thermodynamic entropy is the von Neumann entanglement entropy of a large subsystem embedded in an infinite system. Also motivated by cold-atom experiments, here we consider the generalization to Rényi entropies. We develop a new technique to calculate the diagonal Rényi entropy in the quench action formalism. In the spirit of the replica treatment for the entanglement entropy, the diagonal Rényi entropies are generalized free energies evaluated over a thermodynamic macrostate which depends on the Rényi index and, in particular, is not the same state describing von Neumann entropy. The technical reason for this perhaps surprising result is that the evaluation of the moments of the diagonal density matrix shifts the saddle point of the quench action. An interesting consequence is that different Rényi entropies encode information about different regions of the spectrum of the postquench Hamiltonian. Our approach provides a very simple proof of the long-standing issue that, for integrable systems, the diagonal entropy is half of the thermodynamic one and it allows us to generalize this result to the case of arbitrary Rényi entropy.

Theoretical Studies of Spectroscopic Line Mixing in Remote Sensing Applications

NASA Technical Reports Server (NTRS)

Ma, Q.; Boulet, C.; Tipping, R. H.

2015-01-01

The phenomenon of collisional transfer of intensity due to line mixing has an increasing importance for atmospheric monitoring. From a theoretical point of view, all relevant information about the collisional processes is contained in the relaxation matrix where the diagonal elements give half-widths and shifts, and the off-diagonal elements correspond to line interferences. For simple systems such as those consisting of diatom-atom or diatom-diatom, accurate fully quantum calculations based on interaction potentials are feasible. However, fully quantum calculations become unrealistic for more complex systems. On the other hand, the semi-classical Robert-Bonamy (RB) formalism, which has been widely used to calculate half-widths and shifts for decades, fails in calculating the off-diagonal matrix elements. As a result, in order to simulate atmospheric spectra where the effects from line mixing are important, semi-empirical fitting or scaling laws such as the ECS (Energy-Corrected Sudden) and IOS (Infinite-Order Sudden) models are commonly used. Recently, while scrutinizing the development of the RB formalism, we have found that these authors applied the isolated line approximation in their evaluating matrix elements of the Liouville scattering operator given in exponential form. Since the criterion of this assumption is so stringent, it is not valid for many systems of interest in atmospheric applications. Furthermore, it is this assumption that blocks the possibility to calculate the whole relaxation matrix at all. By eliminating this unjustified application, and accurately evaluating matrix elements of the exponential operators, we have developed a more capable formalism. With this new formalism, we are now able not only to reduce uncertainties for calculated half-widths and shifts, but also to remove a once insurmountable obstacle to calculate the whole relaxation matrix. This implies that we can address the line mixing with the semi-classical theory based on interaction potentials between molecular absorber and molecular perturber. We have applied this formalism to address the line mixing for Raman and infrared spectra of molecules such as N2, C2H2, CO2, NH3, and H2O. By carrying out rigorous calculations, our calculated relaxation matrices are in good agreement with both experimental data and results derived from the ECS model.

D IR Line Shapes for Determining the Structure of a Peptide in a Bilayer

NASA Astrophysics Data System (ADS)

Woys, Ann Marie; Lin, Y. S.; Skinner, J. S.; Zanni, M. T.; Reddy, A. S.; de Pablo, J. J.

2010-06-01

Structure of the antimicrobial peptide, ovispirin, on a lipid bilayer was determined using 2D IR spectroscopy and spectra calculated from molecular dynamics simulations. Ovispirin is an 18 residue amphipathic peptide that binds parallel to the membrane in a mostly alpha helical conformation. 15 of the 18 residues were ^1^3C^1^8O isotopically labeled on the backbone to isolate the amide I vibration at each position. 2D IR spectra were collected for each labeled peptide in 3:1 POPC/POPG vesicles, and peak width along the diagonal was measured. The diagonal line width is sensitive to the vibrator's electrostatic environment, which varies through the bilayer. We observe an oscillatory line width spanning 10 to 24 cm-1 and with a period of nearly 3.6 residues. To further investigate the position of ovispirin in a bilayer, molecular dynamics simulations determined the peptide depth to be just below the lipid headgroups. The trajectory of ovispirin at this depth was used to calculate 2D IR spectra, from which the diagonal line width is measured. Both experimental and simulated line widths are similar in periodicity and suggest a kink in the peptide backbone and the tilt in the bilayer. A. Woys, Y. S. Lin, A. S. Reddy, W. Xiong, J. J. de Pablo, J. S. Skinner, and M. T. Zanni, JACS 132, 2832-2838 (2010).

The effect of Fisher information matrix approximation methods in population optimal design calculations.

PubMed

Strömberg, Eric A; Nyberg, Joakim; Hooker, Andrew C

2016-12-01

With the increasing popularity of optimal design in drug development it is important to understand how the approximations and implementations of the Fisher information matrix (FIM) affect the resulting optimal designs. The aim of this work was to investigate the impact on design performance when using two common approximations to the population model and the full or block-diagonal FIM implementations for optimization of sampling points. Sampling schedules for two example experiments based on population models were optimized using the FO and FOCE approximations and the full and block-diagonal FIM implementations. The number of support points was compared between the designs for each example experiment. The performance of these designs based on simulation/estimations was investigated by computing bias of the parameters as well as through the use of an empirical D-criterion confidence interval. Simulations were performed when the design was computed with the true parameter values as well as with misspecified parameter values. The FOCE approximation and the Full FIM implementation yielded designs with more support points and less clustering of sample points than designs optimized with the FO approximation and the block-diagonal implementation. The D-criterion confidence intervals showed no performance differences between the full and block diagonal FIM optimal designs when assuming true parameter values. However, the FO approximated block-reduced FIM designs had higher bias than the other designs. When assuming parameter misspecification in the design evaluation, the FO Full FIM optimal design was superior to the FO block-diagonal FIM design in both of the examples.

Dissociation between exact and approximate addition in developmental dyslexia.

PubMed

Yang, Xiujie; Meng, Xiangzhi

2016-09-01

Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.

Many-body Green’s function theory for electron-phonon interactions: Ground state properties of the Holstein dimer

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

Säkkinen, Niko; Leeuwen, Robert van; Peng, Yang

2015-12-21

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is stronglymore » correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.« less

The Hartree product and the description of local and global quantities in atomic systems: A study within Kohn-Sham theory

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

Garza, Jorge; Nichols, Jeffrey A.; Dixon, David A.

2000-01-15

The Hartree product is analyzed in the context of Kohn-Sham theory. The differential equations that emerge from this theory are solved with the optimized effective potential using the Krieger, Li, and Iafrate approximation, in order to get a local potential as required by the ordinary Kohn-Sham procedure. Because the diagonal terms of the exact exchange energy are included in Hartree theory, it is self-interaction free and the exchange potential has the proper asymptotic behavior. We have examined the impact of this correct asymptotic behavior on local and global properties using this simple model to approximate the exchange energy. Local quantities,more » such as the exchange potential and the average local electrostatic potential are used to examine whether the shell structure in an atom is revealed by this theory. Global quantities, such as the highest occupied orbital energy (related to the ionization potential) and the exchange energy are also calculated. These quantities are contrasted with those obtained from calculations with the local density approximation, the generalized gradient approximation, and the self-interaction correction approach proposed by Perdew and Zunger. We conclude that the main characteristics in an atomic system are preserved with the Hartree theory. In particular, the behavior of the exchange potential obtained in this theory is similar to those obtained within other Kohn-Sham approximations. (c) 2000 American Institute of Physics.« less

Thermal transport in dimerized harmonic lattices: Exact solution, crossover behavior, and extended reservoirs

NASA Astrophysics Data System (ADS)

Chien, Chih-Chun; Kouachi, Said; Velizhanin, Kirill A.; Dubi, Yonatan; Zwolak, Michael

2017-01-01

We present a method for calculating analytically the thermal conductance of a classical harmonic lattice with both alternating masses and nearest-neighbor couplings when placed between individual Langevin reservoirs at different temperatures. The method utilizes recent advances in analytic diagonalization techniques for certain classes of tridiagonal matrices. It recovers the results from a previous method that was applicable for alternating on-site parameters only, and extends the applicability to realistic systems in which masses and couplings alternate simultaneously. With this analytic result in hand, we show that the thermal conductance is highly sensitive to the modulation of the couplings. This is due to the existence of topologically induced edge modes at the lattice-reservoir interface and is also a reflection of the symmetries of the lattice. We make a connection to a recent work that demonstrates thermal transport is analogous to chemical reaction rates in solution given by Kramers' theory [Velizhanin et al., Sci. Rep. 5, 17506 (2015)], 10.1038/srep17506. In particular, we show that the turnover behavior in the presence of edge modes prevents calculations based on single-site reservoirs from coming close to the natural—or intrinsic—conductance of the lattice. Obtaining the correct value of the intrinsic conductance through simulation of even a small lattice where ballistic effects are important requires quite large extended reservoir regions. Our results thus offer a route for both the design and proper simulation of thermal conductance of nanoscale devices.

Electronic excitations in electron-doped cuprate superconductors

NASA Astrophysics Data System (ADS)

Unger, P.; Fulde, P.

1995-04-01

We calculate the electronic single-particle spectrum of an electron-doped cuprate superconductor such as Nd2-xCexCuO4-y. The dynamics of holes in the Cu-O planes is described by the extended Hubbard or Emery model. We consider the system at half-filling (one hole per unit cell, nh=1) and in the case of electron doping where the ground state is paramagnetic. The projection technique of Mori and Zwanzig is applied to derive the equations of motion for the Green's functions of Cu and O holes. These equations are solved self-consistently as in a previous calculation, where we considered the case of hole doping. At half-filling the system exhibits a charge-transfer gap bounded by Zhang-Rice singlet states and the upper Hubbard band. Upon electron doping the upper Hubbard band crosses the Fermi level and the system becomes metallic. With increasing electron doping the singlet band loses intensity and finally vanishes for nh=0. The corresponding spectral weight is transferred to the upper Hubbard band, which becomes a usual tight-binding band for zero hole concentration. The shape of the flat band crossing the Fermi level fits well to angle-resolved photoemission spectra of Nd2-xCexCuO4-y for x=0.15 and 0.22. Furthermore, our findings are in excellent agreement with exact diagonalization studies of 2×2 CuO2 cluster with periodic boundary conditions.

Yet another family of diagonal metrics for de Sitter and anti-de Sitter spacetimes

NASA Astrophysics Data System (ADS)

Podolský, Jiří; Hruška, Ondřej

2017-06-01

In this work we present and analyze a new class of coordinate representations of de Sitter and anti-de Sitter spacetimes for which the metrics are diagonal and (typically) static and axially symmetric. Contrary to the well-known forms of these fundamental geometries, that usually correspond to a 1 +3 foliation with the 3-space of a constant spatial curvature, the new metrics are adapted to a 2 +2 foliation, and are warped products of two 2-spaces of constant curvature. This new class of (anti-)de Sitter metrics depends on the value of cosmological constant Λ and two discrete parameters +1 ,0 ,-1 related to the curvature of the 2-spaces. The class admits 3 distinct subcases for Λ >0 and 8 subcases for Λ <0 . We systematically study all these possibilities. In particular, we explicitly present the corresponding parametrizations of the (anti-)de Sitter hyperboloid, visualize the coordinate lines and surfaces within the global conformal cylinder, investigate their mutual relations, present some closely related forms of the metrics, and give transformations to standard de Sitter and anti-de Sitter metrics. Using these results, we also provide a physical interpretation of B -metrics as exact gravitational fields of a tachyon.

Quantum critical spin-2 chain with emergent SU(3) symmetry.

PubMed

Chen, Pochung; Xue, Zhi-Long; McCulloch, I P; Chung, Ming-Chiang; Huang, Chao-Chun; Yip, S-K

2015-04-10

We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.

Experimental observation of the 1/3 magnetization plateau in the diamond-chain compound Cu3(CO3)2(OH)2.

PubMed

Kikuchi, H; Fujii, Y; Chiba, M; Mitsudo, S; Idehara, T; Tonegawa, T; Okamoto, K; Sakai, T; Kuwai, T; Ohta, H

2005-06-10

The magnetic susceptibility, high field magnetization, and specific heat measurements of Cu3(CO3)2(OH)2, which is a model substance for the frustrating diamond spin chain model, have been performed using single crystals. Two broad peaks are observed at around 20 and 5 K in both magnetic susceptibility and specific heat results. The magnetization curve has a clear plateau at one third of the saturation magnetization. The experimental results are examined in terms of theoretical expectations based on exact diagonalization and density matrix renormalization group methods. An origin of magnetic anisotropy is also discussed.

Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

NASA Astrophysics Data System (ADS)

Nishiyama, Yoshihiro

2017-09-01

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρs in the ordered phase and the vortex-condensate stiffness ρv in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρs,v/Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρs/ρv admits a quantitative measure of deviation from selfduality.

Interband excitations in the 1D limit of two-band fractional Chern insulators

NASA Astrophysics Data System (ADS)

Jaworowski, Błażej; Kaczmarkiewicz, Piotr; Potasz, Paweł; Wójs, Arkadiusz

2018-05-01

We investigate the stability of the one-dimensional limit of ν = 1 / 3 Laughlin-like fractional Chern insulator with respect to the interband interaction. We propose a construction for the excitations in the infinite-interaction case and show that the energy gap remains finite in the thermodynamic limit. Next, by means of exact diagonalization and Density Matrix Renormalization Group approaches, we consider deviations from ideal dimerization and show that they reduce the stability of the FCI-like states. Finally, to show that our approach is not restricted to one model, we identify the dimer structure behind the thin-torus limit of other system - the checkerboard lattice.

Fidelity Study of Superconductivity in Extended Hubbard Models

NASA Astrophysics Data System (ADS)

Plonka, Nachum; Jia, Chunjing; Moritz, Brian; Wang, Yao; Devereaux, Thomas

2015-03-01

The role of strong electronic correlations on unconventional superconductivity remains an important open question. Here, we explore the influence of long-range Coulomb interactions, present in real material systems, through nearest and next-nearest neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing large scale, numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find that these extended interactions enhance charge fluctuations with various wave vectors. These suppress superconductivity in general, but in certain parameter regimes superconductivity is sustained. This has implications for tuning extended interactions in real materials.

Low-rank factorization of electron integral tensors and its application in electronic structure theory

DOE PAGES

Peng, Bo; Kowalski, Karol

2017-01-25

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

Dynamic current susceptibility as a probe of Majorana bound states in nanowire-based Josephson junctions

NASA Astrophysics Data System (ADS)

Trif, Mircea; Dmytruk, Olesia; Bouchiat, Hélène; Aguado, Ramón; Simon, Pascal

2018-02-01

We theoretically study a Josephson junction based on a semiconducting nanowire subject to a time-dependent flux bias. We establish a general density-matrix approach for the dynamical response of the Majorana junction and calculate the resulting flux-dependent susceptibility using both microscopic and effective low-energy descriptions for the nanowire. We find that the diagonal component of the susceptibility, associated with the dynamics of the Majorana state populations, dominates over the standard Kubo contribution for a wide range of experimentally relevant parameters. The diagonal term, explored, in this Rapid Communication, in the context of Majorana physics, allows probing accurately the presence of Majorana bound states in the junction.

An implict LU scheme for the Euler equations applied to arbitrary cascades. [new method of factoring

NASA Technical Reports Server (NTRS)

Buratynski, E. K.; Caughey, D. A.

1984-01-01

An implicit scheme for solving the Euler equations is derived and demonstrated. The alternating-direction implicit (ADI) technique is modified, using two implicit-operator factors corresponding to lower-block-diagonal (L) or upper-block-diagonal (U) algebraic systems which can be easily inverted. The resulting LU scheme is implemented in finite-volume mode and applied to 2D subsonic and transonic cascade flows with differing degrees of geometric complexity. The results are presented graphically and found to be in good agreement with those of other numerical and analytical approaches. The LU method is also 2.0-3.4 times faster than ADI, suggesting its value in calculating 3D problems.

Thermodynamic limit and boundary energy of the su(3) spin chain with non-diagonal boundary fields

NASA Astrophysics Data System (ADS)

Wen, Fakai; Yang, Tao; Yang, Zhanying; Cao, Junpeng; Hao, Kun; Yang, Wen-Li

2017-02-01

We investigate the thermodynamic limit of the su (n)-invariant spin chain models with unparallel boundary fields. It is found that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy does vanish in the thermodynamic limit. This fact allows us to calculate the boundary energy of the system. Taking the su (2) (or the XXX) spin chain and the su (3) spin chain as concrete examples, we have studied the corresponding boundary energies of the models. The method used in this paper can be generalized to study the thermodynamic properties and boundary energy of other high rank models with non-diagonal boundary fields.

Low-rank factorization of electron integral tensors and its application in electronic structure theory

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

Peng, Bo; Kowalski, Karol

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations.

PubMed

Banerjee, Amartya S; Lin, Lin; Suryanarayana, Phanish; Yang, Chao; Pask, John E

2018-06-12

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).

A multi-state fragment charge difference approach for diabatic states in electron transfer: Extension and automation

NASA Astrophysics Data System (ADS)

Yang, Chou-Hsun; Hsu, Chao-Ping

2013-10-01

The electron transfer (ET) rate prediction requires the electronic coupling values. The Generalized Mulliken-Hush (GMH) and Fragment Charge Difference (FCD) schemes have been useful approaches to calculate ET coupling from an excited state calculation. In their typical form, both methods use two eigenstates in forming the target charge-localized diabatic states. For problems involve three or four states, a direct generalization is possible, but it is necessary to pick and assign the locally excited or charge-transfer states involved. In this work, we generalize the 3-state scheme for a multi-state FCD without the need of manual pick or assignment for the states. In this scheme, the diabatic states are obtained separately in the charge-transfer or neutral excited subspaces, defined by their eigenvalues in the fragment charge-difference matrix. In each subspace, the Hamiltonians are diagonalized, and there exist off-diagonal Hamiltonian matrix elements between different subspaces, particularly the charge-transfer and neutral excited diabatic states. The ET coupling values are obtained as the corresponding off-diagonal Hamiltonian matrix elements. A similar multi-state GMH scheme can also be developed. We test the new multi-state schemes for the performance in systems that have been studied using more than two states with FCD or GMH. We found that the multi-state approach yields much better charge-localized states in these systems. We further test for the dependence on the number of state included in the calculation of ET couplings. The final coupling values are converged when the number of state included is increased. In one system where experimental value is available, the multi-state FCD coupling value agrees better with the previous experimental result. We found that the multi-state GMH and FCD are useful when the original two-state approach fails.

Computer Control and Activation of Six-Degree-of-Freedom Simulator

DTIC Science & Technology

1983-01-01

Evaluation of Matrices 54 Calculation of Linear Coefficients 54 Off-Line Calculations for Aircraft 59 Off-Line Calculations for Combat Vehicle 61 Table...468 in. 59 Physical concept tail-boom control system 203 Vlll 60 Tail-boom control system block diagram 204 61 Block diagram for position...configuration. Now, since Z must be diagonal, it follows that the principal elements of Z are given by 13 where and a) = ^11 ^12’ 2 2 ^21 ^22 ’ 61

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.

Fidelity decay in interacting two-level boson systems: Freezing and revivals

NASA Astrophysics Data System (ADS)

Benet, Luis; Hernández-Quiroz, Saúl; Seligman, Thomas H.

2011-05-01

We study the fidelity decay in the k-body embedded ensembles of random matrices for bosons distributed in two single-particle states, considering the reference or unperturbed Hamiltonian as the one-body terms and the diagonal part of the k-body embedded ensemble of random matrices and the perturbation as the residual off-diagonal part of the interaction. We calculate the ensemble-averaged fidelity with respect to an initial random state within linear response theory to second order on the perturbation strength and demonstrate that it displays the freeze of the fidelity. During the freeze, the average fidelity exhibits periodic revivals at integer values of the Heisenberg time tH. By selecting specific k-body terms of the residual interaction, we find that the periodicity of the revivals during the freeze of fidelity is an integer fraction of tH, thus relating the period of the revivals with the range of the interaction k of the perturbing terms. Numerical calculations confirm the analytical results.

On the Origins of the Linear Free Energy Relationships: Exploring the Nature of the Off-Diagonal Coupling Elements in SN2 Reactions

PubMed Central

Rosta, Edina; Warshel, Arieh

2012-01-01

Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of Linear Free Energy Relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. This study follows our earlier works1,2 and uses the ab initio frozen density functional theory (FDFT) method3 to evaluate both the diabatic and adiabatic free energy surfaces and to determine the corresponding off-diagonal coupling matrix elements for a series of SN2 reactions. It is found that the off-diagonal coupling matrix elements are almost the same regardless of the nucleophile and the leaving group but change upon changing the central group. Furthermore, it is also found that the off diagonal elements are basically the same in gas phase and in solution, even when the solvent is explicitly included in the ab initio calculations. Furthermore, our study establishes that the FDFT diabatic profiles are parabolic to a good approximation thus providing a first principle support to the origin of LFER. These findings further support the basic approximation of the EVB treatment. PMID:23329895

Workshop report on large-scale matrix diagonalization methods in chemistry theory institute

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

Bischof, C.H.; Shepard, R.L.; Huss-Lederman, S.

The Large-Scale Matrix Diagonalization Methods in Chemistry theory institute brought together 41 computational chemists and numerical analysts. The goal was to understand the needs of the computational chemistry community in problems that utilize matrix diagonalization techniques. This was accomplished by reviewing the current state of the art and looking toward future directions in matrix diagonalization techniques. This institute occurred about 20 years after a related meeting of similar size. During those 20 years the Davidson method continued to dominate the problem of finding a few extremal eigenvalues for many computational chemistry problems. Work on non-diagonally dominant and non-Hermitian problems asmore » well as parallel computing has also brought new methods to bear. The changes and similarities in problems and methods over the past two decades offered an interesting viewpoint for the success in this area. One important area covered by the talks was overviews of the source and nature of the chemistry problems. The numerical analysts were uniformly grateful for the efforts to convey a better understanding of the problems and issues faced in computational chemistry. An important outcome was an understanding of the wide range of eigenproblems encountered in computational chemistry. The workshop covered problems involving self- consistent-field (SCF), configuration interaction (CI), intramolecular vibrational relaxation (IVR), and scattering problems. In atomic structure calculations using the Hartree-Fock method (SCF), the symmetric matrices can range from order hundreds to thousands. These matrices often include large clusters of eigenvalues which can be as much as 25% of the spectrum. However, if Cl methods are also used, the matrix size can be between 10{sup 4} and 10{sup 9} where only one or a few extremal eigenvalues and eigenvectors are needed. Working with very large matrices has lead to the development of« less

Accurate determinations of one-bond 13C-13C couplings in 13C-labeled carbohydrates

NASA Astrophysics Data System (ADS)

Azurmendi, Hugo F.; Freedberg, Darón I.

2013-03-01

Carbon plays a central role in the molecular architecture of carbohydrates, yet the availability of accurate methods for 1DCC determination has not been sufficiently explored, despite the importance that such data could play in structural studies of oligo- and polysaccharides. Existing methods require fitting intensity ratios of cross- to diagonal-peaks as a function of the constant-time (CT) in CT-COSY experiments, while other methods utilize measurement of peak separation. The former strategies suffer from complications due to peak overlap, primarily in regions close to the diagonal, while the latter strategies are negatively impacted by the common occurrence of strong coupling in sugars, which requires a reliable assessment of their influence in the context of RDC determination. We detail a 13C-13C CT-COSY method that combines a variation in the CT processed with diagonal filtering to yield 1JCC and RDCs. The strategy, which relies solely on cross-peak intensity modulation, is inspired in the cross-peak nulling method used for JHH determinations, but adapted and extended to applications where, like in sugars, large one-bond 13C-13C couplings coexist with relatively small long-range couplings. Because diagonal peaks are not utilized, overlap problems are greatly alleviated. Thus, one-bond couplings can be determined from different cross-peaks as either active or passive coupling. This results in increased accuracy when more than one determination is available, and in more opportunities to measure a specific coupling in the presence of severe overlap. In addition, we evaluate the influence of strong couplings on the determination of RDCs by computer simulations. We show that individual scalar couplings are notably affected by the presence of strong couplings but, at least for the simple cases studied, the obtained RDC values for use in structural calculations were not, because the errors introduced by strong couplings for the isotropic and oriented phases are very similar and therefore cancel when calculating the difference to determine 1DCC values.

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

NASA Astrophysics Data System (ADS)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

Electrophoresis for genotyping: microtiter array diagonal gel electrophoresis on horizontal polyacrylamide gels, hydrolink, or agarose.

PubMed

Day, I N; Humphries, S E

1994-11-01

Electrophoresis of DNA has been performed traditionally in either an agarose or acrylamide gel matrix. Considerable effort has been directed to improved quality agaroses capable of high resolution, but for small fragments, such as those from polymerase chain reaction (PCR) and post-PCR digests, acrylamide still offers the highest resolution. Although agarose gels can easily be prepared in an open-faced format to gain the conveniences of horizontal electrophoresis, acrylamide does not polymerize in the presence of air and the usual configurations for gel preparation lead to electrophoresis in the vertical dimension. We describe here a very simple device and method to prepare and manipulate horizontal polyacrylamide gels (H-PAGE). In addition, the open-faced horizontal arrangement enables loading of arrays of wells. Since many procedures are undertaken in standard 96-well microtiter plates, we have also designed a device which preserves the exact configuration of the 8 x 12 array and enables electrophoresis in tracks following a 71.6 degrees diagonal between wells (MADGE, microtiter array diagonal gel electrophoresis), using either acrylamide or agarose. This eliminates almost all of the staff time taken in setup, loading, and recordkeeping and offers high resolution for genotyping pattern recognition. The nature and size of the gels allow direct stacking of gels in one tank, so that a tank used typically to analyze 30-60 samples can readily be used to analyze 1000-2000 samples. The gels would also enable robotic loading. Electrophoresis allows analysis of size and charge, parameters inaccessible to liquid-phase methods: thus, genotyping size patterns, variable length repeats, and haplotypes is possible, as well as adaptability to typing of point variations using protocols which create a difference detectable by electrophoresis.

Quasi-two-dimensional Bose-Einstein condensation of spin triplets in the dimerized quantum magnet Ba 2 CuSi 2 O 6 Cl 2

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

Okada, Makiko; Tanaka, Hidekazu; Kurita, Nobuyuki

We synthesized single crystals of composition Ba 2CuSi 2O 6Cl 2 and investigated their quantum magnetic properties. The crystal structure is closely related to that of the quasi-two-dimensional (2D) dimerized magnet BaCuSi 2O 6 also known as Han purple. Ba 2CuSi 2O 6Cl 2 has a singlet ground state with an excitation gap of Δ/k B = 20.8 K. The magnetization curves for two different field directions almost perfectly coincide when normalized by the g factor except for a small jump anomaly for a magnetic field perpendicular to the c axis. The magnetization curve with a nonlinear slope above themore » critical field is in excellent agreement with exact-diagonalization calculations based on a 2D coupled spin-dimer model. Individual exchange constants are also evaluated using density functional theory (DFT). The DFT results demonstrate a 2D exchange network and weak frustration between interdimer exchange interactions, supported by weak spin-lattice coupling implied from our magnetostriction data. Lastly, the magnetic-field-induced spin ordering in Ba 2CuSi 2O 6Cl 2 is described as the quasi-2D Bose-Einstein condensation of triplets.« less

Pick-off annihilation of positronium in matter using full correlation single particle potentials: solid He.

PubMed

Zubiaga, A; Tuomisto, F; Puska, M J

2015-01-29

We investigate the modeling of positronium (Ps) states and their pick-off annihilation trapped at open volumes pockets in condensed molecular matter. Our starting point is the interacting many-body system of Ps and a He atom because it is the smallest entity that can mimic the energy gap between the highest occupied and lowest unoccupied molecular orbitals of molecules, and yet the many-body structure of the HePs system can be calculated accurately enough. The exact-diagonalization solution of the HePs system enables us to construct a pairwise full-correlation single-particle potential for the Ps-He interaction, and the total potential in solids is obtained as a superposition of the pairwise potentials. We study in detail Ps states and their pick-off annihilation rates in voids inside solid He and analyze experimental results for Ps-induced voids in liquid He obtaining the radii of the voids. More importantly, we generalize our conclusions by testing the validity of the Tao-Eldrup model, widely used to analyze ortho-Ps annihilation measurements for voids in molecular matter, against our theoretical results for the solid He. Moreover, we discuss the influence of the partial charges of polar molecules and the strength of the van der Waals interaction on the pick-off annihilation rate.

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.

Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Fu, Liang; Sheng, D. N.

2017-10-01

We study the phase diagram of quantum Hall bilayer systems with total filing νT=1 /2 +1 /2 of the lowest Landau level as a function of layer distances d . Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d , a composite Fermi liquid at large d , and an intermediate phase for 1.1

Quasi-two-dimensional Bose-Einstein condensation of spin triplets in the dimerized quantum magnet Ba 2 CuSi 2 O 6 Cl 2

DOE PAGES

Okada, Makiko; Tanaka, Hidekazu; Kurita, Nobuyuki; ...

2016-09-20

We synthesized single crystals of composition Ba 2CuSi 2O 6Cl 2 and investigated their quantum magnetic properties. The crystal structure is closely related to that of the quasi-two-dimensional (2D) dimerized magnet BaCuSi 2O 6 also known as Han purple. Ba 2CuSi 2O 6Cl 2 has a singlet ground state with an excitation gap of Δ/k B = 20.8 K. The magnetization curves for two different field directions almost perfectly coincide when normalized by the g factor except for a small jump anomaly for a magnetic field perpendicular to the c axis. The magnetization curve with a nonlinear slope above themore » critical field is in excellent agreement with exact-diagonalization calculations based on a 2D coupled spin-dimer model. Individual exchange constants are also evaluated using density functional theory (DFT). The DFT results demonstrate a 2D exchange network and weak frustration between interdimer exchange interactions, supported by weak spin-lattice coupling implied from our magnetostriction data. Lastly, the magnetic-field-induced spin ordering in Ba 2CuSi 2O 6Cl 2 is described as the quasi-2D Bose-Einstein condensation of triplets.« less

Many-body localization in Ising models with random long-range interactions

NASA Astrophysics Data System (ADS)

Li, Haoyuan; Wang, Jia; Liu, Xia-Ji; Hu, Hui

2016-12-01

We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, Vi j∝|i-j |-α , where the exponent of the interaction range α can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing α , the critical exponent experiences a sharp increase at about αc≃1.2 and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For α <αc , we find that the system is mostly localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for α >αc , the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.

Fidelity study of the superconducting phase diagram in the two-dimensional single-band Hubbard model

NASA Astrophysics Data System (ADS)

Jia, C. J.; Moritz, B.; Chen, C.-C.; Shastry, B. Sriram; Devereaux, T. P.

2011-09-01

Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range d-wave pair field term, which precipitates a superconducting state in the d-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the d-wave pair/spin/charge-density matrices. The calculations show a d-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion U and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping t'. We also demonstrate that negative t' plays an important role in facilitating d-wave superconductivity.

Negative tunnel magnetoresistance and differential conductance in transport through double quantum dots

NASA Astrophysics Data System (ADS)

Trocha, Piotr; Weymann, Ireneusz; Barnaś, Józef

2009-10-01

Spin-dependent transport through two coupled single-level quantum dots weakly connected to ferromagnetic leads with collinear magnetizations is considered theoretically. Transport characteristics, including the current, linear and nonlinear conductances, and tunnel magnetoresistance are calculated using the real-time diagrammatic technique in the parallel, serial, and intermediate geometries. The effects due to virtual tunneling processes between the two dots via the leads, associated with off-diagonal coupling matrix elements, are also considered. Negative differential conductance and negative tunnel magnetoresistance have been found in the case of serial and intermediate geometries, while no such behavior has been observed for double quantum dots coupled in parallel. It is also shown that transport characteristics strongly depend on the magnitude of the off-diagonal coupling matrix elements.

Angle and frequency dependence of self-energy from spin fluctuation mediated d-wave pairing for high temperature superconductors.

PubMed

Hong, Seung Hwan; Choi, Han-Yong

2013-09-11

We investigated the characteristics of spin fluctuation mediated superconductivity employing the Eliashberg formalism. The effective interaction between electrons was modeled in terms of the spin susceptibility measured by inelastic neutron scattering experiments on single crystal La(2-x)Sr(x)CuO4 superconductors. The diagonal self-energy and off-diagonal self-energy were calculated by solving the coupled Eliashberg equation self-consistently for the chosen spin susceptibility and tight-binding dispersion of electrons. The full momentum and frequency dependence of the self-energy is presented for optimally doped, overdoped, and underdoped LSCO cuprates in a superconductive state. These results may be compared with the experimentally deduced self-energy from ARPES experiments.

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

DOE PAGES

Smith, J. C.; Pribram-Jones, A.; Burke, K.

2016-06-14

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

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

Smith, J. C.; Pribram-Jones, A.; Burke, K.

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

Almost conserved operators in nearly many-body localized systems

NASA Astrophysics Data System (ADS)

Pancotti, Nicola; Knap, Michael; Huse, David A.; Cirac, J. Ignacio; Bañuls, Mari Carmen

2018-03-01

We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slow operators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and subdiffusive dynamics in the thermal phase.

Is the ground state of 5d4 double-perovskite Iridate Ba2YIrO6 magnetic or nonmagnetic?

NASA Astrophysics Data System (ADS)

Gong, Hoshin; Kim, Kyoo; Kim, Beom Hyun; Kim, Bongjae; Kim, Junwon; Min, B. I.

2018-05-01

We have investigated electronic structures and magnetic properties of double perovskite Iridate Ba2YIrO6 with 5d4 configuration, employing the exact diagonalization method for multi-site clusters. We have considered a many-body Hamiltonian for all d states (eg and t2g) including all relevant physical parameters such as the Coulomb correlation, spin-orbit coupling, crystal-field effect, and Hund coupling. We have found that the ground state of Ba2YIrO6 is nonmagnetic and that the Hund coupling plays an important role in the magnetic properties of the 5d4 systems, unlike the well-studied 5d5 systems.

Stress Response of Granular Systems

NASA Astrophysics Data System (ADS)

Ramola, Kabir; Chakraborty, Bulbul

2017-10-01

We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degrees of freedom that determine the response of contact forces between constituent grains on a given, disordered, contact network, to external perturbations. By mapping this response to the spectral properties of the graph Laplacian corresponding to the underlying contact network, we show that this naturally leads to spatial localization of forces. We present numerical evidence for localization using exact diagonalization studies of network Laplacians of soft disk packings. Finally, we discuss the role of other constraints, such as torque balance, in determining the stability of a granular packing to external perturbations.

Relativistic energy-dispersion relations of 2D rectangular lattices

NASA Astrophysics Data System (ADS)

Ata, Engin; Demirhan, Doğan; Büyükkılıç, Fevzi

2017-04-01

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters V0, core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.

Phase transition in one Josephson junction with a side-coupled magnetic impurity

NASA Astrophysics Data System (ADS)

Zhi, Li-Ming; Wang, Xiao-Qi; Jiang, Cui; Yi, Guang-Yu; Gong, Wei-Jiang

2018-04-01

This work focuses on one Josephson junction with a side-coupled magnetic impurity. And then, the Josephson phase transition is theoretically investigated, with the help of the exact diagonalization approach. It is found that even in the absence of intradot Coulomb interaction, the magnetic impurity can efficiently induce the phenomenon of Josephson phase transition, which is tightly related to the spin correlation manners (i.e., ferromagnetic or antiferromagnetic) between the impurity and the junction. Moreover, the impurity plays different roles when it couples to the dot and superconductor, respectively. This work can be helpful in describing the influence of one magnetic impurity on the supercurrent through the Josephson junction.

Fidelity study of superconductivity in extended Hubbard models

NASA Astrophysics Data System (ADS)

Plonka, N.; Jia, C. J.; Wang, Y.; Moritz, B.; Devereaux, T. P.

2015-07-01

The Hubbard model with local on-site repulsion is generally thought to possess a superconducting ground state for appropriate parameters, but the effects of more realistic long-range Coulomb interactions have not been studied extensively. We study the influence of these interactions on superconductivity by including nearest- and next-nearest-neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find that nearest and next-nearest neighbor interactions have thresholds above which they destabilize superconductivity regardless of whether they are attractive or repulsive, seemingly due to competing charge fluctuations.

Positron collisions with acetylene calculated using the R-matrix with pseudo-states method

NASA Astrophysics Data System (ADS)

Zhang, Rui; Galiatsatos, Pavlos G.; Tennyson, Jonathan

2011-10-01

Eigenphase sums, total cross sections and differential cross sections are calculated for low-energy collisions of positrons with C2H2. The calculations demonstrate that the use of appropriate pseudo-state expansions very significantly improves the representation of this process giving both realistic eigenphases and cross sections. Differential cross sections are strongly forward peaked in agreement with the measurements. These calculations are computationally very demanding; even with improved procedures for matrix diagonalization, fully converged calculations are too expensive with current computer resources. Nonetheless, the calculations show clear evidence for the formation of a virtual state but no indication that acetylene actually binds a positron at its equilibrium geometry.

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

PubMed Central

Vitalis, Andreas; Pappu, Rohit V.

2014-01-01

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear in the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom. PMID:25053299

Scaling of the polarization amplitude in quantum many-body systems in one dimension

NASA Astrophysics Data System (ADS)

Kobayashi, Ryohei; Nakagawa, Yuya O.; Fukusumi, Yoshiki; Oshikawa, Masaki

2018-04-01

Resta proposed a definition of the electric polarization in one-dimensional systems in terms of the ground-state expectation value of the large gauge transformation operator. Vanishing of the expectation value in the thermodynamic limit implies that the system is a conductor. We study Resta's polarization amplitude (expectation value) in the S =1 /2 XXZ chain and its several generalizations, in the gapless conducting Tomonaga-Luttinger liquid phase. We obtain an analytical expression in the lowest-order perturbation theory about the free fermion point (XY chain) and an exact result for the Haldane-Shastry model with long-range interactions. We also obtain numerical results, mostly using the exact diagonalization method. We find that the amplitude exhibits a power-law scaling in the system size (chain length) and vanishes in the thermodynamic limit. On the other hand, the exponent depends on the model even when the low-energy limit is described by the Tomonaga-Luttinger liquid with the same Luttinger parameter. We find that a change in the exponent occurs when the Umklapp term(s) are eliminated, suggesting the importance of the Umklapp terms.

Modified conjugate gradient method for diagonalizing large matrices.

PubMed

Jie, Quanlin; Liu, Dunhuan

2003-11-01

We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.

Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

NASA Astrophysics Data System (ADS)

Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.

2016-05-01

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Greengard, Leslie F; Waag, Robert C

2010-02-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators

PubMed Central

Hesford, Andrew J.; Astheimer, Jeffrey P.; Greengard, Leslie F.; Waag, Robert C.

2010-01-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method. PMID:20136208

Two dimensional symmetric correlation functions of the S-circumflex operator and two dimensional Fourier transforms: Considering the line coupling for P and R lines of linear molecules

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

Ma, Q.; Boulet, C.; Tipping, R. H.

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS{sub 1} − S{sub 2} introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonalmore » elements do not require extra correlation functions of the S-circumflex operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters’ two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C{sub 2}H{sub 2} broadened by N{sub 2}. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.« less

State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons

NASA Astrophysics Data System (ADS)

Coimbatore Balram, Ajit; Wójs, Arkadiusz; Jain, Jainendra

2014-03-01

Exact diagonalization studies have revealed that the energy spectrum of interacting electrons in the lowest Landau level splits, non-perturbatively, into bands. The theory of nearly free composite fermions (CFs) has been shown to be valid for the lowest band, and thus to capture the low temperature physics, but it over-predicts the number of states for the excited bands. We explain the state counting of higher bands in terms of composite fermions with an infinitely strong short range interaction between a CF particle and a CF hole. This interaction, the form of which we derive from the microscopic CF theory, eliminates configurations containing certain tightly bound CF excitons. With this modification, the CF theory reproduces, for all well-defined excited bands, an exact counting for ν > 1 / 3 , and an almost exact counting for ν <= 1 / 3 . The resulting insight clarifies that the corrections to the nearly free CF theory are not thermodynamically significant at sufficiently low temperatures, thus providing a microscopic explanation for why it has proved successful for the analysis of the various properties of the CF Fermi sea. NSF grants DMR-1005536 and DMR-0820404, Polish NCN grant 2011/01/B/ST3/04504 and EU Marie Curie Grant PCIG09-GA-2011-294186, Research Computing and Cyberinfrastructure, PSU and Wroclaw Centre for Networking and Supercomputing

Fractional charge and emergent mass hierarchy in diagonal two-leg t – J cylinders

DOE PAGES

Jiang, Yi-Fan; Jiang, Hong-Chen; Yao, Hong; ...

2017-06-06

Here, we define a class of “diagonal” tmore » $-$ J ladders rotated by π / 4 relative to the canonical lattice directions of the square lattice, and study it using density matrix renormalization group. Here, we focus on the two-leg cylinder with a doped hole concentration near x = $$\\frac{1}{4}$$ . At exactly x = $$\\frac{1}{4}$$, the system forms a period 4 charge density wave and exhibits spin-charge separation. Slightly away from $$\\frac{1}{4}$$ doping, we observe several topologically distinct types of solitons with well-defined fractionalized quantum numbers. Remarkably, given the absence of any obvious small parameter, the effective masses of the emergent solitons differ by several orders of magnitude.« less

Light-Enhanced Spin Fluctuations and d -Wave Superconductivity at a Phase Boundary

NASA Astrophysics Data System (ADS)

Wang, Yao; Chen, Cheng-Chien; Moritz, B.; Devereaux, T. P.

2018-06-01

Time-domain techniques have shown the potential of photomanipulating existing orders and inducing new states of matter in strongly correlated materials. Using time-resolved exact diagonalization, we perform numerical studies of pump dynamics in a Mott-Peierls system with competing charge and spin density waves. A light-enhanced d -wave superconductivity is observed when the system resides near a quantum phase boundary. By examining the evolution of spin, charge, and superconducting susceptibilities, we show that a subdominant state in equilibrium can be stabilized by photomanipulating the charge order to allow superconductivity to appear and dominate. This work provides an interpretation of light-induced superconductivity from the perspective of order competition and offers a promising approach for designing novel emergent states out of equilibrium.

Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains

NASA Technical Reports Server (NTRS)

Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy

1989-01-01

A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.

Hubbard pair cluster in the external fields. Studies of the magnetic properties

NASA Astrophysics Data System (ADS)

Balcerzak, T.; Szałowski, K.

2018-06-01

The magnetic properties of the two-site Hubbard cluster (dimer or pair), embedded in the external electric and magnetic fields and treated as the open system, are studied by means of the exact diagonalization of the Hamiltonian. The formalism of the grand canonical ensemble is adopted. The phase diagrams, on-site magnetizations, spin-spin correlations, mean occupation numbers and hopping energy are investigated and illustrated in figures. An influence of temperature, mean electron concentration, Coulomb U parameter and external fields on the quantities of interest is presented and discussed. In particular, the anomalous behaviour of the magnetization and correlation function vs. temperature near the critical magnetic field is found. Also, the effect of magnetization switching by the external fields is demonstrated.

Fidelity study of superconductivity in extended Hubbard models

DOE PAGES

Plonka, N.; Jia, C. J.; Wang, Y.; ...

2015-07-08

The Hubbard model with local on-site repulsion is generally thought to possess a superconducting ground state for appropriate parameters, but the effects of more realistic long-range Coulomb interactions have not been studied extensively. We study the influence of these interactions on superconductivity by including nearest- and next-nearest-neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. Finally, we find that nearest and next-nearest neighbor interactions have thresholds above which they destabilize superconductivity regardless of whether they aremore » attractive or repulsive, seemingly due to competing charge fluctuations.« less

Exact diagonalization of quantum lattice models on coprocessors

NASA Astrophysics Data System (ADS)

Siro, T.; Harju, A.

2016-10-01

We implement the Lanczos algorithm on an Intel Xeon Phi coprocessor and compare its performance to a multi-core Intel Xeon CPU and an NVIDIA graphics processor. The Xeon and the Xeon Phi are parallelized with OpenMP and the graphics processor is programmed with CUDA. The performance is evaluated by measuring the execution time of a single step in the Lanczos algorithm. We study two quantum lattice models with different particle numbers, and conclude that for small systems, the multi-core CPU is the fastest platform, while for large systems, the graphics processor is the clear winner, reaching speedups of up to 7.6 compared to the CPU. The Xeon Phi outperforms the CPU with sufficiently large particle number, reaching a speedup of 2.5.

Novel half-magnetization plateau and nematiclike transition in the S =1 skew chain Ni2V2O7

NASA Astrophysics Data System (ADS)

Ouyang, Z. W.; Sun, Y. C.; Wang, J. F.; Yue, X. Y.; Chen, R.; Wang, Z. X.; He, Z. Z.; Xia, Z. C.; Liu, Y.; Rao, G. H.

2018-04-01

A quantized magnetization plateau is usually not expected when a classic spin-flop transition occurs in a low-dimensional antiferromagnet. Here, we report an experimental observation of a spin-flop transition followed by a wide half-magnetization plateau in the S =1 skew-chain system Ni2V2O7 . This plateau, which is stabilized in fields of 8-30 T, is realized through an exotic nematiclike phase transition for magnetic fields applied along all three crystallographic axes, resulting in rich anisotropic phase diagrams. We discuss a possible mechanism whereby the magnetic frustration and interchain interactions may cause this half-magnetization plateau, which is in agreement with our exact diagonalization result.

Quantum phases of spinful Fermi gases in optical cavities

NASA Astrophysics Data System (ADS)

Colella, E.; Citro, R.; Barsanti, M.; Rossini, D.; Chiofalo, M.-L.

2018-04-01

We explore the quantum phases emerging from the interplay between spin and motional degrees of freedom of a one-dimensional quantum fluid of spinful fermionic atoms, effectively interacting via a photon-mediating mechanism with tunable sign and strength g , as it can be realized in present-day experiments with optical cavities. We find the emergence, in the very same system, of spin- and atomic-density wave ordering, accompanied by the occurrence of superfluidity for g >0 , while cavity photons are seen to drive strong correlations at all g values, with fermionic character for g >0 , and bosonic character for g <0 . Due to the long-range nature of interactions, to infer these results we combine mean-field and exact-diagonalization methods supported by bosonization analysis.

Multiparticle instability in a spin-imbalanced Fermi gas

NASA Astrophysics Data System (ADS)

Whitehead, T. M.; Conduit, G. J.

2018-01-01

Weak attractive interactions in a spin-imbalanced Fermi gas induce a multiparticle instability, binding multiple fermions together. The maximum binding energy per particle is achieved when the ratio of the number of up- and down-spin particles in the instability is equal to the ratio of the up- and down-spin densities of states in momentum at the Fermi surfaces, to utilize the variational freedom of all available momentum states. We derive this result using an analytical approach, and verify it using exact diagonalization. The multiparticle instability extends the Cooper pairing instability of balanced Fermi gases to the imbalanced case, and could form the basis of a many-body state, analogously to the construction of the Bardeen-Cooper-Schrieffer theory of superconductivity out of Cooper pairs.

Many-body localization in a long range XXZ model with random-field

NASA Astrophysics Data System (ADS)

Li, Bo

2016-12-01

Many-body localization (MBL) in a long range interaction XXZ model with random field are investigated. Using the exact diagonal method, the MBL phase diagram with different tuning parameters and interaction range is obtained. It is found that the phase diagram of finite size results supplies strong evidence to confirm that the threshold interaction exponent α = 2. The tuning parameter Δ can efficiently change the MBL edge in high energy density stats, thus the system can be controlled to transfer from thermal phase to MBL phase by changing Δ. The energy level statistics data are consistent with result of the MBL phase diagram. However energy level statistics data cannot detect the thermal phase correctly in extreme long range case.

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.

Electron spin resonance modes in a strong-leg ladder in the Tomonaga-Luttinger liquid phase

NASA Astrophysics Data System (ADS)

Ozerov, M.; Maksymenko, M.; Wosnitza, J.; Honecker, A.; Landee, C. P.; Turnbull, M. M.; Furuya, S. C.; Giamarchi, T.; Zvyagin, S. A.

2015-12-01

Magnetic excitations in the strong-leg quantum spin ladder compound (C7H10N) 2CuBr4 (known as DIMPY) in the field-induced Tomonaga-Luttinger spin-liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual nonlinear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact-diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe their ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

A particle tracking method for analyzing chaotic electroosmotic flow mixing in 3D microchannels with patterned charged surfaces

NASA Astrophysics Data System (ADS)

Chang, Chih-Chang; Yang, Ruey-Jen

2006-08-01

This paper presents a numerical simulation investigation into electroosmotic flow mixing in three-dimensional microchannels with patterned non-uniform surface zeta potentials. Three types of micromixers are investigated, namely a straight diagonal strip mixer (i.e. the non-uniform surface zeta potential is applied along straight, diagonal strips on the lower wall of the mixing channel), a staggered asymmetric herringbone strip mixer and a straight diagonal/symmetric herringbone strip mixer. A particle tracing algorithm is used to visualize and evaluate the mixing performance of the various mixers. The particle trajectories and Poincaré maps of the various mixers are calculated from the three-dimensional flow fields. The surface charge patterns on the lower walls of the microchannels induce electroosmotic chaotic advection in the low Reynolds number flow regime, and hence enhance the passive mixing effect in the microfluidic devices. A quantitative measure of the mixing performance based on Shannon entropy is employed to quantify the mixing of two miscible fluids. The results show that the mixing efficiency increases as the magnitude of the heterogeneous zeta potential ratio (|ζR|) is increased, but decreases as the aspect ratio (H/W) is increased. The mixing efficiency of the straight diagonal strip mixer with a length ratio of l/W = 0.5 is slightly higher than that obtained from the same mixer with l/W = 1.0. Finally, the staggered asymmetric herringbone strip mixer with θ = 45°, ζR = -1, l/W = 0.5 and H/W = 0.2 provides the optimal mixing performance of all the mixers presented in this study.

Quantum Glass of Interacting Bosons with Off-Diagonal Disorder

NASA Astrophysics Data System (ADS)

Piekarska, A. M.; Kopeć, T. K.

2018-04-01

We study disordered interacting bosons described by the Bose-Hubbard model with Gaussian-distributed random tunneling amplitudes. It is shown that the off-diagonal disorder induces a spin-glass-like ground state, characterized by randomly frozen quantum-mechanical U(1) phases of bosons. To access criticality, we employ the "n -replica trick," as in the spin-glass theory, and the Trotter-Suzuki method for decomposition of the statistical density operator, along with numerical calculations. The interplay between disorder, quantum, and thermal fluctuations leads to phase diagrams exhibiting a glassy state of bosons, which are studied as a function of model parameters. The considered system may be relevant for quantum simulators of optical-lattice bosons, where the randomness can be introduced in a controlled way. The latter is supported by a proposition of experimental realization of the system in question.

Adjoint affine fusion and tadpoles

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

Urichuk, Andrew, E-mail: andrew.urichuk@uleth.ca; Walton, Mark A., E-mail: walton@uleth.ca; International School for Advanced Studies

2016-06-15

We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are writtenmore » for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.« less

An Algorithm for the Calculation of Exact Term Discrimination Values.

ERIC Educational Resources Information Center

Willett, Peter

1985-01-01

Reports algorithm for calculation of term discrimination values that is sufficiently fast in operation to permit use of exact values. Evidence is presented to show that relationship between term discrimination and term frequency is crucially dependent upon type of inter-document similarity measure used for calculation of discrimination values. (13…

ADHD and math - The differential effect on calculation and estimation.

PubMed

Ganor-Stern, Dana; Steinhorn, Ofir

2018-05-31

Adults with ADHD were compared to controls when solving multiplication problems exactly and when estimating the results of multidigit multiplication problems relative to reference numbers. The ADHD participants were slower than controls in the exact calculation and in the estimation tasks, but not less accurate. The ADHD participants were similar to controls in showing enhanced accuracy and speed for smaller problem sizes, for trials in which the reference numbers were smaller (vs. larger) than the exact answers and for reference numbers that were far (vs. close) from the exact answer. The two groups similarly used the approximated calculation and the sense of magnitude strategies. They differed however in strategy execution, mainly of the approximated calculation strategy, which requires working memory resources. The increase in reaction time associated with using the approximated calculation strategy was larger for the ADHD compared to the control participants. Thus, ADHD seems to selectively impair calculation processes in estimation tasks that rely on working memory, but it does not hamper estimation skills that are based on sense of magnitude. The educational implications of these findings are discussed. Copyright © 2018. Published by Elsevier B.V.

Studies of quantum dots in the quantum Hall regime

NASA Astrophysics Data System (ADS)

Goldmann, Eyal

We present two studies of quantum dots in the quantum Hall regime. In the first study, presented in Chapter 3, we investigate the edge reconstruction phenomenon believed to occur when the quantum dot filling fraction is n≲1 . Our approach involves the examination of large dots (≤40 electrons) using a partial diagonalization technique in which the occupancies of the deep interior orbitals are frozen. To interpret the results of this calculation, we evaluate the overlap between the diagonalized ground state and a set of trial wavefunctions which we call projected necklace (PN) states. A PN state is simply the angular momentum projection of a maximum density droplet surrounded by a ring of localized electrons. Our calculations reveal that PN states have up to 99% overlap with the diagonalized ground states, and are lower in energy than the states identified in Chamon and Wen's study of the edge reconstruction. In the second study, presented in Chapter 4, we investigate quantum dots in the fractional quantum Hall regime using a Hartree formulation of composite fermion theory. We find that under appropriate conditions, the chemical potential of the dots oscillates periodically with B due to the transfer of composite fermions between quasi-Landau bands. This effect is analogous the addition spectrum oscillations which occur in quantum dots in the integer quantum Hall regime. Period f0 oscillations are found in sharply confined dots with filling factors nu = 2/5 and nu = 2/3. Period 3 f0 oscillations are found in a parabolically confined nu = 2/5 dot. More generally, we argue that the oscillation period of dots with band pinning should vary continuously with B, whereas the period of dots without band pinning is f0 .

Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1,12-benzoperylene and polychrysene

NASA Astrophysics Data System (ADS)

Prodhan, Suryoday; Ramasesha, S.

2018-05-01

The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.

Accurate ab Initio Quartic Force Fields, Vibrational Frequencies, and Heats of Formation for FCN, FNC, ClCN, and ClNC

NASA Technical Reports Server (NTRS)

Lee, Timothy J.; Martin, Jan M. L.; Dateo, Christopher E.; Taylor, Peter R.

1995-01-01

The XCN and XNC (X = F, Cl) isomers have been investigated using the CCSD(T) method in conjunction with correlation consistent basis sets. Equilibrium geometries, harmonic frequencies, anharmonic constants, fundamental frequencies, and heats of formation have been evaluated. Agreement with experiment for the fundamental frequencies is very good, even for nu(sub 2), for CICN, which is subject to a strong Fermi resonance with 2nu(sub 3). It is also shown that a second-order perturbation theory approach to solving the nuclear Schroedinger equation gives results in excellent agreement with essentially exact variational calculations. This is true even for nu(sub 2) of ClCN, provided that near-singular terms are eliminated from the perturbation theory formulas and the appropriate Fermi interaction energy matrix is then diagonalized. A band at 615/cm, tentatively assigned as the Cl-N stretch in ClNC in matrix isolation experiments, is shown not to be due to ClNC. Accurate atomization energies are determined and are used to evaluate accurate heats of formation (3.1 +/- 1.5, 33.2 +/- 1.5, 72.6 +/- 1.5, and 75.9 +/- 1.5 kcal/mol for FCN, ClCN, FNC, and ClNC, respectively). It is expected that the theoretical heats of formation for FCN, FNC, and ClNC are the most accurate available.

Floquet engineering of Haldane Chern insulators and chiral bosonic phase transitions

NASA Astrophysics Data System (ADS)

Plekhanov, Kirill; Roux, Guillaume; Le Hur, Karyn

2017-01-01

The realization of synthetic gauge fields has attracted a lot of attention recently in relation to periodically driven systems and the Floquet theory. In ultracold atom systems in optical lattices and photonic networks, this allows one to simulate exotic phases of matter such as quantum Hall phases, anomalous quantum Hall phases, and analogs of topological insulators. In this paper, we apply the Floquet theory to engineer anisotropic Haldane models on the honeycomb lattice and two-leg ladder systems. We show that these anisotropic Haldane models still possess a topologically nontrivial band structure associated with chiral edge modes. Focusing on (interacting) boson systems in s -wave bands of the lattice, we show how to engineer through the Floquet theory, a quantum phase transition (QPT) between a uniform superfluid and a Bose-Einstein condensate analog of Fulde-Ferrell-Larkin-Ovchinnikov states, where bosons condense at nonzero wave vectors. We perform a Ginzburg-Landau analysis of the QPT on the graphene lattice, and compute observables such as chiral currents and the momentum distribution. The results are supported by exact diagonalization calculations and compared with those of the isotropic situation. The validity of high-frequency expansion in the Floquet theory is also tested using time-dependent simulations for various parameters of the model. Last, we show that the anisotropic choice for the effective vector potential allows a bosonization approach in equivalent ladder (strip) geometries.

Ground-state phase diagram of an anisotropic spin-1/2 model on the triangular lattice

NASA Astrophysics Data System (ADS)

Luo, Qiang; Hu, Shijie; Xi, Bin; Zhao, Jize; Wang, Xiaoqun

2017-04-01

Motivated by a recent experiment on the rare-earth material YbMgGaO4 [Y. Li et al., Phys. Rev. Lett. 115, 167203 (2015), 10.1103/PhysRevLett.115.167203], which found that the ground state of YbMgGaO4 is a quantum spin liquid, we study the ground-state phase diagram of an anisotropic spin-1 /2 model that was proposed to describe YbMgGaO4. Using the density matrix renormalization-group method in combination with the exact-diagonalization method, we calculate a variety of physical quantities, including the ground-state energy, the fidelity, the entanglement entropy and spin-spin correlation functions. Our studies show that in the quantum phase diagram, there is a 120∘ phase and two distinct stripe phases. The transitions from the two stripe phases to the 120∘ phase are of the first order. However, the transition between the two stripe phases is not of the first order, which is different from its classical counterpart. Additionally, we find no evidence for a quantum spin liquid in this model. Our results suggest that additional terms may also be important to model the material YbMgGaO4. These findings will stimulate further experimental and theoretical works in understanding the quantum spin-liquid ground state in YbMgGaO4.

Representation of the exact relativistic electronic Hamiltonian within the regular approximation

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2003-12-01

The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c-20. Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations.

Elementary exact calculations of degree growth and entropy for discrete equations.

PubMed

Halburd, R G

2017-05-01

Second-order discrete equations are studied over the field of rational functions [Formula: see text], where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confinement analysis, even when the singularities are not confined. This produces elementary yet rigorous entropy calculations.

Size Reduction of Hamiltonian Matrix for Large-Scale Energy Band Calculations Using Plane Wave Bases

NASA Astrophysics Data System (ADS)

Morifuji, Masato

2018-01-01

We present a method of reducing the size of a Hamiltonian matrix used in calculations of electronic states. In the electronic states calculations using plane wave basis functions, a large number of plane waves are often required to obtain precise results. Even using state-of-the-art techniques, the Hamiltonian matrix often becomes very large. The large computational time and memory necessary for diagonalization limit the widespread use of band calculations. We show a procedure of deriving a reduced Hamiltonian constructed using a small number of low-energy bases by renormalizing high-energy bases. We demonstrate numerically that the significant speedup of eigenstates evaluation is achieved without losing accuracy.

Exact p-values for pairwise comparison of Friedman rank sums, with application to comparing classifiers.

PubMed

Eisinga, Rob; Heskes, Tom; Pelzer, Ben; Te Grotenhuis, Manfred

2017-01-25

The Friedman rank sum test is a widely-used nonparametric method in computational biology. In addition to examining the overall null hypothesis of no significant difference among any of the rank sums, it is typically of interest to conduct pairwise comparison tests. Current approaches to such tests rely on large-sample approximations, due to the numerical complexity of computing the exact distribution. These approximate methods lead to inaccurate estimates in the tail of the distribution, which is most relevant for p-value calculation. We propose an efficient, combinatorial exact approach for calculating the probability mass distribution of the rank sum difference statistic for pairwise comparison of Friedman rank sums, and compare exact results with recommended asymptotic approximations. Whereas the chi-squared approximation performs inferiorly to exact computation overall, others, particularly the normal, perform well, except for the extreme tail. Hence exact calculation offers an improvement when small p-values occur following multiple testing correction. Exact inference also enhances the identification of significant differences whenever the observed values are close to the approximate critical value. We illustrate the proposed method in the context of biological machine learning, were Friedman rank sum difference tests are commonly used for the comparison of classifiers over multiple datasets. We provide a computationally fast method to determine the exact p-value of the absolute rank sum difference of a pair of Friedman rank sums, making asymptotic tests obsolete. Calculation of exact p-values is easy to implement in statistical software and the implementation in R is provided in one of the Additional files and is also available at http://www.ru.nl/publish/pages/726696/friedmanrsd.zip .

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

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

Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch; Pappu, Rohit V.

2014-07-21

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear inmore » the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom.« less

Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration

NASA Astrophysics Data System (ADS)

Eshuis, Henk; Yarkony, Julian; Furche, Filipp

2010-06-01

The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Møller-Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend et al., Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O(N4 log N) operations and O(N3) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the number of grid points. For most systems, 30-40 grid points yield μH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approximation to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2 [J. Jung et al., Phys. Rev. B 70, 205107 (2004)]. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.

Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration.

PubMed

Eshuis, Henk; Yarkony, Julian; Furche, Filipp

2010-06-21

The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Møller-Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend et al., Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O(N(4) log N) operations and O(N(3)) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the number of grid points. For most systems, 30-40 grid points yield muH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approximation to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2 [J. Jung et al., Phys. Rev. B 70, 205107 (2004)]. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.

Spin-orbit coupled systems in the atomic limit: rhenates, osmates, iridates

NASA Astrophysics Data System (ADS)

Paramekanti, Arun; Singh, David J.; Yuan, Bo; Casa, Diego; Said, Ayman; Kim, Young-June; Christianson, A. D.

2018-06-01

Motivated by RIXS experiments on a wide range of complex heavy oxides, including rhenates, osmates, and iridates, we discuss the theory of RIXS for site-localized t2 g orbital systems with strong spin-orbit coupling. For such systems, we present exact diagonalization results for the spectrum at different electron fillings, showing that it accesses "single-particle" and "multiparticle" excitations. This leads to a simple picture for the energies and intensities of the RIXS spectra in Mott insulators such as double perovskites which feature highly localized electrons, and yields estimates of the spin-orbit coupling and Hund's coupling in correlated 5 d oxides. We present new higher resolution RIXS data at the Re L3 edge in Ba2YReO6 which finds a previously unresolved peak splitting, providing further confirmation of our theoretical predictions. Using ab initio electronic structure calculations on Ba2M ReO6 (with M =Re , Os, Ir) we show that while the atomic limit yields a reasonable effective Hamiltonian description of the experimental observations, effects such as t2 g-eg interactions and hybridization with oxygen are important. Our ab initio estimate for the strength of the intersite exchange coupling shows that, compared to the d3 systems, the exchange is one or two orders of magnitude weaker in the d2 and d4 materials, which may partly explain the suppression of long-range magnetic order in the latter compounds. As a way to interpolate between the site-localized picture and our electronic structure band calculations, we discuss the spin-orbital levels of the M O6 cluster. This suggests a possible role for intracluster excitons in Ba2YIrO6 which may lead to a weak breakdown of the atomic Jeff=0 picture and to small magnetic moments.

Calibration-quality adiabatic potential energy surfaces for H3(+) and its isotopologues.

PubMed

Pavanello, Michele; Adamowicz, Ludwik; Alijah, Alexander; Zobov, Nikolai F; Mizus, Irina I; Polyansky, Oleg L; Tennyson, Jonathan; Szidarovszky, Tamás; Császár, Attila G

2012-05-14

Calibration-quality ab initio adiabatic potential energy surfaces (PES) have been determined for all isotopologues of the molecular ion H(3)(+). The underlying Born-Oppenheimer electronic structure computations used optimized explicitly correlated shifted Gaussian functions. The surfaces include diagonal Born-Oppenheimer corrections computed from the accurate electronic wave functions. A fit to the 41,655 ab initio points is presented which gives a standard deviation better than 0.1 cm(-1) when restricted to the points up to 6000 cm(-1) above the first dissociation asymptote. Nuclear motion calculations utilizing this PES, called GLH3P, and an exact kinetic energy operator given in orthogonal internal coordinates are presented. The ro-vibrational transition frequencies for H(3)(+), H(2)D(+), and HD(2)(+) are compared with high resolution measurements. The most sophisticated and complete procedure employed to compute ro-vibrational energy levels, which makes explicit allowance for the inclusion of non-adiabatic effects, reproduces all the known ro-vibrational levels of the H(3)(+) isotopologues considered to better than 0.2 cm(-1). This represents a significant (order-of-magnitude) improvement compared to previous studies of transitions in the visible. Careful treatment of linear geometries is important for high frequency transitions and leads to new assignments for some of the previously observed lines. Prospects for further investigations of non-adiabatic effects in the H(3)(+) isotopologues are discussed. In short, the paper presents (a) an extremely accurate global potential energy surface of H(3)(+) resulting from high accuracy ab initio computations and global fit, (b) very accurate nuclear motion calculations of all available experimental line data up to 16,000 cm(-1), and (c) results suggest that we can predict accurately the lines of H(3)(+) towards dissociation and thus facilitate their experimental observation.

Refraction traveltime tomography based on damped wave equation for irregular topographic model

NASA Astrophysics Data System (ADS)

Park, Yunhui; Pyun, Sukjoon

2018-03-01

Land seismic data generally have time-static issues due to irregular topography and weathered layers at shallow depths. Unless the time static is handled appropriately, interpretation of the subsurface structures can be easily distorted. Therefore, static corrections are commonly applied to land seismic data. The near-surface velocity, which is required for static corrections, can be inferred from first-arrival traveltime tomography, which must consider the irregular topography, as the land seismic data are generally obtained in irregular topography. This paper proposes a refraction traveltime tomography technique that is applicable to an irregular topographic model. This technique uses unstructured meshes to express an irregular topography, and traveltimes calculated from the frequency-domain damped wavefields using the finite element method. The diagonal elements of the approximate Hessian matrix were adopted for preconditioning, and the principle of reciprocity was introduced to efficiently calculate the Fréchet derivative. We also included regularization to resolve the ill-posed inverse problem, and used the nonlinear conjugate gradient method to solve the inverse problem. As the damped wavefields were used, there were no issues associated with artificial reflections caused by unstructured meshes. In addition, the shadow zone problem could be circumvented because this method is based on the exact wave equation, which does not require a high-frequency assumption. Furthermore, the proposed method was both robust to an initial velocity model and efficient compared to full wavefield inversions. Through synthetic and field data examples, our method was shown to successfully reconstruct shallow velocity structures. To verify our method, static corrections were roughly applied to the field data using the estimated near-surface velocity. By comparing common shot gathers and stack sections with and without static corrections, we confirmed that the proposed tomography algorithm can be used to correct the statics of land seismic data.

Calibration-quality adiabatic potential energy surfaces for H3+ and its isotopologues

NASA Astrophysics Data System (ADS)

Pavanello, Michele; Adamowicz, Ludwik; Alijah, Alexander; Zobov, Nikolai F.; Mizus, Irina I.; Polyansky, Oleg L.; Tennyson, Jonathan; Szidarovszky, Tamás; Császár, Attila G.

2012-05-01

Calibration-quality ab initio adiabatic potential energy surfaces (PES) have been determined for all isotopologues of the molecular ion H_3^+. The underlying Born-Oppenheimer electronic structure computations used optimized explicitly correlated shifted Gaussian functions. The surfaces include diagonal Born-Oppenheimer corrections computed from the accurate electronic wave functions. A fit to the 41 655 ab initio points is presented which gives a standard deviation better than 0.1 cm-1 when restricted to the points up to 6000 cm-1 above the first dissociation asymptote. Nuclear motion calculations utilizing this PES, called GLH3P, and an exact kinetic energy operator given in orthogonal internal coordinates are presented. The ro-vibrational transition frequencies for H_3^+, H2D+, and HD_2^+ are compared with high resolution measurements. The most sophisticated and complete procedure employed to compute ro-vibrational energy levels, which makes explicit allowance for the inclusion of non-adiabatic effects, reproduces all the known ro-vibrational levels of the H_3^+ isotopologues considered to better than 0.2 cm-1. This represents a significant (order-of-magnitude) improvement compared to previous studies of transitions in the visible. Careful treatment of linear geometries is important for high frequency transitions and leads to new assignments for some of the previously observed lines. Prospects for further investigations of non-adiabatic effects in the H_3^+ isotopologues are discussed. In short, the paper presents (a) an extremely accurate global potential energy surface of H_3^+ resulting from high accuracy ab initio computations and global fit, (b) very accurate nuclear motion calculations of all available experimental line data up to 16 000 cm-1, and (c) results suggest that we can predict accurately the lines of H_3^+ towards dissociation and thus facilitate their experimental observation.

Fidelity decay of the two-level bosonic embedded ensembles of random matrices

NASA Astrophysics Data System (ADS)

Benet, Luis; Hernández-Quiroz, Saúl; Seligman, Thomas H.

2010-12-01

We study the fidelity decay of the k-body embedded ensembles of random matrices for bosons distributed over two single-particle states. Fidelity is defined in terms of a reference Hamiltonian, which is a purely diagonal matrix consisting of a fixed one-body term and includes the diagonal of the perturbing k-body embedded ensemble matrix, and the perturbed Hamiltonian which includes the residual off-diagonal elements of the k-body interaction. This choice mimics the typical mean-field basis used in many calculations. We study separately the cases k = 2 and 3. We compute the ensemble-averaged fidelity decay as well as the fidelity of typical members with respect to an initial random state. Average fidelity displays a revival at the Heisenberg time, t = tH = 1, and a freeze in the fidelity decay, during which periodic revivals of period tH are observed. We obtain the relevant scaling properties with respect to the number of bosons and the strength of the perturbation. For certain members of the ensemble, we find that the period of the revivals during the freeze of fidelity occurs at fractional times of tH. These fractional periodic revivals are related to the dominance of specific k-body terms in the perturbation.

Step-Tapered Active-Region Mid-Infrared Quantum Cascade Lasers and Novel Fabrication Processes for Buried Heterostructures

DTIC Science & Technology

2015-07-28

up, g, IFR , E54 (or E43), and 54 (or 43) in STA-DPR, STA-SPR, and shallow-well QCL structures. 1 CHAPTER ONE INTRODUCTION 1.1 Introduction...much less transition diagonality than in shallow-well TA-QCL devices. To that effect, when calculating the IFR factor, summed over all transition...219 Å2 ps vs. 239 Å2 ps). However, when calculating the IFR factor, summed over all transition energies, affecting the EL linewidth [i.e., Eqn. (1

Study of electron-related intersubband optical properties in three coupled quantum wells wires with triangular transversal section

NASA Astrophysics Data System (ADS)

Tiutiunnyk, A.; Tulupenko, V.; Akimov, V.; Demediuk, R.; Morales, A. L.; Mora-Ramos, M. E.; Radu, A.; Duque, C. A.

2015-11-01

This work concerns theoretical study of confined electrons in a low-dimensional structure consisting of three coupled triangular GaAs/AlxGa1-xAs quantum wires. Calculations have been made in the effective mass and parabolic band approximations. In the calculations a diagonalization method to find the eigenfunctions and eigenvalues of the Hamiltonian was used. A comparative analysis of linear and nonlinear optical absorption coefficients and the relative change in the refractive index was made, which is tied to the intersubband electron transitions.

Implementation of a finite-amplitude method in a relativistic meson-exchange model

NASA Astrophysics Data System (ADS)

Sun, Xuwei; Lu, Dinghui

2017-08-01

The finite-amplitude method is a feasible numerical approach to large scale random phase approximation calculations. It avoids the storage and calculation of residual interaction elements as well as the diagonalization of the RPA matrix, which will be prohibitive when the configuration space is huge. In this work we finished the implementation of a finite-amplitude method in a relativistic meson exchange mean field model with axial symmetry. The direct variation approach makes our FAM scheme capable of being extended to the multipole excitation case.

Activation of the serratus anterior and upper trapezius in a population with winged and tipped scapulae during push-up-plus and diagonal shoulder-elevation.

PubMed

Park, Se-Yeon; Yoo, Won-Gyu

2015-01-01

Scapular winging and tipping are types of abnormal scapular kinematics, which is caused by not only the entrapment of peripheral nerve, but also imbalance of the scapulothoracic musculatures. The purpose of this study was to investigate the presence of muscular imbalance in the middle and lower parts of the serratus anterior and upper trapezius in people with scapular winging and tipping. Twenty male participants (age, 23.0 ± 1.92 y) were placed into symptomatic group (n = 10) and control group (n = 10). Participants completed two individual trials of a push-up plus, and a diagonal shoulder elevation, while electromyography (EMG) recorded muscle activity of the low and middle serratus anterior and upper trapezius. The root mean squared EMG values for three muscles were normalized using maximum voluntary isometric contractions (%MVIC). The value was calculated using modified isolation equation for comparing activation of middle and lower serratus anterior (%isolation). During a diagonal shoulder elevation, the % maximal voluntary isometric contraction (%MVIC) data showed that the symptomatic participants had significantly greater activation of the middle serratus anterior compared to the control group (P = 0.01). During a diagonal shoulder elevation, the symptomatic participants had not only significantly increased %isolation of the middle serratus anterior, but also significantly decreased for the lower serratus anterior compare with the control group (p = 0.00). Present result indicated that different muscle activation between middle and lower serratus anterior could represent in group with scapular dyskinesis, and need for selective activation of the lower serratus anterior in patients with scapular winging and tipping.

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X.

PubMed

Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A; Sondhi, S L

2017-12-13

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'. © 2017 The Author(s).

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A.; Sondhi, S. L.

2017-10-01

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Density-Functional Theory description of transport in the single-electron transistor

NASA Astrophysics Data System (ADS)

Zawadzki, Krissia; Oliveira, Luiz N.

The Kondo effect governs the low-temperature transport properties of the single electron transistor (SET), a quantum dot bridging two electron gases. In the weak coupling limit, for odd dot occupation, the gate-potential profile of the conductance approaches a step, known as the Kondo plateau. The plateau and other SET properties being well understood on the basis of the Anderson model, more realistic (i. e., DFT) descriptions of the device are now desired. This poses a challenge, since the SET is strongly correlated. DFT computations that reproduce the conductance plateau have been reported, e. g., by, which rely on the exact functional provided by the Bethe-Ansatz solution for the Anderson model. Here, sticking to DFT tradition, we employ a functional derived from a homogeneous system: the parametrization of the Lieb-Wu solution for the Hubbard model due to. Our computations reproduce the plateau and yield other results in accurate agreement with the exact diagonalization of the Anderson Hamiltonian. The prospects for extensions to realistic descriptions of two-dimensional nanostructured devices will be discussed. Luiz N. Oliveira thanks CNPq (312658/2013-3) and Krissia Zawadzki thanks CNPq (140703/2014-4) for financial support.

Time-dependent Gutzwiller theory of magnetic excitations in the Hubbard model

NASA Astrophysics Data System (ADS)

Seibold, G.; Becca, F.; Rubin, P.; Lorenzana, J.

2004-04-01

We use a spin-rotational invariant Gutzwiller energy functional to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). The method can be viewed as an extension of the previously developed GA+RPA approach for the charge sector [G. Seibold and J. Lorenzana, Phys. Rev. Lett. 86, 2605 (2001)] with respect to the inclusion of the magnetic excitations. Unlike the charge case, no assumptions about the time evolution of the double occupancy are needed in this case. Interestingly, in a spin-rotational invariant system, we find the correct degeneracy between triplet excitations, showing the consistency of both computations. Since no restrictions are imposed on the symmetry of the underlying saddle-point solution, our approach is suitable for the evaluation of the magnetic susceptibility and dynamical structure factor in strongly correlated inhomogeneous systems. We present a detailed study of the quality of our approach by comparing with exact diagonalization results and show its much higher accuracy compared to the conventional Hartree-Fock+RPA theory. In infinite dimensions, where the GA becomes exact for the Gutzwiller variational energy, we evaluate ferromagnetic and antiferromagnetic instabilities from the transverse magnetic susceptibility. The resulting phase diagram is in complete agreement with previous variational computations.

Inner Space Perturbation Theory in Matrix Product States: Replacing Expensive Iterative Diagonalization.

PubMed

Ren, Jiajun; Yi, Yuanping; Shuai, Zhigang

2016-10-11

We propose an inner space perturbation theory (isPT) to replace the expensive iterative diagonalization in the standard density matrix renormalization group theory (DMRG). The retained reduced density matrix eigenstates are partitioned into the active and secondary space. The first-order wave function and the second- and third-order energies are easily computed by using one step Davidson iteration. Our formulation has several advantages including (i) keeping a balance between the efficiency and accuracy, (ii) capturing more entanglement with the same amount of computational time, (iii) recovery of the standard DMRG when all the basis states belong to the active space. Numerical examples for the polyacenes and periacene show that the efficiency gain is considerable and the accuracy loss due to the perturbation treatment is very small, when half of the total basis states belong to the active space. Moreover, the perturbation calculations converge in all our numerical examples.

Multiple-body simulation with emphasis on integrated Space Shuttle vehicle

NASA Technical Reports Server (NTRS)

Chiu, Ing-Tsau

1993-01-01

The program to obtain intergrid communications - Pegasus - was enhanced to make better use of computing resources. Periodic block tridiagonal and penta-diagonal diagonal routines in OVERFLOW were modified to use a better algorithm to speed up the calculation for grids with periodic boundary conditions. Several programs were added to collar grid tools and a user friendly shell script was developed to help users generate collar grids. User interface for HYPGEN was modified to cope with the changes in HYPGEN. ET/SRB attach hardware grids were added to the computational model for the space shuttle and is currently incorporated into the refined shuttle model jointly developed at Johnson Space Center and Ames Research Center. Flow simulation for the integrated space shuttle vehicle at flight Reynolds number was carried out and compared with flight data as well as the earlier simulation for wind tunnel Reynolds number.

Enhanced magneto-optical Kerr effect at Fe/insulator interfaces

NASA Astrophysics Data System (ADS)

Gu, Bo; Takahashi, Saburo; Maekawa, Sadamichi

2017-12-01

Using density functional theory calculations, we have found an enhanced magneto-optical Kerr effect in Fe/insulator interfaces. The results of our study indicate that interfacial Fe atoms in the Fe films have a low-dimensional nature, which causes the following two effects: (i) The diagonal component σx x of the optical conductivity decreases dramatically because the hopping integral for electrons between Fe atoms is suppressed by the low dimensionality. (ii) The off-diagonal component σx y of the optical conductivity does not change at low photon energies, but it is enhanced at photon energies around 2 eV, where we obtain enhanced orbital magnetic moments and spin-orbit correlations for the interfacial Fe atoms. A large Kerr angle develops in proportion to the ratio σx y/σx x . Our findings indicate an efficient way to enhance the effect of spin-orbit coupling at metal/insulator interfaces without using heavy elements.

Long-Range Adiabatic Corrections to the Ground Molecular State of Alkali-Metal Dimers.

NASA Astrophysics Data System (ADS)

Marinescu, M.; Dalgarno, A.

1997-04-01

The structure of the long-range limit of the diagonal adiabatic corrections to the ground molecular state of diatomic molecules, may be expressed as a series of inverse powers of internuclear distance, R. The coefficients of this expansion are proportional to the inverse of the nuclear mass. Thus, they may be interpreted as a nuclear mass-dependent corrections to the dispersion coefficients. Using perturbation theory we have calculated the long-range coefficients of the diagonal adiabatic corrections up to the order of R-10. The final expressions are in terms of integrals over imaginary frequencies of products of atomic matrix elements involving Green's functions of complex energy. Thus, in our approach the molecular problem is reduced to an atomic one. Numerical evaluations have been done for all alkali-metal dimers. We acknowledge the support of the U.S. Dept. of Energy.

Negative Magnetoresistance in Viscous Flow of Two-Dimensional Electrons.

PubMed

Alekseev, P S

2016-10-14

At low temperatures, in very clean two-dimensional (2D) samples, the electron mean free path for collisions with static defects and phonons becomes greater than the sample width. Under this condition, the electron transport occurs by formation of a viscous flow of an electron fluid. We study the viscous flow of 2D electrons in a magnetic field perpendicular to the 2D layer. We calculate the viscosity coefficients as the functions of magnetic field and temperature. The off-diagonal viscosity coefficient determines the dispersion of the 2D hydrodynamic waves. The decrease of the diagonal viscosity in magnetic field leads to negative magnetoresistance which is temperature and size dependent. Our analysis demonstrates that this viscous mechanism is responsible for the giant negative magnetoresistance recently observed in the ultrahigh-mobility GaAs quantum wells. We conclude that 2D electrons in those structures in moderate magnetic fields should be treated as a viscous fluid.

Negative Magnetoresistance in Viscous Flow of Two-Dimensional Electrons

NASA Astrophysics Data System (ADS)

Alekseev, P. S.

2016-10-01

At low temperatures, in very clean two-dimensional (2D) samples, the electron mean free path for collisions with static defects and phonons becomes greater than the sample width. Under this condition, the electron transport occurs by formation of a viscous flow of an electron fluid. We study the viscous flow of 2D electrons in a magnetic field perpendicular to the 2D layer. We calculate the viscosity coefficients as the functions of magnetic field and temperature. The off-diagonal viscosity coefficient determines the dispersion of the 2D hydrodynamic waves. The decrease of the diagonal viscosity in magnetic field leads to negative magnetoresistance which is temperature and size dependent. Our analysis demonstrates that this viscous mechanism is responsible for the giant negative magnetoresistance recently observed in the ultrahigh-mobility GaAs quantum wells. We conclude that 2D electrons in those structures in moderate magnetic fields should be treated as a viscous fluid.

Low-rank factorization of electron integral tensors and its application in electronic structure theory

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

Peng, Bo; Kowalski, Karol

In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doublesmore » (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.« less

Infrared singularities of scattering amplitudes in perturbative QCD

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

Becher, Thomas; Neubert, Matthias

2013-11-01

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficientsmore » of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.« less

High-Power Collective Charging of a Solid-State Quantum Battery

NASA Astrophysics Data System (ADS)

Ferraro, Dario; Campisi, Michele; Andolina, Gian Marcello; Pellegrini, Vittorio; Polini, Marco

2018-03-01

Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of N two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model ("Dicke QB"), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode ("Rabi QB"). By employing exact diagonalization, we demonstrate the emergence of a quantum advantage in the charging power of Dicke QBs, which scales like √{N } for N ≫1 .

Perfect Diode in Quantum Spin Chains

NASA Astrophysics Data System (ADS)

Balachandran, Vinitha; Benenti, Giuliano; Pereira, Emmanuel; Casati, Giulio; Poletti, Dario

2018-05-01

We study the rectification of the spin current in X X Z chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product state algorithm, we find that a large rectification (of the order of 1 04) is attainable even using a short chain of N =8 spins, when one-half of the chain is gapless while the other has a large enough anisotropy. We present evidence of diffusive transport when the current is driven in one direction and of a transition to an insulating behavior of the system when driven in the opposite direction, leading to a perfect diode in the thermodynamic limit. The above results are explained in terms of matching of the spectrum of magnon excitations between the two halves of the chain.

Anisotropy-driven transition from the Moore-Read state to quantum Hall stripes

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Sodemann, Inti; Sheng, D. N.; Fu, Liang

2017-05-01

We investigate the nature of the quantum Hall liquid in a half-filled second Landau level (n =1 ) as a function of band mass anisotropy using numerical exact diagonalization and density matrix renormalization group methods. We find increasing the mass anisotropy induces a quantum phase transition from the Moore-Read state to a charge density wave state. By analyzing the energy spectrum, guiding center structure factors, and by adding weak pinning potentials, we show that this charge density wave is a unidirectional quantum Hall stripe, which has a periodicity of a few magnetic lengths and survives in the thermodynamic limit. We find smooth profiles for the guiding center occupation function that reveal the strong coupling nature of the array of chiral Luttinger liquids residing at the stripe edges.

Formation of helical domain walls in the fractional quantum Hall regime as a step toward realization of high-order non-Abelian excitations

NASA Astrophysics Data System (ADS)

Wu, Tailung; Wan, Zhong; Kazakov, Aleksandr; Wang, Ying; Simion, George; Liang, Jingcheng; West, Kenneth W.; Baldwin, Kirk; Pfeiffer, Loren N.; Lyanda-Geller, Yuli; Rokhinson, Leonid P.

2018-06-01

We propose an experimentally feasible platform to realize parafermions (high-order non-Abelian excitations) based on spin transitions in the fractional quantum Hall effect regime. As a proof of concept we demonstrate a local control of the spin transition at a filling factor 2/3 and formation of a conducting fractional helical domain wall (fhDW) along a gate boundary. Coupled to an s -wave superconductor these fhDWs are expected to support parafermionic excitations. We present exact diagonalization numerical studies of fhDWs and show that they indeed possess electronic and magnetic structures needed for the formation of parafermions. A reconfigurable network of fhDWs will allow manipulation and braiding of parafermionic excitations in multigate devices.

Emergent Fermi Sea in A System of Interacting Bosons

NASA Astrophysics Data System (ADS)

Wu, Yinghai; Jain, Jainendra

2015-03-01

An understanding of the possible ways in which interactions can produce fundamentally new emergent many-body states is a central problem of condensed matter physics. We ask if a Fermi sea can arise in a system of bosons subject to contact interaction. Based on exact diagonalization studies and variational wave functions, we predict that such a state is likely to occur when a system of two-component bosons in two dimensions, interacting via a species independent contact interaction, is exposed to a synthetic magnetic field of strength that corresponds to a filling factor of unity. The bosons each bind a single vortex as a result of the repulsive interaction, and these fermionic bound states, namely composite fermions, form a spin-singlet Fermi sea. Financial support from the DOE under Grant No. DE-SC0005042.

Crossover between few and many fermions in a harmonic trap

NASA Astrophysics Data System (ADS)

Grining, Tomasz; Tomza, Michał; Lesiuk, Michał; Przybytek, Michał; Musiał, Monika; Moszynski, Robert; Lewenstein, Maciej; Massignan, Pietro

2015-12-01

The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled-cluster method. For few fermions we recover the results of exact diagonalization, yet with this method we are able to study much larger systems. We compute the energy, the chemical potential, the pairing gap, and the density profile of the trapped clouds, smoothly mapping the crossover between the few-body and many-body limits. The energy is found to converge surprisingly rapidly to the many-body result for every value of the interaction strength. Many more particles are instead needed to give rise to the nonanalytic behavior of the pairing gap, and to smoothen the pronounced even-odd oscillations of the chemical potential induced by the shell structure of the trap.

Improved treatment of exact exchange in Quantum ESPRESSO

DOE PAGES

Barnes, Taylor A.; Kurth, Thorsten; Carrier, Pierre; ...

2017-01-18

Here, we present an algorithm and implementation for the parallel computation of exact exchange in Quantum ESPRESSO (QE) that exhibits greatly improved strong scaling. QE is an open-source software package for electronic structure calculations using plane wave density functional theory, and supports the use of local, semi-local, and hybrid DFT functionals. Wider application of hybrid functionals is desirable for the improved simulation of electronic band energy alignments and thermodynamic properties, but the computational complexity of evaluating the exact exchange potential limits the practical application of hybrid functionals to large systems and requires efficient implementations. We demonstrate that existing implementations ofmore » hybrid DFT that utilize a single data structure for both the local and exact exchange regions of the code are significantly limited in the degree of parallelization achievable. We present a band-pair parallelization approach, in which the calculation of exact exchange is parallelized and evaluated independently from the parallelization of the remainder of the calculation, with the wavefunction data being efficiently transformed on-the-fly into a form that is optimal for each part of the calculation. For a 64 water molecule supercell, our new algorithm reduces the overall time to solution by nearly an order of magnitude.« less

Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation

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

Zhang, Du; Yang, Weitao

An efficient method for calculating excitation energies based on the particle-particle random phase approximation (ppRPA) is presented. Neglecting the contributions from the high-lying virtual states and the low-lying core states leads to the significantly smaller active-space ppRPA matrix while keeping the error to within 0.05 eV from the corresponding full ppRPA excitation energies. The resulting computational cost is significantly reduced and becomes less than the construction of the non-local Fock exchange potential matrix in the self-consistent-field (SCF) procedure. With only a modest number of active orbitals, the original ppRPA singlet-triplet (ST) gaps as well as the low-lying single and doublemore » excitation energies can be accurately reproduced at much reduced computational costs, up to 100 times faster than the iterative Davidson diagonalization of the original full ppRPA matrix. For high-lying Rydberg excitations where the Davidson algorithm fails, the computational savings of active-space ppRPA with respect to the direct diagonalization is even more dramatic. The virtues of the underlying full ppRPA combined with the significantly lower computational cost of the active-space approach will significantly expand the applicability of the ppRPA method to calculate excitation energies at a cost of O(K^{4}), with a prefactor much smaller than a single SCF Hartree-Fock (HF)/hybrid functional calculation, thus opening up new possibilities for the quantum mechanical study of excited state electronic structure of large systems.« less

Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation

DOE PAGES

Zhang, Du; Yang, Weitao

2016-10-13

An efficient method for calculating excitation energies based on the particle-particle random phase approximation (ppRPA) is presented. Neglecting the contributions from the high-lying virtual states and the low-lying core states leads to the significantly smaller active-space ppRPA matrix while keeping the error to within 0.05 eV from the corresponding full ppRPA excitation energies. The resulting computational cost is significantly reduced and becomes less than the construction of the non-local Fock exchange potential matrix in the self-consistent-field (SCF) procedure. With only a modest number of active orbitals, the original ppRPA singlet-triplet (ST) gaps as well as the low-lying single and doublemore » excitation energies can be accurately reproduced at much reduced computational costs, up to 100 times faster than the iterative Davidson diagonalization of the original full ppRPA matrix. For high-lying Rydberg excitations where the Davidson algorithm fails, the computational savings of active-space ppRPA with respect to the direct diagonalization is even more dramatic. The virtues of the underlying full ppRPA combined with the significantly lower computational cost of the active-space approach will significantly expand the applicability of the ppRPA method to calculate excitation energies at a cost of O(K^{4}), with a prefactor much smaller than a single SCF Hartree-Fock (HF)/hybrid functional calculation, thus opening up new possibilities for the quantum mechanical study of excited state electronic structure of large systems.« less

Distilling perfect GHZ states from two copies of non-GHZ-diagonal mixed states

NASA Astrophysics Data System (ADS)

Wang, Xin-Wen; Tang, Shi-Qing; Yuan, Ji-Bing; Zhang, Deng-Yu

2017-06-01

It has been shown that a nearly pure Greenberger-Horne-Zeilinger (GHZ) state could be distilled from a large (even infinite) number of GHZ-diagonal states that can be obtained by depolarizing general multipartite mixed states (non-GHZ-diagonal states) through sequences of (probabilistic) local operations and classical communications. We here demonstrate that perfect GHZ states can be extracted, with certain probabilities, from two copies of non-GHZ-diagonal mixed states when some conditions are satisfied. This result implies that it is not necessary to depolarize these entangled mixed states to the GHZ-diagonal type, and that they are better than GHZ-diagonal states for distillation of pure GHZ states. We find a wide class of multipartite entangled mixed states that fulfill the requirements. Moreover, we display that the obtained result can be applied to practical noisy environments, e.g., amplitude-damping channels. Our findings provide an important complementarity to conventional GHZ-state distillation protocols (designed for GHZ-diagonal states) in theory, as well as having practical applications.

Iterative algorithm for joint zero diagonalization with application in blind source separation.

PubMed

Zhang, Wei-Tao; Lou, Shun-Tian

2011-07-01

A new iterative algorithm for the nonunitary joint zero diagonalization of a set of matrices is proposed for blind source separation applications. On one hand, since the zero diagonalizer of the proposed algorithm is constructed iteratively by successive multiplications of an invertible matrix, the singular solutions that occur in the existing nonunitary iterative algorithms are naturally avoided. On the other hand, compared to the algebraic method for joint zero diagonalization, the proposed algorithm requires fewer matrices to be zero diagonalized to yield even better performance. The extension of the algorithm to the complex and nonsquare mixing cases is also addressed. Numerical simulations on both synthetic data and blind source separation using time-frequency distributions illustrate the performance of the algorithm and provide a comparison to the leading joint zero diagonalization schemes.

LSMS

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

Eisenbach, Markus; Li, Ying Wai; Liu, Xianglin

2017-12-01

LSMS is a first principles, Density Functional theory based, electronic structure code targeted mainly at materials applications. LSMS calculates the local spin density approximation to the diagonal part of the electron Green's function. The electron/spin density and energy are easily determined once the Green's function is known. Linear scaling with system size is achieved in the LSMS by using several unique properties of the real space multiple scattering approach to the Green's function.

Large scale shell model study of the evolution of mixed-symmetry states in chains of nuclei around 132Sn

NASA Astrophysics Data System (ADS)

Lo Iudice, N.; Bianco, D.; Andreozzi, F.; Porrino, A.; Knapp, F.

2012-10-01

Large scale shell model calculations based on a new diagonalization algorithm are performed in order to investigate the mixed symmetry states in chains of nuclei in the proximity of N=82. The resulting spectra and transitions are in agreement with the experiments and consistent with the scheme provided by the interacting boson model.

Effects on Calculated Half-Widths and Shifts from the Line Coupling for Asymmetric-Top Molecules

NASA Technical Reports Server (NTRS)

Ma, Q.; Boulet, C.; Tipping, R. H.

2014-01-01

The refinement of the Robert-Bonamy formalism by considering the line coupling for linear molecules developed in our previous studies [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013); 140, 104304 (2014)] have been extended to asymmetric-top molecules. For H2O immersed in N2 bath, the line coupling selection rules applicable for the pure rotational band to determine whether two specified lines are coupled or not are established. Meanwhile, because the coupling strengths are determined by relative importance of off-diagonal matrix elements versus diagonal elements of the operator -iS1 -S2, quantitative tools are developed with which one is able to remove weakly coupled lines from consideration. By applying these tools, we have found that within reasonable tolerances, most of the H2O lines in the pure rotational band are not coupled. This reflects the fact that differences of energy levels of the H2O states are pretty large. But, there are several dozen strongly coupled lines and they can be categorized into different groups such that the line couplings occur only within the same groups. In practice, to identify those strongly coupled lines and to confine them into sub-linespaces are crucial steps in considering the line coupling. We have calculated half-widths and shifts for some groups, including the line coupling. Based on these calculations, one can conclude that for most of the H2O lines, it is unnecessary to consider the line coupling. However, for several dozens of lines, effects on the calculated half-widths from the line coupling are small, but remain noticeable and reductions of calculated half-widths due to including the line coupling could reach to 5%. Meanwhile, effects on the calculated shifts are very significant and variations of calculated shifts could be as large as 25%.

Effects on calculated half-widths and shifts from the line coupling for asymmetric-top molecules

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

Ma, Q.; Boulet, C.; Tipping, R. H.

2014-06-28

The refinement of the Robert-Bonamy formalism by considering the line coupling for linear molecules developed in our previous studies [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013); 140, 104304 (2014)] have been extended to asymmetric-top molecules. For H{sub 2}O immersed in N{sub 2} bath, the line coupling selection rules applicable for the pure rotational band to determine whether two specified lines are coupled or not are established. Meanwhile, because the coupling strengths are determined by relative importance of off-diagonal matrix elements versus diagonal elements of the operator −iS{sub 1} − S{sub 2}, quantitative toolsmore » are developed with which one is able to remove weakly coupled lines from consideration. By applying these tools, we have found that within reasonable tolerances, most of the H{sub 2}O lines in the pure rotational band are not coupled. This reflects the fact that differences of energy levels of the H{sub 2}O states are pretty large. But, there are several dozen strongly coupled lines and they can be categorized into different groups such that the line couplings occur only within the same groups. In practice, to identify those strongly coupled lines and to confine them into sub-linespaces are crucial steps in considering the line coupling. We have calculated half-widths and shifts for some groups, including the line coupling. Based on these calculations, one can conclude that for most of the H{sub 2}O lines, it is unnecessary to consider the line coupling. However, for several dozens of lines, effects on the calculated half-widths from the line coupling are small, but remain noticeable and reductions of calculated half-widths due to including the line coupling could reach to 5%. Meanwhile, effects on the calculated shifts are very significant and variations of calculated shifts could be as large as 25%.« less

Exotic emergent phenomena in the fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

Coimbatore Balram, Ajit

When two-dimensional electron systems are subjected to a perpendicular magnetic field, they exhibit the marvelous phenomenon known as the fractional quantum Hall effect (FQHE). This arises as a result of the formation of composite fermions (CFs), which are bound states of electrons and an even number of vortices. The FQHE of electrons is understood as arising from the integer QHE (IQHE) of CFs. Alongside superconductivity, Bose-Einstein condensation and spin-liquids, the CF quantum fluid provides a model system for understanding strongly correlated systems and their collective behavior. Although it has been more than three decades since the experimental discovery of FQHE, the field continues to produce profound insights and pose interesting problems some of which have been addressed in this thesis. A major unanswered question in the field of FQHE is the mechanism of FQHE for the 1/3 state in the second Landau level (7/3 state). Numerical studies of this state have brought out the following puzzle: exact diagonalization studies suggest that the ground state and excitations of 1/3 state in the second Landau level are different from its counterpart in the lowest Landau level (LLL), while entanglement spectra of the two states point to the fact that they fall in the same universality class. Using methods from CF theory we show that the excitations of the 7/3 FQHE lie in the same universality class as those of the 1/3 state but are strongly modified due to screening by CF excitons, thereby settling the above discrepancy. Armed with the exciton calculation, we illustrate that by imposing certain exclusion rules for CF excitons one can build the full spectrum of FQHE in the lowest Landau level. Equipped with the techniques to calculate the spectra of FQHE systems, we carry out an extensive study of FQHE of multi-component CFs (systems possessing degrees of freedom for eg: valley and spin degeneracy), which is applicable to FQHE in systems such as graphene, AlAs and GaAs quantum wells. We provide a comprehensive list of the possible fractions, their ground state energies and the critical "Zeeman" energies for the "spin" transitions between the states and compare them with the experimental observations. In the lowest Landau level of graphene, we find an excellent agreement between theory and experiments. However, in the second Landau level of graphene we find an unexpected spontaneous spin polarization of CFs. We predict that there are no spin transitions to be expected in the second Landau level of graphene, a result that could be tested out in experiments. We reanalyzed some old experimental data showing excitation modes below the Zeeman energy in the vicinity of 1/3 filling of the lowest Landau level whose theoretical origin was unexplained. Using methods of exact diagonalization and CF theory we demonstrate that these modes arise as a result of formation of trions of CFs which have sub-Zeeman energy due to skyrmion-like physics. In the past couple of years, the Fermi wave vector of CFs has been measured very accurately in pioneering experiments at Princeton University. Motivated by these experiments we address the issue of the validity of Luttinger's theorem (which is a fundamental tenet of Landau Fermi liquid theory) for the Fermi sea of CFs. Our calculations suggest that the CF Fermi sea may violate Luttinger's theorem slightly. This not only provides a nontrivial example of a non-Fermi liquid, but gives new insight into the nature of the CF Fermi sea state and opens a new line of inquiry in the field of FQHE.

Exact Exchange calculations for periodic systems: a real space approach

NASA Astrophysics Data System (ADS)

Natan, Amir; Marom, Noa; Makmal, Adi; Kronik, Leeor; Kuemmel, Stephan

2011-03-01

We present a real-space method for exact-exchange Kohn-Sham calculations of periodic systems. The method is based on self-consistent solutions of the optimized effective potential (OEP) equation on a three-dimensional non-orthogonal grid, using norm conserving pseudopotentials. These solutions can be either exact, using the S-iteration approach, or approximate, using the Krieger, Li, and Iafrate (KLI) approach. We demonstrate, using a variety of systems, the importance of singularity corrections and use of appropriate pseudopotentials.

High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

NASA Astrophysics Data System (ADS)

Farnell, D. J. J.; Richter, J.; Zinke, R.; Bishop, R. F.

2009-04-01

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. Néel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half J 1- J 2 model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at J 2/ J 1=0.5. The dimerized phase is stable over a range of values for J 2/ J 1 around 0.5, and results for the ground-state energies are in good agreement with the results of exact diagonalizations of finite-length chains in this regime. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of J 2/ J 1. A radical change is also observed in the behavior of the CCM sublattice magnetization as we enter the dimerized phase. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the Néel and the dimerized phases. Once again, very good results for the ground-state energies are obtained. We find CCM critical points of the bra-state equations that are in agreement with the known phase transition point for this model. The results for the sublattice magnetization remain near to the "true" value of zero over much of the dimerized regime, although they diverge exactly at the critical point. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV4O9 (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, Néel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits. Furthermore, we estimate the range over which the Néel order is stable, and we find the CCM result is in reasonable agreement with the results obtained by other methods. Our new approach has the dual advantages that it is simple to implement and that existing CCM codes for independent-spin product model states may be used from the outset. Furthermore, it also greatly extends the range of applicability to which the CCM may be applied. We believe that the CCM now provides an excellent choice of method for the study of systems with valence-bond quantum ground states.

Interaction and charge transfer between dielectric spheres: Exact and approximate analytical solutions.

PubMed

Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning

2016-11-21

We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.

NLTE steady-state response matrix method.

NASA Astrophysics Data System (ADS)

Faussurier, G.; More, R. M.

2000-05-01

A connection between atomic kinetics and non-equilibrium thermodynamics has been recently established by using a collisional-radiative model modified to include line absorption. The calculated net emission can be expressed as a non-local thermodynamic equilibrium (NLTE) symmetric response matrix. In the paper, this connection is extended to both cases of the average-atom model and the Busquet's model (RAdiative-Dependent IOnization Model, RADIOM). The main properties of the response matrix still remain valid. The RADIOM source function found in the literature leads to a diagonal response matrix, stressing the absence of any frequency redistribution among the frequency groups at this order of calculation.

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Rössler, Thomas

2015-11-01

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark flow technique.

Monte Carlo exploration of Mikheyev-Smirnov-Wolfenstein solutions to the solar neutrino problem

NASA Technical Reports Server (NTRS)

Shi, X.; Schramm, D. N.; Bahcall, J. N.

1992-01-01

The paper explores the impact of astrophysical uncertainties on the Mikheyev-Smirnov-Wolfenstein (MSW) solution by calculating the allowed MSW solutions for 1000 different solar models with a Monte Carlo selection of solar model input parameters, assuming a full three-family MSW mixing. Applications are made to the chlorine, gallium, Kamiokande, and Borexino experiments. The initial GALLEX result limits the mixing parameters to the upper diagonal and the vertical regions of the MSW triangle. The expected event rates in the Borexino experiment are also calculated, assuming the MSW solutions implied by GALLEX.

Forces and mechanical energy fluctuations during diagonal stride roller skiing; running on wheels?

PubMed

Kehler, Alyse L; Hajkova, Eliska; Holmberg, Hans-Christer; Kram, Rodger

2014-11-01

Mechanical energy can be conserved during terrestrial locomotion in two ways: the inverted pendulum mechanism for walking and the spring-mass mechanism for running. Here, we investigated whether diagonal stride cross-country roller skiing (DIA) utilizes similar mechanisms. Based on previous studies, we hypothesized that running and DIA would share similar phase relationships and magnitudes of kinetic energy (KE), and gravitational potential energy (GPE) fluctuations, indicating elastic energy storage and return, as if roller skiing is like 'running on wheels'. Experienced skiers (N=9) walked and ran at 1.25 and 3 m s(-1), respectively, and roller skied with DIA at both speeds on a level dual-belt treadmill that recorded perpendicular and parallel forces. We calculated the KE and GPE of the center of mass from the force recordings. As expected, the KE and GPE fluctuated with an out-of-phase pattern during walking and an in-phase pattern during running. Unlike walking, during DIA, the KE and GPE fluctuations were in phase, as they are in running. However, during the glide phase, KE was dissipated as frictional heat and could not be stored elastically in the tendons, as in running. Elastic energy storage and return epitomize running and thus we reject our hypothesis. Diagonal stride cross-country skiing is a biomechanically unique movement that only superficially resembles walking or running. © 2014. Published by The Company of Biologists Ltd.

NON-GAUSSIANITIES IN THE LOCAL CURVATURE OF THE FIVE-YEAR WMAP DATA

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

Rudjord, Oeystein; Groeneboom, Nicolaas E.; Hansen, Frode K.

Using the five-year WMAP data, we re-investigate claims of non-Gaussianities and asymmetries detected in local curvature statistics of the one-year WMAP data. In Hansen et al., it was found that the northern ecliptic hemisphere was non-Gaussian at the {approx}1% level testing the densities of hill, lake, and saddle points based on the second derivatives of the cosmic microwave background temperature map. The five-year WMAP data have a much lower noise level and better control of systematics. Using these, we find that the anomalies are still present at a consistent level. Also the direction of maximum non-Gaussianity remains. Due to limitedmore » availability of computer resources, Hansen et al. were unable to calculate the full covariance matrix for the {chi}{sup 2}-test used. Here, we apply the full covariance matrix instead of the diagonal approximation and find that the non-Gaussianities disappear and there is no preferred non-Gaussian direction. We compare with simulations of weak lensing to see if this may cause the observed non-Gaussianity when using a diagonal covariance matrix. We conclude that weak lensing does not produce non-Gaussianity in the local curvature statistics at the scales investigated in this paper. The cause of the non-Gaussian detection in the case of a diagonal matrix remains unclear.« less

Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections

NASA Astrophysics Data System (ADS)

Amaral, Marcelo M.; Aschheim, Raymond; Bubuianu, Laurenţiu; Irwin, Klee; Vacaru, Sergiu I.; Woolridge, Daniel

2017-09-01

The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/aperiodic/fractal/stochastic/(super) cluster/filament/polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off-diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi-one-dimensionality

NASA Astrophysics Data System (ADS)

Nandy, Atanu; Pal, Biplab; Chakrabarti, Arunava

2016-08-01

It is shown that an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight-binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side-coupled to a suitable subset of sites in the backbone, and if the nearest-neighbor hopping integrals, in the backbone and in the side-coupled cluster, bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone and that in the side attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or a singular continuous one for deterministically disordered lattices) with exponentially (or power law) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization (Anderson P. W., Phys. Rev., 109 (1958) 1492), pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) (Dunlap D. H. et al., Phys. Rev. Lett., 65 (1990) 88).

Calculation of electronic coupling matrix elements for ground and excited state electron transfer reactions: Comparison of the generalized Mulliken-Hush and block diagonalization methods

NASA Astrophysics Data System (ADS)

Cave, Robert J.; Newton, Marshall D.

1997-06-01

Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (Hab) for electron transfer reactions using ab initio electronic structure theory. The first is based on the generalized Mulliken-Hush (GMH) model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization (BD) approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for (a) several states of the system Zn2OH2+ and (b) the low-lying states of the benzene-Cl atom complex and its contact ion pair. Generally good agreement between the two methods is obtained over a range of geometries. Either method can be applied at an arbitrary nuclear geometry and, as a result, may be used to test the validity of the Condon approximation. Examples of nonmonotonic behavior of the electronic coupling as a function of nuclear coordinates are observed for Zn2OH2+. Both methods also yield a natural definition of the effective distance (rDA) between donor (D) and acceptor (A) sites, in contrast to earlier approaches which required independent estimates of rDA, generally based on molecular structure data.

Analysis of superimposed ultrasonic guided waves in long bones by the joint approximate diagonalization of eigen-matrices algorithm.

PubMed

Song, Xiaojun; Ta, Dean; Wang, Weiqi

2011-10-01

The parameters of ultrasonic guided waves (GWs) are very sensitive to mechanical and structural changes in long cortical bones. However, it is a challenge to obtain the group velocity and other parameters of GWs because of the presence of mixed multiple modes. This paper proposes a blind identification algorithm using the joint approximate diagonalization of eigen-matrices (JADE) and applies it to the separation of superimposed GWs in long bones. For the simulation case, the velocity of the single mode was calculated after separation. A strong agreement was obtained between the estimated velocity and the theoretical expectation. For the experiments in bovine long bones, by using the calculated velocity and a theoretical model, the cortical thickness (CTh) was obtained. For comparison with the JADE approach, an adaptive Gaussian chirplet time-frequency (ACGTF) method was also used to estimate the CTh. The results showed that the mean error of the CTh acquired by the JADE approach was 4.3%, which was smaller than that of the ACGTF method (13.6%). This suggested that the JADE algorithm may be used to separate the superimposed GWs and that the JADE algorithm could potentially be used to evaluate long bones. Copyright © 2011 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Multiorbital kinetic effects on charge ordering of frustrated electrons on the triangular lattice

NASA Astrophysics Data System (ADS)

Février, C.; Fratini, S.; Ralko, A.

2015-06-01

The role of the multiorbital effects on the emergence of frustrated electronic orders on the triangular lattice at half filling is investigated through an extended spinless fermion Hubbard model. By using two complementary approaches, unrestricted Hartree-Fock and exact diagonalizations, we unravel a very rich phase diagram controlled by the strength of both local and off-site Coulomb interactions and by the interorbital hopping anisotropy ratio t'/t . Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell √{12 }×√{12 } droplet phase, are found to be generic in the triangular geometry, being controlled by the band structure parameters. The latter are also stabilized in the isotropic limit of our microscopic model, which recovers the standard SU(2) spinful extended single-band Hubbard model.

Trace identities and their semiclassical implications

NASA Astrophysics Data System (ADS)

Smilansky, Uzy

2000-03-01

The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces of powers of the evolution operator. For classically integrable maps, the semiclassical approximation is shown to be compatible with the trace identities. This is done by the identification of stationary phase manifolds which give the main contributions to the result. The compatibility of the semiclassical quantization with the trace identities demonstrates the crucial importance of non-diagonal contributions. The same technique is not applicable for chaotic maps, and the compatibility of the semiclassical theory in this case remains unsettled. However, the trace identities are applied to maps which appear naturally in the theory of quantum graphs, revealing some features of the periodic orbit theory for these paradigms of quantum chaos.

Cobalt adatoms on graphene: Effects of anisotropies on the correlated electronic structure

NASA Astrophysics Data System (ADS)

Mozara, R.; Valentyuk, M.; Krivenko, I.; Şaşıoǧlu, E.; Kolorenč, J.; Lichtenstein, A. I.

2018-02-01

Impurities on surfaces experience a geometric symmetry breaking induced not only by the on-site crystal-field splitting and the orbital-dependent hybridization, but also by different screening of the Coulomb interaction in different directions. We present a many-body study of the Anderson impurity model representing a Co adatom on graphene, taking into account all anisotropies of the effective Coulomb interaction, which we obtained by the constrained random-phase approximation. The most pronounced differences are naturally displayed by the many-body self-energy projected onto the single-particle states. For the solution of the Anderson impurity model and analytical continuation of the Matsubara data, we employed new implementations of the continuous-time hybridization expansion quantum Monte Carlo and the stochastic optimization method, and we verified the results in parallel with the exact diagonalization method.

Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

DOE PAGES

Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; ...

2016-08-25

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionicmore » symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.« less

Conservative DEC Discretization of Incompressible Navier-Stokes Equations on Arbitrary Surface Simplicial Meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh; Hirani, Anil; Samtaney, Ravi

2017-11-01

A conservative discretization of incompressible Navier-Stokes equations over surfaces is developed using discrete exterior calculus (DEC). The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of signed diagonal Hodge star operators, while using the circumcentric dual defined on arbitrary meshes, is shown to produce correct solutions even when many non-Delaunay triangles pairs exist. This allows the DEC discretization to admit arbitrary surface simplicial meshes, in contrast to the previously held notion that DEC was limited only to Delaunay meshes. The discretization scheme is presented along with several numerical test cases demonstrating its numerical convergence and conservation properties. Recent developments regarding the extension to conservative higher order methods are also presented. KAUST Baseline Research Funds of R. Samtaney.

A numerical projection technique for large-scale eigenvalue problems

NASA Astrophysics Data System (ADS)

Gamillscheg, Ralf; Haase, Gundolf; von der Linden, Wolfgang

2011-10-01

We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity is constructed by projecting out high energy degrees of freedom and in turn solving the resulting model by some standard eigenvalue solver. Here we introduce a generalization of this idea, where both steps are performed numerically and which in contrast to the standard projection technique converges in principle to the exact eigenvalues. This approach is not just applicable to eigenvalue problems encountered in many-body systems but also in other areas of research that result in large-scale eigenvalue problems for matrices which have, roughly speaking, mostly a pronounced dominant diagonal part. We will present detailed studies of the approach guided by two many-body models.

Electron-Phonon Systems on a Universal Quantum Computer

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

Macridin, Alexandru; Spentzouris, Panagiotis; Amundson, James

We present an algorithm that extends existing quantum algorithms forsimulating fermion systems in quantum chemistry and condensed matter physics toinclude phonons. The phonon degrees of freedom are represented with exponentialaccuracy on a truncated Hilbert space with a size that increases linearly withthe cutoff of the maximum phonon number. The additional number of qubitsrequired by the presence of phonons scales linearly with the size of thesystem. The additional circuit depth is constant for systems with finite-rangeelectron-phonon and phonon-phonon interactions and linear for long-rangeelectron-phonon interactions. Our algorithm for a Holstein polaron problem wasimplemented on an Atos Quantum Learning Machine (QLM) quantum simulatoremployingmore » the Quantum Phase Estimation method. The energy and the phonon numberdistribution of the polaron state agree with exact diagonalization results forweak, intermediate and strong electron-phonon coupling regimes.« less

Spectral function of a hole in the t - J model

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

Liu, Z.; Manousakis, E.

1991-08-01

We give numerical solutions, on finite but large-size square lattices, of the equation for the single-hole Green's function obtained by the self-consistent approach of Schmitt-Rink {ital et} {ital al}. and Kane {ital et} {ital al}. The spectral function of the hole in a quantum antiferromagnet shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the 4{sup 2} lattice in the region of {ital J}/{ital t}{le}0.2. Our results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function survive in the thermodynamic limit while others changemore » due to finite-size effects. We find that the leading nonzero vertex correction is given by a two-loop diagram, which has a small contribution.« less

Excitation spectrum for an inhomogeneously dipole-field-coupled superconducting qubit chain

NASA Astrophysics Data System (ADS)

Ian, Hou; Liu, Yu-xi; Nori, Franco

2012-05-01

When a chain of N superconducting qubits couples to a coplanar resonator, each of the qubits experiences a different dipole-field coupling strength due to the wave form of the cavity field. We find that this inhomogeneous coupling leads to a dependence of the collective ladder operators of the qubit chain on the qubit-interspacing l. Varying the spacing l changes the transition amplitudes between the angular momentum levels. We derive an exact diagonalization of the general N-qubit Hamiltonian and, through the N=4 case, demonstrate how the l-dependent operators lead to a denser one-excitation spectrum and a probability redistribution of the eigenstates. Moreover, we show that the variation of l between its two limiting values coincides with the crossover between Frenkel- and Wannier-type excitons in the superconducting qubit chain.

Why do we need three levels to understand the molecular optical response?

NASA Astrophysics Data System (ADS)

Perez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.

2011-10-01

Traditionally, the nonlinear optical response at the molecular level has been modeled using the two-level approximation, under the assumption that the behavior of the exact sum-over-states (SOS) expressions for the molecular polarizabilities is well represented by the contribution of only two levels. We show how, a rigorous application of the Thomas-Kuhn sum-rules over the SOS expression for the diagonal component of the first-hyperpolarziability proves that the two-level approximation is unphysical. In addition, we indicate how the contributions of potentially infinite number of states to the SOS expressions for the first-hyperpolarizability are well represented by the contributions of a generic three-level system. This explains why the analysis of the three-level model in conjugation with the sum rules has lead to successful paradigms for the optimization of organic chromophores.

Formulation of the relativistic quantum Hall effect and parity anomaly

NASA Astrophysics Data System (ADS)

Yonaga, Kouki; Hasebe, Kazuki; Shibata, Naokazu

2016-06-01

We present a relativistic formulation of the quantum Hall effect on Haldane sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term. We clarify particular features of the relativistic quantum Hall states with the use of the exact diagonalization study of the pseudopotential Hamiltonian. Physical effects of the mass term to the relativistic quantum Hall states are investigated in detail. The mass term acts as an interpolating parameter between the relativistic and nonrelativistic quantum Hall effects. It is pointed out that the mass term unevenly affects the many-body physics of the positive and negative Landau levels as a manifestation of the "parity anomaly." In particular, we explicitly demonstrate the instability of the Laughlin state of the positive first relativistic Landau level with the reduction of the charge gap.

Ground state of a Heisenberg chain with next-nearest-neighbor bond alternation

NASA Astrophysics Data System (ADS)

Capriotti, Luca; Becca, Federico; Sorella, Sandro; Parola, Alberto

2003-05-01

We investigate the ground-state properties of the spin-half J1-J2 Heisenberg chain with a next-nearest-neighbor spin-Peierls dimerization using conformal field theory and Lanczos exact diagonalizations. In agreement with the results of a recent bosonization analysis by Sarkar and Sen [Phys. Rev. B 65, 172408 (2002)], we find that for small frustration (J2/J1) the system is in a Luttinger spin-fluid phase, with gapless excitations, and a finite spin-wave velocity. In the regime of strong frustration the ground state is spontaneously dimerized and the bond alternation reduces the triplet gap, leading to a slight enhancement of the critical point separating the Luttinger phase from the gapped one. An accurate determination of the phase boundary is obtained numerically from the study of the excitation spectrum.

Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg and t-J models

NASA Astrophysics Data System (ADS)

Yannouleas, Constantine; Brandt, Benedikt B.; Landman, Uzi

2016-07-01

Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly correlated behavior of ultracold strongly repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric DWs reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t-J-like model, akin to that used in investigations of high T c superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, DWs suggest three-cold-atom DW quantum computing qubits.

The physicist's companion to current fluctuations: one-dimensional bulk-driven lattice gases

NASA Astrophysics Data System (ADS)

Lazarescu, Alexandre

2015-12-01

One of the main features of statistical systems out of equilibrium is the currents they exhibit in their stationary state: microscopic currents of probability between configurations, which translate into macroscopic currents of mass, charge, etc. Understanding the general behaviour of these currents is an important step towards building a universal framework for non-equilibrium steady states akin to the Gibbs-Boltzmann distribution for equilibrium systems. In this review, we consider one-dimensional bulk-driven particle gases, and in particular the asymmetric simple exclusion process (ASEP) with open boundaries, which is one of the most popular models of one-dimensional transport. We focus, in particular, on the current of particles flowing through the system in its steady state, and on its fluctuations. We show how one can obtain the complete statistics of that current, through its large deviation function, by combining results from various methods: exact calculation of the cumulants of the current, using the integrability of the model; direct diagonalization of a biased process in the limits of very high or low current; hydrodynamic description of the model in the continuous limit using the macroscopic fluctuation theory. We give a pedagogical account of these techniques, starting with a quick introduction to the necessary mathematical tools, as well as a short overview of the existing works relating to the ASEP. We conclude by drawing the complete dynamical phase diagram of the current. We also remark on a few possible generalizations of these results.

GPU-accelerated algorithms for many-particle continuous-time quantum walks

NASA Astrophysics Data System (ADS)

Piccinini, Enrico; Benedetti, Claudia; Siloi, Ilaria; Paris, Matteo G. A.; Bordone, Paolo

2017-06-01

Many-particle continuous-time quantum walks (CTQWs) represent a resource for several tasks in quantum technology, including quantum search algorithms and universal quantum computation. In order to design and implement CTQWs in a realistic scenario, one needs effective simulation tools for Hamiltonians that take into account static noise and fluctuations in the lattice, i.e. Hamiltonians containing stochastic terms. To this aim, we suggest a parallel algorithm based on the Taylor series expansion of the evolution operator, and compare its performances with those of algorithms based on the exact diagonalization of the Hamiltonian or a 4th order Runge-Kutta integration. We prove that both Taylor-series expansion and Runge-Kutta algorithms are reliable and have a low computational cost, the Taylor-series expansion showing the additional advantage of a memory allocation not depending on the precision of calculation. Both algorithms are also highly parallelizable within the SIMT paradigm, and are thus suitable for GPGPU computing. In turn, we have benchmarked 4 NVIDIA GPUs and 3 quad-core Intel CPUs for a 2-particle system over lattices of increasing dimension, showing that the speedup provided by GPU computing, with respect to the OPENMP parallelization, lies in the range between 8x and (more than) 20x, depending on the frequency of post-processing. GPU-accelerated codes thus allow one to overcome concerns about the execution time, and make it possible simulations with many interacting particles on large lattices, with the only limit of the memory available on the device.

A method to calculate the gamma ray detection efficiency of a cylindrical NaI (Tl) crystal

NASA Astrophysics Data System (ADS)

Ahmadi, S.; Ashrafi, S.; Yazdansetad, F.

2018-05-01

Given a wide range application of NaI(Tl) detector in industrial and medical sectors, computation of the related detection efficiency in different distances of a radioactive source, especially for calibration purposes, is the subject of radiation detection studies. In this work, a 2in both in radius and height cylindrical NaI (Tl) scintillator was used, and by changing the radial, axial, and diagonal positions of an isotropic 137Cs point source relative to the detector, the solid angles and the interaction probabilities of gamma photons with the detector's sensitive area have been calculated. The calculations present the geometric and intrinsic efficiency as the functions of detector's dimensions and the position of the source. The calculation model is in good agreement with experiment, and MCNPX simulation.

Configuration-constrained cranking Hartree-Fock pairing calculations for sidebands of nuclei

NASA Astrophysics Data System (ADS)

Liang, W. Y.; Jiao, C. F.; Wu, Q.; Fu, X. M.; Xu, F. R.

2015-12-01

Background: Nuclear collective rotations have been successfully described by the cranking Hartree-Fock-Bogoliubov (HFB) model. However, for rotational sidebands which are built on intrinsic excited configurations, it may not be easy to find converged cranking HFB solutions. The nonconservation of the particle number in the BCS pairing is another shortcoming. To improve the pairing treatment, a particle-number-conserving (PNC) pairing method was suggested. But the existing PNC calculations were performed within a phenomenological one-body potential (e.g., Nilsson or Woods-Saxon) in which one has to deal the double-counting problem. Purpose: The present work aims at an improved description of nuclear rotations, particularly for the rotations of excited configurations, i.e., sidebands. Methods: We developed a configuration-constrained cranking Skyrme Hartree-Fock (SHF) calculation with the pairing correlation treated by the PNC method. The PNC pairing takes the philosophy of the shell model which diagonalizes the Hamiltonian in a truncated model space. The cranked deformed SHF basis provides a small but efficient model space for the PNC diagonalization. Results: We have applied the present method to the calculations of collective rotations of hafnium isotopes for both ground-state bands and sidebands, reproducing well experimental observations. The first up-bendings observed in the yrast bands of the hafnium isotopes are reproduced, and the second up-bendings are predicted. Calculations for rotational bands built on broken-pair excited configurations agree well with experimental data. The band-mixing between two Kπ=6+ bands observed in 176Hf and the K purity of the 178Hf rotational state built on the famous 31 yr Kπ=16+ isomer are discussed. Conclusions: The developed configuration-constrained cranking calculation has been proved to be a powerful tool to describe both the yrast bands and sidebands of deformed nuclei. The analyses of rotational moments of inertia help to understand the structures of nuclei, including rotational alignments, configurations, and competitions between collective and single-particle excitations.

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

Jin Jiasen; Yu Changshui; Song Heshan

We propose a scheme for identifying an unknown Bell diagonal state. In our scheme the measurements are performed on the probe qubits instead of the Bell diagonal state. The distinct advantage is that the quantum state of the evolved Bell diagonal state ensemble plus probe states will still collapse on the original Bell diagonal state ensemble after the measurement on probe states; i.e., our identification is quantum state nondestructive. How to realize our scheme in the framework of cavity electrodynamics is also shown.

Isovector and isoscalar tensor charges of the nucleon from lattice QCD

DOE PAGES

Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Cohen, Saul D.; ...

2015-11-01

Here, we present results for the isovector and flavor diagonal tensor charges g u–d T, g u T, g d T, and g s T needed to probe novel tensor interactions at the TeV scale in neutron and nuclear β-decays and the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice QCD calculations were done using nine ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06, 0.09 and 0.12 fm and three quark masses corresponding to the pionmore » masses M π ≈ 130, 220 and 310 MeV. Using estimates from these ensembles, we quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, volume and light quark masses for the connected contributions. The final estimates of the connected nucleon (proton) tensor charge for the isovector combination is g u–d T = 1.020(76) in the MS¯ scheme at 2 GeV. The additional disconnected quark loop contributions needed for the flavor-diagonal matrix elements are calculated using a stochastic estimator employing the truncated solver method with the all-mode-averaging technique. We find that the size of the disconnected contribution is smaller than the statistical error in the connected contribution. This allows us to bound the disconnected contribution and include it as an additional uncertainty in the flavor-diagonal charges. After a continuum extrapolation, we find g u T = 0.774(66), g d T = –0.233(28) and g u+d T = 0.541(67). The strangeness tensor charge, that can make a significant contribution to the neutron EDM due to the large ratio m s/m u,d, is g s T = 0.008(9) in the continuum limit.« less

Time-domain calculations of the polarized Raman spectra, the transient infrared absorption anisotropy, and the extent of delocalization of the OH stretching mode of liquid water.

PubMed

Torii, Hajime

2006-08-03

The polarized Raman spectrum and the time dependence of the transient infrared (TRIR) absorption anisotropy are calculated for the OH stretching mode of liquid water (neat liquid H2O) by using time-domain formulations, which include the effects of both the diagonal frequency modulations (of individual oscillators) induced by the interactions between the dipole derivatives and the intermolecular electric field, and the off-diagonal (intermolecular) vibrational coupling described by the transition dipole coupling (TDC) mechanism. The IR spectrum of neat liquid H2O and the TRIR anisotropy of a liquid mixture of H2O/HDO/D2O are also calculated. It is shown that the calculated features of these optical signals, including the temperature dependence of the polarized Raman and IR spectra, are in reasonable agreement with the experimental results, indicating that the frequency separation between the isotropic and anisotropic components of the polarized Raman spectrum and the rapid decay (approximately 0.1 ps) of the TRIR anisotropy of the OH stretching mode of neat liquid H2O are mainly controlled by the resonant intermolecular vibrational coupling described by the TDC mechanism. Comparing with the time evolution of vibrational excitations, it is suggested that the TRIR anisotropy decays in the time needed for the initially localized vibrational excitations to delocalize over a few oscillators. It is also shown that the enhancement of the dipole derivatives by the interactions with surrounding molecules is an important factor in generating the spectral profiles of the OH stretching Raman band. The time-domain behavior of the molecular motions that affect the spectroscopic features is discussed.

Pressure profiles in detonation cells with rectangular and diagonal structures

NASA Astrophysics Data System (ADS)

Hanana, M.; Lefebvre, M. H.

Experimental results presented in this work enable us to classify the three-dimensional structure of the detonation into two fundamental types: a rectangular structure and a diagonal structure. The rectangular structure is well documented in the literature and consists of orthogonal waves travelling independently from each another. The soot record in this case shows the classical diamond detonation cell exhibiting `slapping waves'. The experiments indicate that the diagonal structure is a structure with the triple point intersections moving along the diagonal line of the tube cross section. The axes of the transverse waves are canted at 45 degrees to the wall, accounting for the lack of slapping waves. It is possible to reproduce these diagonal structures by appropriately controlling the experimental ignition procedure. The characteristics of the diagonal structure show some similarities with detonation structure in round tube. Pressure measurements recorded along the central axis of the cellular structure show a series of pressure peaks, depending on the type of structure and the position inside the detonation cell. Pressure profiles measured for the whole length of the two types of detonation cells show that the intensity of the shock front is higher and the length of the detonation cell is shorter for the diagonal structures.

2. VIEW OF CENTRAL BEND OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

2. VIEW OF CENTRAL BEND OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 2932 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

Tradeoffs between oscillator strength and lifetime in terahertz quantum cascade lasers

DOE PAGES

Chan, Chun Wang I.; Albo, Asaf; Hu, Qing; ...

2016-11-14

Contemporary research into diagonal active region terahertz quantum cascade lasers for high temperature operation has yielded little success. We present evidence that the failure of high diagonality alone as a design strategy is due to a fundamental trade-off between large optical oscillator strength and long upper-level lifetime. Here, we hypothesize that diagonality needs to be paired with increased doping in order to succeed, and present evidence that highly diagonal designs can benefit from much higher doping than normally found in terahertz quantum cascade lasers. In assuming the benefits of high diagonality paired with high doping, we also highlight important challengesmore » that need to be overcome, specifically the increased importance of carrier induced band-bending and impurity scattering.« less

Conditional spectrum computation incorporating multiple causal earthquakes and ground-motion prediction models

USGS Publications Warehouse

Lin, Ting; Harmsen, Stephen C.; Baker, Jack W.; Luco, Nicolas

2013-01-01

The conditional spectrum (CS) is a target spectrum (with conditional mean and conditional standard deviation) that links seismic hazard information with ground-motion selection for nonlinear dynamic analysis. Probabilistic seismic hazard analysis (PSHA) estimates the ground-motion hazard by incorporating the aleatory uncertainties in all earthquake scenarios and resulting ground motions, as well as the epistemic uncertainties in ground-motion prediction models (GMPMs) and seismic source models. Typical CS calculations to date are produced for a single earthquake scenario using a single GMPM, but more precise use requires consideration of at least multiple causal earthquakes and multiple GMPMs that are often considered in a PSHA computation. This paper presents the mathematics underlying these more precise CS calculations. Despite requiring more effort to compute than approximate calculations using a single causal earthquake and GMPM, the proposed approach produces an exact output that has a theoretical basis. To demonstrate the results of this approach and compare the exact and approximate calculations, several example calculations are performed for real sites in the western United States. The results also provide some insights regarding the circumstances under which approximate results are likely to closely match more exact results. To facilitate these more precise calculations for real applications, the exact CS calculations can now be performed for real sites in the United States using new deaggregation features in the U.S. Geological Survey hazard mapping tools. Details regarding this implementation are discussed in this paper.

Diagonal ordering operation technique applied to Morse oscillator

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

Popov, Dušan, E-mail: dusan_popov@yahoo.co.uk; Dong, Shi-Hai; Popov, Miodrag

2015-11-15

We generalize the technique called as the integration within a normally ordered product (IWOP) of operators referring to the creation and annihilation operators of the harmonic oscillator coherent states to a new operatorial approach, i.e. the diagonal ordering operation technique (DOOT) about the calculations connected with the normally ordered product of generalized creation and annihilation operators that generate the generalized hypergeometric coherent states. We apply this technique to the coherent states of the Morse oscillator including the mixed (thermal) state case and get the well-known results achieved by other methods in the corresponding coherent state representation. Also, in the lastmore » section we construct the coherent states for the continuous dynamics of the Morse oscillator by using two new methods: the discrete–continuous limit, respectively by solving a finite difference equation. Finally, we construct the coherent states corresponding to the whole Morse spectrum (discrete plus continuous) and demonstrate their properties according the Klauder’s prescriptions.« less

Reorientation-effect measurement of the <21+∥E2̂∥21+> matrix element in 10Be

NASA Astrophysics Data System (ADS)

Orce, J. N.; Drake, T. E.; Djongolov, M. K.; Navrátil, P.; Triambak, S.; Ball, G. C.; Al Falou, H.; Churchman, R.; Cross, D. S.; Finlay, P.; Forssén, C.; Garnsworthy, A. B.; Garrett, P. E.; Hackman, G.; Hayes, A. B.; Kshetri, R.; Lassen, J.; Leach, K. G.; Li, R.; Meissner, J.; Pearson, C. J.; Rand, E. T.; Sarazin, F.; Sjue, S. K. L.; Stoyer, M. A.; Sumithrarachchi, C. S.; Svensson, C. E.; Tardiff, E. R.; Teigelhoefer, A.; Williams, S. J.; Wong, J.; Wu, C. Y.

2012-10-01

The highly-efficient and segmented TIGRESS γ-ray spectrometer at TRIUMF has been used to perform a reorientation-effect Coulomb-excitation study of the 21+ state at 3.368 MeV in 10Be. This is the first Coulomb-excitation measurement that enables one to obtain information on diagonal matrix elements for such a high-lying first excited state from γ-ray data. With the availability of accurate lifetime data, a value of -0.110±0.087 eb is determined for the <21+∥E2̂∥21+> diagonal matrix element, which assuming the rotor model, leads to a negative spectroscopic quadrupole moment of QS(21+)=-0.083±0.066 eb. This result is in agreement with both no-core shell-model calculations performed in this work with the CD-Bonn 2000 two-nucleon potential and large shell-model spaces, and Green's function Monte Carlo predictions with two- plus three-nucleon potentials.

Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions

NASA Astrophysics Data System (ADS)

Kraberger, Gernot J.; Triebl, Robert; Zingl, Manuel; Aichhorn, Markus

2017-10-01

We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO3, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.

Decay of correlations between cross-polarized electromagnetic waves in a two-dimensional random medium.

PubMed

Gorodnichev, E E

2018-04-01

The problem of multiple scattering of polarized light in a two-dimensional medium composed of fiberlike inhomogeneities is studied. The attenuation lengths for the density matrix elements are calculated. For a highly absorbing medium it is found that, as the sample thickness increases, the intensity of waves polarized along the fibers decays faster than the other density matrix elements. With further increase in the sample thickness, the off-diagonal elements which are responsible for correlations between the cross-polarized waves disappear. In the asymptotic limit of very thick samples the scattered light proves to be polarized perpendicular to the fibers. The difference in the attenuation lengths between the density matrix elements results in a nonmonotonic depth dependence of the degree of polarization. In the opposite case of a weakly absorbing medium, the off-diagonal element of the density matrix and, correspondingly, the correlations between the cross-polarized fields are shown to decay faster than the intensity of waves polarized along and perpendicular to the fibers.

R4 terms in supergravities via T -duality constraint

NASA Astrophysics Data System (ADS)

Razaghian, Hamid; Garousi, Mohammad R.

2018-05-01

It has been speculated in the literature that the effective actions of string theories at any order of α' should be invariant under the Buscher rules plus their higher covariant-derivative corrections. This may be used as a constraint to find effective actions at any order of α', in particular, the metric, the B -field, and the dilaton couplings in supergravities at order α'3 up to an overall factor. For the simple case of zero B -field and diagonal metric in which we have done the calculations explicitly, we have found that the constraint fixes almost all of the seven independent Riemann curvature couplings. There is only one term which is not fixed, because when metric is diagonal, the reduction of two R4 terms becomes identical. The Riemann curvature couplings that the T -duality constraint produces for both type II and heterotic theories are fully consistent with the existing couplings in the literature which have been found by the S-matrix and by the sigma-model approaches.

Measurement system of the refractive power of spherical and sphero-cylindrical lenses with the magnification ellipse fitting method.

PubMed

Ko, Wooseok; Kim, Soohyun

2009-11-01

This paper proposes a new measurement system for measuring the refractive power of spherical and sphero-cylindrical lenses with a six-point light source, which is composed of a light emitting diode and a six-hole pattern aperture, and magnification ellipse fitting method. The position of the six light sources is changed into a circular or elliptical form subjected to the lens refractive power and meridian rotation angle. The magnification ellipse fitting method calculates the lens refractive power based on the ellipse equation with magnifications that are the ratios between initial diagonal lengths and measured diagonal lengths of the conjugated light sources changed by the target lens. The refractive powers of the spherical and sphero-cylindrical lenses certified in the Korea Research Institute of Standard and Science were measured to verify the measurement performance. The proposed method is estimated to have a repeatability of +/-0.01 D and an error value below 1%.

Diffusion of Conserved Charges in Relativistic Heavy Ion Collisions

NASA Astrophysics Data System (ADS)

Greif, Moritz; Fotakis, Jan. A.; Denicol, Gabriel S.; Greiner, Carsten

2018-06-01

We demonstrate that the diffusion currents do not depend only on gradients of their corresponding charge density, but that the different diffusion charge currents are coupled. This happens in such a way that it is possible for density gradients of a given charge to generate dissipative currents of another charge. Within this scheme, the charge diffusion coefficient is best viewed as a matrix, in which the diagonal terms correspond to the usual charge diffusion coefficients, while the off-diagonal terms describe the coupling between the different currents. In this Letter, we calculate for the first time the complete diffusion matrix for hot and dense nuclear matter, including baryon, electric, and strangeness charges. We find that the baryon diffusion current is strongly affected by baryon charge gradients but also by its coupling to gradients in strangeness. The electric charge diffusion current is found to be strongly affected by electric and strangeness gradients, whereas strangeness currents depend mostly on strange and baryon gradients.

6. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

6. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 2502 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

7. VIEW OF WEAPONS DELIVERY ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

7. VIEW OF WEAPONS DELIVERY ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 522 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

5. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

5. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 323' EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

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.

Global Coordinates and Exact Aberration Calculations Applied to Physical Optics Modeling of Complex Optical Systems

NASA Astrophysics Data System (ADS)

Lawrence, G.; Barnard, C.; Viswanathan, V.

1986-11-01

Historically, wave optics computer codes have been paraxial in nature. Folded systems could be modeled by "unfolding" the optical system. Calculation of optical aberrations is, in general, left for the analyst to do with off-line codes. While such paraxial codes were adequate for the simpler systems being studied 10 years ago, current problems such as phased arrays, ring resonators, coupled resonators, and grazing incidence optics require a major advance in analytical capability. This paper describes extension of the physical optics codes GLAD and GLAD V to include a global coordinate system and exact ray aberration calculations. The global coordinate system allows components to be positioned and rotated arbitrarily. Exact aberrations are calculated for components in aligned or misaligned configurations by using ray tracing to compute optical path differences and diffraction propagation. Optical path lengths between components and beam rotations in complex mirror systems are calculated accurately so that coherent interactions in phased arrays and coupled devices may be treated correctly.

Modeling of Impact Properties of Auxetic Materials Phase 2

DTIC Science & Technology

2014-03-01

over the more conventional engineering materials, such as higher indentation resistance, higher fracture toughness and greater resistance to impact...entrant materials were fixed at L=H=1.0 mm from which the rib lengths and thickness for each test case could be calculated using Equations (5) and (6...specimen. In all finite element models, the horizontal (2h) and diagonal (l) ribs shown in Figure 2 were idealized by ten and five shell elements

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

NASA Astrophysics Data System (ADS)

Szederkényi, Gábor; Hangos, Katalin M.

2004-04-01

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

Exciton States in a Gaussian Confining Potential Well

NASA Astrophysics Data System (ADS)

Xie, Wen-Fang; Gu, Juan

2003-11-01

We consider the problem of an electron-hole pair in a Gaussian confining potential well. This problem is treated within the effective-mass approximation framework using the method of numerical matrix diagonalization. The energy levels of the low-lying states are calculated as a function of the electron-hole effective mass ratio and the size of the confining potential. The project supported by National Natural Science Foundation of China under Grant No. 10275014

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model.

PubMed

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-28

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model

NASA Astrophysics Data System (ADS)

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-01

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

The diagonalization of cubic matrices

NASA Astrophysics Data System (ADS)

Cocolicchio, D.; Viggiano, M.

2000-08-01

This paper is devoted to analysing the problem of the diagonalization of cubic matrices. We extend the familiar algebraic approach which is based on the Cardano formulae. We rewrite the complex roots of the associated resolvent secular equation in terms of transcendental functions and we derive the diagonalizing matrix.

Chaos in non-diagonal spatially homogeneous cosmological models in spacetime dimensions <=10

NASA Astrophysics Data System (ADS)

Demaret, Jacques; de Rop, Yves; Henneaux, Marc

1988-08-01

It is shown that the chaotic oscillatory behaviour, absent in diagonal homogeneous cosmological models in spacetime dimensions between 5 and 10, can be reestablished when off-diagonal terms are included. Also at Centro de Estudios Cientificos de Santiago, Casilla 16443, Santiago 9, Chile

Interplay between snake and quantum edge states in a graphene Hall bar with a pn-junction

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

Milovanović, S. P., E-mail: slavisa.milovanovic@uantwerpen.be; Peeters, F. M., E-mail: francois.peeters@uantwerpen.be; Ramezani Masir, M., E-mail: mrmphys@gmail.com

2014-09-22

The magneto- and Hall resistance of a locally gated cross shaped graphene Hall bar is calculated. The edge of the top gate is placed diagonally across the center of the Hall cross. Four-probe resistance is calculated using the Landauer-Büttiker formalism, while the transmission coefficients are obtained using the non-equilibrium Green's function approach. The interplay between transport due to edge channels and snake states is investigated. When two edge channels are occupied, we predict oscillations in the Hall and the bend resistance as function of the magnetic field, which are a consequence of quantum interference between the occupied snake states.

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

Barnes, Taylor A.; Kurth, Thorsten; Carrier, Pierre

Here, we present an algorithm and implementation for the parallel computation of exact exchange in Quantum ESPRESSO (QE) that exhibits greatly improved strong scaling. QE is an open-source software package for electronic structure calculations using plane wave density functional theory, and supports the use of local, semi-local, and hybrid DFT functionals. Wider application of hybrid functionals is desirable for the improved simulation of electronic band energy alignments and thermodynamic properties, but the computational complexity of evaluating the exact exchange potential limits the practical application of hybrid functionals to large systems and requires efficient implementations. We demonstrate that existing implementations ofmore » hybrid DFT that utilize a single data structure for both the local and exact exchange regions of the code are significantly limited in the degree of parallelization achievable. We present a band-pair parallelization approach, in which the calculation of exact exchange is parallelized and evaluated independently from the parallelization of the remainder of the calculation, with the wavefunction data being efficiently transformed on-the-fly into a form that is optimal for each part of the calculation. For a 64 water molecule supercell, our new algorithm reduces the overall time to solution by nearly an order of magnitude.« less

4. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

4. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE CENTRAL BEND, LOOKING 270t EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

1. VIEW OF WEST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

1. VIEW OF WEST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE WEST GATE ROAD CULVERT, LOOKING 3052 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

3. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

3. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE CENTRAL BEND, LOOKING 2742 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

Simplicity and Typical Rank Results for Three-Way Arrays

ERIC Educational Resources Information Center

ten Berge, Jos M. F.

2011-01-01

Matrices can be diagonalized by singular vectors or, when they are symmetric, by eigenvectors. Pairs of square matrices often admit simultaneous diagonalization, and always admit block wise simultaneous diagonalization. Generalizing these possibilities to more than two (non-square) matrices leads to methods of simplifying three-way arrays by…

G W calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods

DOE PAGES

Pham, T. Anh; Nguyen, Huy -Viet; Rocca, Dario; ...

2013-04-26

Inmore » a recent paper we presented an approach to evaluate quasiparticle energies based on the spectral decomposition of the static dielectric matrix. This method does not require the calculation of unoccupied electronic states or the direct diagonalization of large dielectric matrices, and it avoids the use of plasmon-pole models. The numerical accuracy of the approach is controlled by a single parameter, i.e., the number of eigenvectors used in the spectral decomposition of the dielectric matrix. Here we present a comprehensive validation of the method, encompassing calculations of ionization potentials and electron affinities of various molecules and of band gaps for several crystalline and disordered semiconductors. Lastly, we demonstrate the efficiency of our approach by carrying out G W calculations for systems with several hundred valence electrons.« less

A cross-sectional study comparing lateral and diagonal maximum weight shift in people with stroke and healthy controls and the correlation with balance, gait and fear of falling

PubMed Central

Meyer, Sarah; Beyens, Hilde; Dejaeger, Eddy; Verheyden, Geert

2017-01-01

Impaired balance is common post stroke and can be assessed by means of force-platforms measuring center of pressure (COP) displacements during static standing, or more dynamically during lateral maximum weight shift (MWS). However, activities of daily life also include diagonal MWS and since force platforms are nowadays commercially available, investigating lateral and diagonal MWS in a clinical setting might be feasible and clinically relevant. We investigated lateral and diagonal MWS while standing in patients with stroke (PwS) and healthy controls (HC), evaluated MWS towards the affected and the non-affected side for PwS and correlated MWS with measures of balance, gait and fear of falling. In a cross-sectional observational study including 36 ambulatory sub-acute inpatients and 32 age-matched HC, a force platform (BioRescue, RM Ingénierie, France) was used to measure lateral and diagonal MWS in standing. Clinical outcome measures collected were Berg Balance Scale and Community Balance and Mobility Scale (CBMS) for balance, 10-meter walk test (10MWT) for gait speed and Falls Efficacy Scale–international version for fear of falling. MWS for PwS towards the affected side was significantly smaller compared to HC (lateral: p = 0.029; diagonal-forward: p = 0.000). MWS for PwS was also significantly reduced towards the affected side in the diagonal-forward direction (p = 0.019) compared to the non-affected side of PwS. Strong correlations were found for MWS for PwS in the diagonal-forward direction towards the affected side, and clinical measures of balance (CBMS: r = 0.66) and gait speed (10MWT: r = 0.66). Our study showed that ambulatory sub-acute PwS, in comparison to HC, have decreased ability to shift their body weight diagonally forward in standing towards their affected side. This reduced ability is strongly related to clinical measures of balance and gait speed. Our results suggest that MWS in a diagonal-forward direction should receive attention in rehabilitation of ambulatory sub-acute PwS in an inpatient setting. PMID:28809939

A cross-sectional study comparing lateral and diagonal maximum weight shift in people with stroke and healthy controls and the correlation with balance, gait and fear of falling.

PubMed

van Dijk, Margaretha M; Meyer, Sarah; Sandstad, Solveig; Wiskerke, Evelyne; Thuwis, Rhea; Vandekerckhove, Chesny; Myny, Charlotte; Ghosh, Nitesh; Beyens, Hilde; Dejaeger, Eddy; Verheyden, Geert

2017-01-01

Impaired balance is common post stroke and can be assessed by means of force-platforms measuring center of pressure (COP) displacements during static standing, or more dynamically during lateral maximum weight shift (MWS). However, activities of daily life also include diagonal MWS and since force platforms are nowadays commercially available, investigating lateral and diagonal MWS in a clinical setting might be feasible and clinically relevant. We investigated lateral and diagonal MWS while standing in patients with stroke (PwS) and healthy controls (HC), evaluated MWS towards the affected and the non-affected side for PwS and correlated MWS with measures of balance, gait and fear of falling. In a cross-sectional observational study including 36 ambulatory sub-acute inpatients and 32 age-matched HC, a force platform (BioRescue, RM Ingénierie, France) was used to measure lateral and diagonal MWS in standing. Clinical outcome measures collected were Berg Balance Scale and Community Balance and Mobility Scale (CBMS) for balance, 10-meter walk test (10MWT) for gait speed and Falls Efficacy Scale-international version for fear of falling. MWS for PwS towards the affected side was significantly smaller compared to HC (lateral: p = 0.029; diagonal-forward: p = 0.000). MWS for PwS was also significantly reduced towards the affected side in the diagonal-forward direction (p = 0.019) compared to the non-affected side of PwS. Strong correlations were found for MWS for PwS in the diagonal-forward direction towards the affected side, and clinical measures of balance (CBMS: r = 0.66) and gait speed (10MWT: r = 0.66). Our study showed that ambulatory sub-acute PwS, in comparison to HC, have decreased ability to shift their body weight diagonally forward in standing towards their affected side. This reduced ability is strongly related to clinical measures of balance and gait speed. Our results suggest that MWS in a diagonal-forward direction should receive attention in rehabilitation of ambulatory sub-acute PwS in an inpatient setting.

Entangled scalar and tensor fluctuations during inflation

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

Collins, Hael; Vardanyan, Tereza

2016-11-29

We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with amore » simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.« less

Anisotropic exchange interaction induced by a single photon in semiconductor microcavities

NASA Astrophysics Data System (ADS)

Chiappe, G.; Fernández-Rossier, J.; Louis, E.; Anda, E. V.

2005-12-01

We investigate coupling of localized spins in a semiconductor quantum dot embedded in a microcavity. The lowest cavity mode and the quantum dot exciton are coupled and close in energy, forming a polariton. The fermions forming the exciton interact with localized spins via exchange. Exact diagonalization of a Hamiltonian in which photons, spins, and excitons are treated quantum mechanically shows that a single polariton induces a sizable indirect anisotropic exchange interaction between spins. At sufficiently low temperatures strong ferromagnetic correlations show up without an appreciable increase in exciton population. In the case of a (Cd,Mn)Te quantum dot, Mn-Mn ferromagnetic coupling is still significant at 1 K : spin-spin correlation around 3 for exciton occupation smaller than 0.3. We find that the interaction mediated by photon-polaritons is 10 times stronger than the one induced by a classical field for equal Rabi splitting.

Ground-state information geometry and quantum criticality in an inhomogeneous spin model

NASA Astrophysics Data System (ADS)

Ma, Yu-Quan

2015-09-01

We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the fermionic Hamiltonian mapped from the spin system. The ground-state Riemannian metric is derived exactly on a parameter manifold ring S1, which is introduced by performing a gauge transformation to the spin Hamiltonian through a twist operator. The cyclic ground-state quantum distance and the second derivative of the ground-state energy are studied in different exchange coupling parameter regions. Particularly, we show that, in the case of exchange coupling parameter Ja = Jb, the quantum ferromagnetic phase can be characterized by an invariant quantum distance and this distance will decay to zero rapidly in the paramagnetic phase. Project supported by the National Natural Science Foundation of China (Grant Nos. 11404023 and 11347131).

Magnetic Phase Diagrams and Magnetization Plateaus of the Spin-1/2 Antiferromagnetic Heisenberg Model on a Square-Kagome Lattice with Three Nonequivalent Exchange Interactions

NASA Astrophysics Data System (ADS)

Morita, Katsuhiro; Tohyama, Takami

2018-04-01

Magnetization plateaus in quantum spin systems emerge in two-dimensional frustrated systems such as a kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on a square-kagome lattice is also appropriate for the study of the magnetization plateau. Motivated by recent experimental findings of such a square kagome lattice with three nonequivalent bonds, we investigate the phase diagrams and magnetization plateaus of the lattice using the exact diagonalization method. In addition to the previously reported 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose magnetic structure is characterized by spontaneously broken four-fold rotational symmetry. The plateau appears only in the case of three nonequivalent bonds. We propose the possibility of finding plateaus including the new one.

Role of spin-orbit coupling in the Kugel-Khomskii model on the honeycomb lattice

NASA Astrophysics Data System (ADS)

Koga, Akihisa; Nakauchi, Shiryu; Nasu, Joji

2018-03-01

We study the effective spin-orbital model for honeycomb-layered transition metal compounds, applying the second-order perturbation theory to the three-orbital Hubbard model with the anisotropic hoppings. This model is reduced to the Kitaev model in the strong spin-orbit coupling limit. Combining the cluster mean-field approximations with the exact diagonalization, we treat the Kugel-Khomskii type superexchange interaction and spin-orbit coupling on an equal footing to discuss ground-state properties. We find that a zigzag ordered state is realized in the model within nearest-neighbor interactions. We clarify how the ordered state competes with the nonmagnetic state, which is adiabatically connected to the quantum spin liquid state realized in a strong spin-orbit coupling limit. Thermodynamic properties are also addressed. The present paper should provide another route to account for the Kitaev-based magnetic properties in candidate materials.

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

NASA Astrophysics Data System (ADS)

Lang, Johannes; Frank, Bernhard; Halimeh, Jad C.

2018-05-01

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.

Wave Function and Emergent SU(2) Symmetry in the νT=1 Quantum Hall Bilayer

NASA Astrophysics Data System (ADS)

Lian, Biao; Zhang, Shou-Cheng

2018-02-01

We propose a trial wave function for the quantum Hall bilayer system of total filling factor νT=1 at a layer distance d to magnetic length ℓ ratio d /ℓ=κc 1≈1.1 , where the lowest charged excitation is known to have a level crossing. The wave function has two-particle correlations, which fit well with those in previous numerical studies, and can be viewed as a Bose-Einstein condensate of free excitons formed by composite bosons and anticomposite bosons in different layers. We show the free nature of these excitons indicating an emergent SU(2) symmetry for the composite bosons at d /ℓ=κc 1, which leads to the level crossing in low-lying charged excitations. We further show the overlap between the trial wave function, and the ground state of a small size exact diagonalization is peaked near d /ℓ=κc 1, which supports our theory.

Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3

NASA Astrophysics Data System (ADS)

Chaloupka, Jiří; Khaliullin, Giniyat

2016-08-01

We study the ordered moment direction in the extended Kitaev-Heisenberg model relevant to honeycomb lattice magnets with strong spin-orbit coupling. We utilize numerical diagonalization and analyze the exact cluster ground states using a particular set of spin-coherent states, obtaining thereby quantum corrections to the magnetic anisotropy beyond conventional perturbative methods. It is found that the quantum fluctuations strongly modify the moment direction obtained at a classical level and are thus crucial for a precise quantification of the interactions. The results show that the moment direction is a sensitive probe of the model parameters in real materials. Focusing on the experimentally relevant zigzag phases of the model, we analyze the currently available neutron-diffraction and resonant x-ray-diffraction data on Na2IrO3 and RuCl3 and discuss the parameter regimes plausible in these Kitaev-Heisenberg model systems.

Singular perturbations and time scales in the design of digital flight control systems

NASA Technical Reports Server (NTRS)

Naidu, Desineni S.; Price, Douglas B.

1988-01-01

The results are presented of application of the methodology of Singular Perturbations and Time Scales (SPATS) to the control of digital flight systems. A block diagonalization method is described to decouple a full order, two time (slow and fast) scale, discrete control system into reduced order slow and fast subsystems. Basic properties and numerical aspects of the method are discussed. A composite, closed-loop, suboptimal control system is constructed as the sum of the slow and fast optimal feedback controls. The application of this technique to an aircraft model shows close agreement between the exact solutions and the decoupled (or composite) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the evaluation of optimal guidance and control laws. The significance of the results is that it can be used for real time, onboard simulation. A brief survey is also presented of digital flight systems.

Maximal coherence and the resource theory of purity

NASA Astrophysics Data System (ADS)

Streltsov, Alexander; Kampermann, Hermann; Wölk, Sabine; Gessner, Manuel; Bruß, Dagmar

2018-05-01

The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.

Anomalous bulk behavior in the free parafermion Z (N ) spin chain

NASA Astrophysics Data System (ADS)

Alcaraz, Francisco C.; Batchelor, Murray T.

2018-06-01

We demonstrate using direct numerical diagonalization and extrapolation methods that boundary conditions have a profound effect on the bulk properties of a simple Z (N ) model for N ≥3 for which the model Hamiltonian is non-Hermitian. For N =2 the model reduces to the well-known quantum Ising model in a transverse field. For open boundary conditions, the Z (N ) model is known to be solved exactly in terms of free parafermions. Once the ends of the open chain are connected by considering the model on a ring, the bulk properties, including the ground-state energy per site, are seen to differ dramatically with increasing N . Other properties, such as the leading finite-size corrections to the ground-state energy, the mass gap exponent, and the specific-heat exponent, are also seen to be dependent on the boundary conditions. We speculate that this anomalous bulk behavior is a topological effect.

Emergence of chiral spin liquids via quantum melting of noncoplanar magnetic orders

DOE PAGES

Hickey, Ciarán; Cincio, Lukasz; Papić, Zlatko; ...

2017-09-11

Quantum spin liquids (QSLs) are highly entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG)we show studies of concrete S U ( 2 ) invariant spin models on honeycomb, triangular, and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple- Q spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Suchmore » ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. We provides a distinct unifying perspective on the emergence of CSLs and suggests that materials with certain noncoplanar magnetic orders might provide a good starting point to search for CSLs.« less

Nuclear spin-lattice relaxation at field-induced level crossings in a Cr8F8 pivalate single crystal

NASA Astrophysics Data System (ADS)

Yamamoto, Shoji

2016-01-01

We construct a microscopic theory for the proton spin-lattice relaxation-rate 1 /T1 measurements around field-induced level crossings in a single crystal of the trivalent chromium ion wheel complex [Cr8F8(OOCtBu)16] at sufficiently low temperatures [E. Micotti et al., Phys. Rev. B 72 (2005) 020405(R)]. Exactly diagonalizing a well-equipped spin Hamiltonian for the individual clusters and giving further consideration to their possible interactions, we reveal the mechanism of 1 /T1 being single-peaked normally at the first level crossing but double-peaked intriguingly around the second level crossing. We wipe out the doubt about poor crystallization and find out a solution-intramolecular alternating Dzyaloshinsky-Moriya interaction combined with intermolecular coupling of antiferromagnetic character, each of which is so weak as several tens of mK in magnitude.

Phase Space Approach to Dynamics of Interacting Fermions

NASA Astrophysics Data System (ADS)

Davidson, Shainen; Sels, Dries; Kasper, Valentin; Polkovnikov, Anatoli

Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of this. Already in equilibrium, fermions are notoriously hard to handle due to the sign problem. Out of equilibrium, an important outstanding problem is the efficient numerical simulation of the dynamics of these systems. In this work we develop a new semiclassical phase-space approach (a.k.a. the truncated Wigner approximation) for simulating the dynamics of interacting lattice fermions in arbitrary dimensions. We demonstrate the strength of the method by comparing the results to exact diagonalization (ED) on small 1D and 2D systems. We furthermore present results on Many-Body Localized (MBL) systems in 1D and 2D, and demonstrate how the method can be used to determine the MBL transition.

Crossover from Super- to Subdiffusive Motion and Memory Effects in Crystalline Organic Semiconductors

NASA Astrophysics Data System (ADS)

De Filippis, G.; Cataudella, V.; Mishchenko, A. S.; Nagaosa, N.; Fierro, A.; de Candia, A.

2015-02-01

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150 ≤T ≤200 K , where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Crossover from super- to subdiffusive motion and memory effects in crystalline organic semiconductors.

PubMed

De Filippis, G; Cataudella, V; Mishchenko, A S; Nagaosa, N; Fierro, A; de Candia, A

2015-02-27

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150≤T≤200  K, where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

We develop an approach to the theory of nonholonomic relativistic stochastic processes in curved spaces. The Itô and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear connection structures. Geometric models of the relativistic diffusion theory are elaborated for nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces. Applying the anholonomic deformation method, the field equations in Einstein's gravity and various modifications are formally integrated in general forms, with generic off-diagonal metrics depending on some classes of generating and integration functions. Choosing random generating functions we can construct various classes of stochastic Einstein manifolds. We show how stochastic gravitational interactions with mixed holonomic/nonholonomic and random variables can be modelled in explicit form and study their main geometric and stochastic properties. Finally, the conditions when non-random classical gravitational processes transform into stochastic ones and inversely are analyzed.

Using nonequilibrium dynamics to probe competing orders in a Mott-Peierls system

DOE PAGES

Wang, Y.; Moritz, B.; Chen, C. -C.; ...

2016-02-24

Competition between ordered phases, and their associated phase transitions, are significant in the study of strongly correlated systems. Here, we examine one aspect, the nonequilibrium dynamics of a photoexcited Mott-Peierls system, using an effective Peierls-Hubbard model and exact diagonalization. Near a transition where spin and charge become strongly intertwined, we observe antiphase dynamics and a coupling-strength-dependent suppression or enhancement in the static structure factors. The renormalized bosonic excitations coupled to a particular photoexcited electron can be extracted, which provides an approach for characterizing the underlying bosonic modes. The results from this analysis for different electronic momenta show an uneven softeningmore » due to a stronger coupling near k F. As a result, this behavior reflects the strong link between the fermionic momenta, the coupling vertices, and ultimately, the bosonic susceptibilities when multiple phases compete for the ground state of the system.« less

Emergence of chiral spin liquids via quantum melting of noncoplanar magnetic orders

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

Hickey, Ciarán; Cincio, Lukasz; Papić, Zlatko

Quantum spin liquids (QSLs) are highly entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG)we show studies of concrete S U ( 2 ) invariant spin models on honeycomb, triangular, and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple- Q spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Suchmore » ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. We provides a distinct unifying perspective on the emergence of CSLs and suggests that materials with certain noncoplanar magnetic orders might provide a good starting point to search for CSLs.« less

A tensor network approach to many-body localization

NASA Astrophysics Data System (ADS)

Yu, Xiongjie; Pekker, David; Clark, Bryan

Understanding the many-body localized phase requires access to eigenstates in the middle of the many-body spectrum. While exact-diagonalization is able to access these eigenstates, it is restricted to systems sizes of about 22 spins. To overcome this limitation, we develop tensor network algorithms which increase the accessible system size by an order of magnitude. We describe both our new algorithms as well as the additional physics about MBL we can extract from them. For example, we demonstrate the power of these methods by verifying the breakdown of the Eigenstate Thermalization Hypothesis (ETH) in the many-body localized phase of the random field Heisenberg model, and show the saturation of entanglement in the MBL phase and generate eigenstates that differ by local excitations. Work was supported by AFOSR FA9550-10-1-0524 and FA9550-12-1-0057, the Kaufmann foundation, and SciDAC FG02-12ER46875.

Stability of the wobbling motion in the triaxially deformed odd-A nucleus

NASA Astrophysics Data System (ADS)

Tanabe, Kosai; Sugawara-Tanabe, Kazuko

2017-12-01

In order to analyze the content of the exact solutions for particle-rotor models with both the rigid and the hydrodynamical moments of inertia (MoI), as a theoretical probe we apply the Holstein-Primakoff (HP) boson expansion method to the total angular momentum I and the single-particle angular momentum j. We study the competition between Coriolis force and the single-particle potential by employing the different choices of the diagonal HP boson representations for the components of I and j along a common coordinate axis, and along perpendicular axes. We do not find any wobbling level sequence associated with the rotation around the principal axis with the medium MoI. The staggering in the alignments of I about the axis with the medium MoI is found in the limited range of I, while the vector R(=I-j) is confined about the axis with the largest MoI.

Steering Bell-diagonal states

PubMed Central

Quan, Quan; Zhu, Huangjun; Liu, Si-Yuan; Fei, Shao-Ming; Fan, Heng; Yang, Wen-Li

2016-01-01

We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality. PMID:26911250

Numerical study of incommensurate and decoupled phases of spin-1/2 chains with isotropic exchange J 1, J 2 between first and second neighbors

NASA Astrophysics Data System (ADS)

Soos, Zoltán G.; Parvej, Aslam; Kumar, Manoranjan

2016-05-01

The spin-1/2 chain with isotropic exchange J 1, J 2  >  0 between first and second neighbors is frustrated for either sign of J 1 and has a singlet ground state (GS) for J 1/J 2  ⩾  -4. Its rich quantum phase diagram supports gapless, gapped, commensurate (C), incommensurate (IC) and other phases. Critical points J 1/J 2 are evaluated using exact diagonalization and density matrix renormalization group calculations. The wave vector q G of spin correlations is related to GS degeneracy and obtained as the peak of the spin structure factor S(q). Variable q G indicates IC phases in two J 1/J 2 intervals, [-4, -  1.24] and [0.44, 2], and a C-IC point at J 1/J 2  =  2. The decoupled C phase in [-1.24, 0.44] has constant q G  =  π/2, nondegenerate GS, and a lowest triplet state with broken spin density on sublattices of odd and even numbered sites. The lowest triplet and singlet excitations, E m and E σ , are degenerate in finite systems at specific frustration J 1/J 2. Level crossing extrapolates in the thermodynamic limit to the same critical points as q G. The S(q) peak diverges at q G  =  π in the gapless phase with J 1/J 2  >  4.148 and quasi-long-range order (QLRO(π)). S(q) diverges at  ±π/2 in the decoupled phase with QLRO(π/2), but is finite in gapped phases with finite-range correlations. Numerical results and field theory agree at small J 2/J 1 but disagree for the decoupled phase with weak exchange J 1 between sublattices. Two related models are summarized: one has an exact gapless decoupled phase with QLRO(π/2) and no IC phases; the other has a single IC phase without a decoupled phase in between.

Applications of finite-size scaling for atomic and non-equilibrium systems

NASA Astrophysics Data System (ADS)

Antillon, Edwin A.

We apply the theory of Finite-size scaling (FSS) to an atomic and a non-equilibrium system in order to extract critical parameters. In atomic systems, we look at the energy dependence on the binding charge near threshold between bound and free states, where we seek the critical nuclear charge for stability. We use different ab initio methods, such as Hartree-Fock, Density Functional Theory, and exact formulations implemented numerically with the finite-element method (FEM). Using Finite-size scaling formalism, where in this case the size of the system is related to the number of elements used in the basis expansion of the wavefunction, we predict critical parameters in the large basis limit. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that this combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. In the second part we look at non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For a specific values of adsorption ( ua) and desorption (ud) the model shows interesting features. At ua = ud, the model is described by a conformal field theory (with conformal charge c = 0) and its stationary probability can be mapped to the ground state of a quantum chain and can also be related a two dimensional statistical model. For ua ≥ ud, the model shows a scale invariant phase in the avalanche distribution. In this work we study the surface dynamics by looking at avalanche distributions using FSS formalism and explore the effect of changing the boundary conditions of the model. The model shows the same universality for the cases with and with our the wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of avalanches released. We provide new conjecture for the probability distribution of avalanches with a wall obtained by using exact diagonalization of small lattices and Monte-Carlo simulations.

Backbendings of superdeformed bands in 36;40Ar

NASA Astrophysics Data System (ADS)

Xiang, Xu-Hui; He, Xiao-Tao

2018-05-01

Experimentally observed superdeformed (SD) rotational bands in 36Ar and 40Ar are studied by the cranked shell model (CSM) with the pairing correlations treated by a particle-number-conserving (PNC) method. This is the first time that PNC-CSM calculations have been performed on the light nuclear mass region around A=40. The experimental kinematic moments of inertia J (1) versus rotational frequency are reproduced well. The backbending of the SD band at frequency around ℏω=1.5 MeV in 36Ar is attributed to the sharp rise of the simultaneous alignments of the neutron and proton 1d 5/2[202]5/2 pairs and 1f 7/2[321]3/2 pairs, which is a consequence of the band crossing between the 1d 5/2[202]5/2 and 1f 7/2[321]3/2 configuration states. The gentle upbending at low frequency of the SD band in 40Ar is mainly affected by the alignments of the neutron 1f 7/2[321]3/2 pairs and proton 1d 5/2[202]5/2 pairs. The PNC-CSM calculations show that besides the diagonal parts, the off-diagonal parts of the alignments play an important role in the rotational behavior of the SD bands. Supported by National Natural Science Foundation of China (11775112 and 11275098) and the Priority Academic Program Development of Jiangsu Higher Education Institutions

Minutia Tensor Matrix: A New Strategy for Fingerprint Matching

PubMed Central

Fu, Xiang; Feng, Jufu

2015-01-01

Establishing correspondences between two minutia sets is a fundamental issue in fingerprint recognition. This paper proposes a new tensor matching strategy. First, the concept of minutia tensor matrix (simplified as MTM) is proposed. It describes the first-order features and second-order features of a matching pair. In the MTM, the diagonal elements indicate similarities of minutia pairs and non-diagonal elements indicate pairwise compatibilities between minutia pairs. Correct minutia pairs are likely to establish both large similarities and large compatibilities, so they form a dense sub-block. Minutia matching is then formulated as recovering the dense sub-block in the MTM. This is a new tensor matching strategy for fingerprint recognition. Second, as fingerprint images show both local rigidity and global nonlinearity, we design two different kinds of MTMs: local MTM and global MTM. Meanwhile, a two-level matching algorithm is proposed. For local matching level, the local MTM is constructed and a novel local similarity calculation strategy is proposed. It makes full use of local rigidity in fingerprints. For global matching level, the global MTM is constructed to calculate similarities of entire minutia sets. It makes full use of global compatibility in fingerprints. Proposed method has stronger description ability and better robustness to noise and nonlinearity. Experiments conducted on Fingerprint Verification Competition databases (FVC2002 and FVC2004) demonstrate the effectiveness and the efficiency. PMID:25822489

Similarity-transformed equation-of-motion vibrational coupled-cluster theory.

PubMed

Faucheaux, Jacob A; Nooijen, Marcel; Hirata, So

2018-02-07

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

A problem with inverse time for a singularly perturbed integro-differential equation with diagonal degeneration of the kernel of high order

NASA Astrophysics Data System (ADS)

Bobodzhanov, A. A.; Safonov, V. F.

2016-04-01

We consider an algorithm for constructing asymptotic solutions regularized in the sense of Lomov (see [1], [2]). We show that such problems can be reduced to integro-differential equations with inverse time. But in contrast to known papers devoted to this topic (see, for example, [3]), in this paper we study a fundamentally new case, which is characterized by the absence, in the differential part, of a linear operator that isolates, in the asymptotics of the solution, constituents described by boundary functions and by the fact that the integral operator has kernel with diagonal degeneration of high order. Furthermore, the spectrum of the regularization operator A(t) (see below) may contain purely imaginary eigenvalues, which causes difficulties in the application of the methods of construction of asymptotic solutions proposed in the monograph [3]. Based on an analysis of the principal term of the asymptotics, we isolate a class of inhomogeneities and initial data for which the exact solution of the original problem tends to the limit solution (as \\varepsilon\\to+0) on the entire time interval under consideration, also including a boundary-layer zone (that is, we solve the so-called initialization problem). The paper is of a theoretical nature and is designed to lead to a greater understanding of the problems in the theory of singular perturbations. There may be applications in various applied areas where models described by integro-differential equations are used (for example, in elasticity theory, the theory of electrical circuits, and so on).

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

NASA Astrophysics Data System (ADS)

Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So

2018-02-01

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Separability of three qubit Greenberger-Horne-Zeilinger diagonal states

NASA Astrophysics Data System (ADS)

Han, Kyung Hoon; Kye, Seung-Hyeok

2017-04-01

We characterize the separability of three qubit GHZ diagonal states in terms of entries. This enables us to check separability of GHZ diagonal states without decomposition into the sum of pure product states. In the course of discussion, we show that the necessary criterion of Gühne (2011 Entanglement criteria and full separability of multi-qubit quantum states Phys. Lett. A 375 406-10) for (full) separability of three qubit GHZ diagonal states is sufficient with a simpler formula. The main tool is to use entanglement witnesses which are tri-partite Choi matrices of positive bi-linear maps.

Diagonalization and Jordan Normal Form--Motivation through "Maple"[R

ERIC Educational Resources Information Center

Glaister, P.

2009-01-01

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package…

Effects of chirp on two-dimensional Fourier transform electronic spectra.

PubMed

Tekavec, Patrick F; Myers, Jeffrey A; Lewis, Kristin L M; Fuller, Franklin D; Ogilvie, Jennifer P

2010-05-24

We examine the effect that pulse chirp has on the shape of two- dimensional electronic spectra through calculations and experiments. For the calculations we use a model two electronic level system with a solvent interaction represented by a simple Gaussian correlation function and compare the resulting spectra to experiments carried out on an organic dye molecule (Rhodamine 800). Both calculations and experiments show that distortions due to chirp are most significant when the pulses used in the experiment have different amounts of chirp, introducing peak shape asymmetry that could be interpreted as spectrally dependent relaxation. When all pulses have similar chirp the distortions are reduced but still affect the anti-diagonal symmetry of the peak shapes and introduce negative features that could be interpreted as excited state absorption.

Numerical method for N electrons bound to a polar quantum dot with a Coulomb impurity

NASA Astrophysics Data System (ADS)

Yau, J. K.; Lee, C. M.

2003-03-01

A numerical method is proposed to calculate the Frohlich Hamiltonian containing N electrons bound to polar quantum dot with a Coulomb impurity without transformation to the coordination frame of the center of mass and by direct diagonalization. As an example to demonstrate the formalism of this method, the low-lying spectra of three interacting electrons bound to an on-center Coulomb impurity, both for accepter and donor, are calculated and analyzed in a polar quantum dot under a perpendicular magnetic field. Taking polaron effect into account, the physical meaning of the phonon-induced terms, both self-square terms and cross terms of the Hamiltonian are discussed. The calculation can also be applied to systems containing particles with opposite charges, such as excitons.

Vibrational spectra from atomic fluctuations in dynamics simulations. I. Theory, limitations, and a sample application

NASA Astrophysics Data System (ADS)

Schmitz, Matthias; Tavan, Paul

2004-12-01

Hybrid molecular dynamics (MD) simulations, which combine density functional theory (DFT) descriptions of a molecule with a molecular mechanics (MM) modeling of its solvent environment, have opened the way towards accurate computations of solvation effects in the vibrational spectra of molecules. Recently, Wheeler et al. [ChemPhysChem 4, 382 (2002)] have suggested to compute these spectra from DFT/MM-MD trajectories by diagonalizing the covariance matrix of atomic fluctuations. This so-called principal mode analysis (PMA) allegedly can replace the well-established approaches, which are based on Fourier transform methods or on conventional normal mode analyses. By scrutinizing and revising the PMA approach we identify five conditions, which must be guaranteed if PMA is supposed to render exact vibrational frequencies. Besides specific choices of (a) coordinates and (b) coordinate systems, these conditions cover (c) a harmonic intramolecular potential, (d) a complete thermal equilibrium within the molecule, and (e) a molecular Hamiltonian independent of time. However, the PMA conditions [(c)-(d)] and [(c)-(e)] are generally violated in gas phase DFT-MD and liquid phase DFT/MM-MD trajectories, respectively. Based on a series of simple analytical model calculations and on the analysis of MD trajectories calculated for the formaldehyde molecule in the gas phase (DFT) and in liquid water (DFT/MM) we show that in both phases the violation of condition (d) can cause huge errors in PMA frequency computations, whereas the inevitable violations of conditions (c) and (e), the latter being generic to the liquid phase, imply systematic and sizable underestimates of the vibrational frequencies by PMA. We demonstrate that the huge errors, which are caused by an incomplete thermal equilibrium violating (d), can be avoided if one introduces mode-specific temperatures Tj and calculates the frequencies from a "generalized virial" (GV) expression instead from PMA. Concerning ways to additionally remove the remaining errors, which GV still shares with PMA, we refer to Paper II of this work [M. Schmitz and P. Tavan, J. Chem. Phys. 121, 12247 (2004)].

Strategic development in exact calculation: group and individual differences in four achievement subtypes.

PubMed

Wylie, Judith; Jordan, Julie-Ann; Mulhern, Gerry

2012-09-01

This longitudinal study sought to identify developmental changes in strategy use between 5 and 7 years of age when solving exact calculation problems. Four mathematics and reading achievement subtypes were examined at four time points. Five strategies were considered: finger counting, verbal counting, delayed retrieval, automatic retrieval, and derived fact retrieval. Results provided unique insights into children's strategic development in exact calculation at this early stage. Group analysis revealed relationships between mathematical and/or reading difficulties and strategy choice, shift, and adaptiveness. Use of derived fact retrieval by 7 years of age distinguished children with mathematical difficulties from other achievement subtypes. Analysis of individual differences revealed marked heterogeneity within all subtypes, suggesting (inter alia) no marked qualitative distinction between our two mathematical difficulty subtypes. Copyright © 2012 Elsevier Inc. All rights reserved.

Automated enzyme-based diagonal capillary electrophoresis: application to phosphopeptide characterization

PubMed Central

Wojcik, Roza; Vannatta, Michael

2010-01-01

Diagonal capillary electrophoresis is a form of two-dimensional capillary electrophoresis that employs identical separation modes in each dimension. The distal end of the first capillary incorporates an enzyme-based microreactor. Analytes that are not modified by the reactor will have identical migration times in the two capillaries and will generate spots that fall on the diagonal in a reconstructed two-dimensional electropherogram. Analytes that undergo enzymatic modification in the reactor will have a different migration time in the second capillary and will generate spots that fall off the diagonal in the electropherogram. We demonstrate the system with immobilized alkaline phosphatase to monitor the phosphorylation status of a mixture of peptides. This enzyme-based diagonal capillary electrophoresis assay appears to be generalizable; any post-translational modification can be detected as long as an immobilized enzyme is available that reacts with the modification under electrophoretic conditions. PMID:20099889

The best of both Reps—Diabatized Gaussians on adiabatic surfaces

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-11-01

When simulating nonadiabatic molecular dynamics, choosing an electronic representation requires consideration of well-known trade-offs. The uniqueness and spatially local couplings of the adiabatic representation come at the expense of an electronic wave function that changes discontinuously with nuclear motion and associated singularities in the nonadiabatic coupling matrix elements. The quasi-diabatic representation offers a smoothly varying wave function and finite couplings, but identification of a globally well-behaved quasi-diabatic representation is a system-specific challenge. In this work, we introduce the diabatized Gaussians on adiabatic surfaces (DGAS) approximation, a variant of the ab initio multiple spawning (AIMS) method that preserves the advantages of both electronic representations while avoiding their respective pitfalls. The DGAS wave function is expanded in a basis of vibronic functions that are continuous in both electronic and nuclear coordinates, but potentially discontinuous in time. Because the time-dependent Schrödinger equation contains only first-order derivatives with respect to time, singularities in the second-derivative nonadiabatic coupling terms (i.e., diagonal Born-Oppenheimer correction; DBOC) at conical intersections are rigorously absent, though singular time-derivative couplings remain. Interpolation of the electronic wave function allows the accurate prediction of population transfer probabilities even in the presence of the remaining singularities. We compare DGAS calculations of the dynamics of photoexcited ethene to AIMS calculations performed in the adiabatic representation, including the DBOC. The 28 fs excited state lifetime observed in DGAS simulations is considerably shorter than the 50 fs lifetime observed in the adiabatic simulations. The slower decay in the adiabatic representation is attributable to the large, repulsive DBOC in the neighborhood of conical intersections. These repulsive DBOC terms are artifacts of the discontinuities in the individual adiabatic vibronic basis functions and therefore cannot reflect the behavior of the exact molecular wave function, which must be continuous.

Spin-orbit coupled systems in the atomic limit: rhenates, osmates, iridates

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

Paramekanti, Arun; Singh, David J.; Yuan, Bo

Motivated by RIXS experiments on a wide range of complex heavy oxides, including rhenates, osmates, and iridates, we discuss the theory of RIXS for site-localized t 2g orbital systems with strong spin-orbit coupling. For such systems, we present exact diagonalization results for the spectrum at different electron fillings, showing that it accesses “single-particle” and “multiparticle” excitations. This leads to a simple picture for the energies and intensities of the RIXS spectra in Mott insulators such as double perovskites which feature highly localized electrons, and yields estimates of the spin-orbit coupling and Hund's coupling in correlated 5d oxides. We present newmore » higher resolution RIXS data at the Re L 3 edge in Ba 2YReO 6 which finds a previously unresolved peak splitting, providing further confirmation of our theoretical predictions. Using ab initio electronic structure calculations on Ba 2MReO 6 (with M=Re, Os, Ir) we show that while the atomic limit yields a reasonable effective Hamiltonian description of the experimental observations, effects such as t 2g–e g interactions and hybridization with oxygen are important. Our ab initio estimate for the strength of the intersite exchange coupling shows that, compared to the d 3 systems, the exchange is one or two orders of magnitude weaker in the d 2 and d 4 materials, which may partly explain the suppression of long-range magnetic order in the latter compounds. As a way to interpolate between the site-localized picture and our electronic structure band calculations, we discuss the spin-orbital levels of the MO 6 cluster. In conclusion, this suggests a possible role for intracluster excitons in Ba 2YIrO 6 which may lead to a weak breakdown of the atomic J eff = 0 picture and to small magnetic moments.« less

Spin-orbit coupled systems in the atomic limit: rhenates, osmates, iridates

DOE PAGES

Paramekanti, Arun; Singh, David J.; Yuan, Bo; ...

2018-06-11

Motivated by RIXS experiments on a wide range of complex heavy oxides, including rhenates, osmates, and iridates, we discuss the theory of RIXS for site-localized t 2g orbital systems with strong spin-orbit coupling. For such systems, we present exact diagonalization results for the spectrum at different electron fillings, showing that it accesses “single-particle” and “multiparticle” excitations. This leads to a simple picture for the energies and intensities of the RIXS spectra in Mott insulators such as double perovskites which feature highly localized electrons, and yields estimates of the spin-orbit coupling and Hund's coupling in correlated 5d oxides. We present newmore » higher resolution RIXS data at the Re L 3 edge in Ba 2YReO 6 which finds a previously unresolved peak splitting, providing further confirmation of our theoretical predictions. Using ab initio electronic structure calculations on Ba 2MReO 6 (with M=Re, Os, Ir) we show that while the atomic limit yields a reasonable effective Hamiltonian description of the experimental observations, effects such as t 2g–e g interactions and hybridization with oxygen are important. Our ab initio estimate for the strength of the intersite exchange coupling shows that, compared to the d 3 systems, the exchange is one or two orders of magnitude weaker in the d 2 and d 4 materials, which may partly explain the suppression of long-range magnetic order in the latter compounds. As a way to interpolate between the site-localized picture and our electronic structure band calculations, we discuss the spin-orbital levels of the MO 6 cluster. In conclusion, this suggests a possible role for intracluster excitons in Ba 2YIrO 6 which may lead to a weak breakdown of the atomic J eff = 0 picture and to small magnetic moments.« less

Effect of exact Coulomb-exchange calculations on band-head spectra of odd-proton nuclei

NASA Astrophysics Data System (ADS)

Koh, Meng-Hock; Nurhafiza, Mohamad Nor

2017-10-01

Previous calculations of band-head energy spectra of odd-mass heavy nuclei in the Hartree-Fock-plus-Bardeen-Cooper-Schrieffer (HF-BCS) framework showed that the agreement with data is better for odd-neutron as compared to odd-proton nuclei. The reason for a poorer agreement with data for the latter have been ascribed to the possible usage of the Slater approximation in calculating the Coulomb-exchange term. In this work, we report the effect of exact Coulomb-exchange calculations on band-head energy spectra of two odd-proton nuclei (namely 237Np and 241Am) as compared to the results obtained using the Slater approximation. We performed self-consistent blocking calculations while taking the breaking of time-reversal symmetry at the mean-field level into account due to the unpaired nucleon. The SkM* and SIII parametrizations of the Skyrme interaction have been employed to approximate the effective nucleon-nucleon interaction while a seniority force is used for the pairing channel. Contrary to what was expected, our preliminary results show no improvement on the band-head spectra as compared to data when the Coulomb-exchange term is calculated exactly.

Loads imposed on intermediate frames of stiffened shells

NASA Technical Reports Server (NTRS)

Kuhn, Paul

1939-01-01

The loads imposed on intermediate frames by the curvature of the longitudinal and by the diagonal-tension effects are treated. A new empirical method is proposed for analyzing diagonal-tension effects. The basic formulas of the pure diagonal-tension theory are used, and the part of the total shear S carried by diagonal tension is assumed to be given the expression S (sub DT) = S (1-tau sub o/tau)(sup n) where tau (sub o) is the critical shear stress, tau the total (nominal shear stress), and n = 3 - sigma/tau where sigma is the stress in the intermediate frame. Numerical examples illustrate all cases treated.

Finite temperature dynamics of a Holstein polaron: The thermo-field dynamics approach

NASA Astrophysics Data System (ADS)

Chen, Lipeng; Zhao, Yang

2017-12-01

Combining the multiple Davydov D2 Ansatz with the method of thermo-field dynamics, we study finite temperature dynamics of a Holstein polaron on a lattice. It has been demonstrated, using the hierarchy equations of motion method as a benchmark, that our approach provides an efficient, robust description of finite temperature dynamics of the Holstein polaron in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. The method of thermo-field dynamics handles temperature effects in the Hilbert space with key numerical advantages over other treatments of finite-temperature dynamics based on quantum master equations in the Liouville space or wave function propagation with Monte Carlo importance sampling. While for weak to moderate diagonal coupling temperature increases inhibit polaron mobility, it is found that off-diagonal coupling induces phonon-assisted transport that dominates at high temperatures. Results on the mean square displacements show that band-like transport features dominate the diagonal coupling cases, and there exists a crossover from band-like to hopping transport with increasing temperature when including off-diagonal coupling. As a proof of concept, our theory provides a unified treatment of coherent and incoherent transport in molecular crystals and is applicable to any temperature.

Thermodynamic Bethe ansatz for non-equilibrium steady states: exact energy current and fluctuations in integrable QFT

NASA Astrophysics Data System (ADS)

Castro-Alvaredo, Olalla; Chen, Yixiong; Doyon, Benjamin; Hoogeveen, Marianne

2014-03-01

We evaluate the exact energy current and scaled cumulant generating function (related to the large-deviation function) in non-equilibrium steady states with energy flow, in any integrable model of relativistic quantum field theory (IQFT) with diagonal scattering. Our derivations are based on various recent results of Bernard and Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures Tl, Tr, and waiting for a long time. We evaluate the current J(Tl, Tr) using the exact QFT density matrix describing these non-equilibrium steady states and using Zamolodchikov’s method of the thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is obtained from the extended fluctuation relations which hold in integrable models. We verify our formula in particular by showing that the conformal field theory (CFT) result is obtained in the high-temperature limit. We analyze numerically our non-equilibrium steady-state TBA equations for three models: the sinh-Gordon model, the roaming trajectories model, and the sine-Gordon model at a particular reflectionless point. Based on the numerics, we conjecture that an infinite family of non-equilibrium c-functions, associated with the scaled cumulants, can be defined, which we interpret physically. We study the full scaled distribution function and find that it can be described by a set of independent Poisson processes. Finally, we show that the ‘additivity’ property of the current, which is known to hold in CFT and was proposed to hold more generally, does not hold in general IQFT—that is, J(Tl, Tr) is not of the form f(Tl) - f(Tr).

Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

NASA Astrophysics Data System (ADS)

MacArt, Jonathan F.; Mueller, Michael E.

2016-12-01

Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

Dynamic Jahn-Teller effect: Calculation of fine structure spectrum, isotope shift and Zeeman behavior at deep center Ni2+ in CdS

NASA Astrophysics Data System (ADS)

Schoepp, Juergen

The internal transition of the deep center Ni2+ in II to IV semiconductor cadmium sulfide is examined with reference to crystal field theory. An algorithm was developed for calculation, in a basis fitted to trigonal symmetry, of fine structure operator matrix which is made of the sum of operators from spin trajectory coupling, trigonal field and electron phonon coupling. The dependence of energy level on the mass was calculated in order to examine the isotropy effect at Ni2+ transition. The mass dependence of phonon energy was estimated in an atomic cluster by using a valence force model from Keating for elastic energy. The Zeeman behavior of Ni2+ transition was examined for magnetic fields; the Zeeman operator was added to the fine structure operator and the resulting matrix was diagonalized. It is noticed that calculations are quantitatively and qualitatively in agreement with experiments.

Extraordinary-mode refractive-index change produced by the linear electro-optic effect in LiNbO3 and reverse-poled LiNbO3

NASA Astrophysics Data System (ADS)

Boyd, Joseph T.; Servizzi, Anthony J.; Sriram, S.; Kingsley, Stuart A.

1995-07-01

To examine aspects of an integrated photonic electric-field sensor, we calculate electro-optically induced refractive-index change in regular and reverse-poled LiNbO3. Specifically, for y-propagating extraordinary modes, we determine how index change depends on electric-field magnitude and direction. To accomplish this, changes in index-ellipsoid shape and orientation are found by the use of a numerical eigenvalue procedure to diagonalize the impermeability tensor; then, refractive index is calculated by the use of a vector reference-frame transformation and a small perturbation approximation. A general formula is inferred from calculations for specific field directions. Electro-optic coefficients for reverse-poled LiNbO3 are obtained by application of a tensor reference-frame transformation to those of LiNbO3. The index-calculation procedure has utility beyond the problem that is considered.

Capillary-wave dynamics and interface structure modulation in binary Bose-Einstein condensate mixtures

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Van Thu, Nguyen; Lin, Chang-You; Phat, Tran Huu

2018-04-01

The localized low-energy interfacial excitations, or interfacial Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically. To this end a double-parabola approximation (DPA) is performed on the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. This DPA entails a model in which analytic expressions are obtained for the excitations underlying capillary waves or ripplons for arbitrary strength K (>1 ) of the phase segregation. The dispersion relation ω (k ) ∝k3 /2 is derived directly from the Bogoliubov-de Gennes equations in the limit that the wavelength 2 π /k is much larger than the interface width. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in ω (k ) of order k5 /2 is calculated analytically within the DPA model. The combined result is tested against numerical diagonalization of the exact Bogoliubov-de Gennes equations. Satisfactory agreement is obtained in the range of physically relevant wavelengths. The ripplon dispersion relation is relevant to state-of-the-art experiments using (quasi)uniform optical-box traps. Furthermore, within the DPA model explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity ω /k to the sound velocity c . For generic mixtures consisting of condensates with unequal healing lengths, an additional modulation is predicted of the common value of the condensate densities at the interface.

Modified spin-wave theory with ordering vector optimization: spatially anisotropic triangular lattice and J1J2J3 model with Heisenberg interactions

NASA Astrophysics Data System (ADS)

Hauke, Philipp; Roscilde, Tommaso; Murg, Valentin; Cirac, J. Ignacio; Schmied, Roman

2011-07-01

We study the ground-state phases of the S=1/2 Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice (SATL) and on the square lattice with up to next-next-nearest-neighbor coupling (the J1J2J3 model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that the MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular, collinear magnetic order is promoted at the expense of non-collinear (spiral) order, and several spiral states that are stable at the classical level disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which the MSW theory breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the SATL, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains. This shows that the MSW theory is—despite its apparent simplicity—a versatile tool for finding candidate regions in the case of spin-liquid phases, which are among prime targets for relevant quantum simulations.

The nuclear quadrupole coupling constants and the structure of the para-para ammonia dimer

NASA Astrophysics Data System (ADS)

Heineking, N.; Stahl, W.; Olthof, E. H. T.; Wormer, P. E. S.; van der Avoird, A.; Havenith, M.

1995-06-01

Expressions are derived for the nuclear quadrupole splittings in the E3 and E4 (para-para) states of (NH3)2 and it is shown that these can be matched with the standard expressions for rigid rotors with two identical quadrupolar nuclei. The matching is exact only when the off-diagonal Coriolis coupling is neglected. However, the selection rules for rotational transitions are just opposite to those for the rigid rotor. Hyperfine splittings are measured for the J=2←1 transitions in the E3 and E4 states with ‖K‖=1; the quadrupole coupling constants χaa=0.1509(83) MHz and χbb-χcc=2.8365(83) MHz are extracted from these measurements by the use of the above mentioned correspondence with the rigid rotor expressions. The corresponding results are also calculated, with and without the Coriolis coupling, from the six-dimensional vibration-rotation-tunneling (VRT) wave functions of (NH3)2, which were previously obtained by Olthof et al. [E.H.T. Olthof, A. van der Avoird, and P.E.S. Wormer, J. Chem. Phys. 101, 8430 (1994)]. From the comparison of χaa with the measured value it follows that the semiempirical potential and the resulting VRT states of Olthof et al. are very accurate along the interchange (ϑA,ϑB) coordinate. From χbb-χcc it follows that this potential is probably too soft in the dihedral angle γ¯=γA-γB, which causes the torsional amplitude to be larger than derived from the experiment.

Derivation of a formula for the resonance integral for a nonorthogonal basis set

PubMed Central

Yim, Yung-Chang; Eyring, Henry

1981-01-01

In a self-consistent field calculation, a formula for the off-diagonal matrix elements of the core Hamiltonian is derived for a nonorthogonal basis set by a polyatomic approach. A set of parameters is then introduced for the repulsion integral formula of Mataga-Nishimoto to fit the experimental data. The matrix elements computed for the nonorthogonal basis set in the π-electron approximation are transformed to those for an orthogonal basis set by the Löwdin symmetrical orthogonalization. PMID:16593009

Automated Change Detection for Synthetic Aperture Sonar

DTIC Science & Technology

2014-01-01

channels, respectively. The canonical coordinates of x and y are defined as u = FHR−1/2xx x v = GHR−1/2yy y where F and G are the mapping matrices...containing the left and right singular vectors of the coherence matrix C, respectively. The canonical coordinate vectors u and v share the diagonal cross...feature set. The coherent change information between canonical coordinates v and u can be calculated using the residual, v −Ku, owing to the fact that

Preparation of freezing quantum state for quantum coherence

NASA Astrophysics Data System (ADS)

Yang, Lian-Wu; Man, Zhong-Xiao; Zhang, Ying-Jie; Han, Feng; Du, Shao-jiang; Xia, Yun-Jie

2018-06-01

We provide a method to prepare the freezing quantum state for quantum coherence via unitary operations. The initial product state consists of the control qubit and target qubit; when it satisfies certain conditions, the initial product state converts into the particular Bell diagonal state under the unitary operations, which have the property of freezing of quantum coherence under quantum channels. We calculate the frozen quantum coherence and corresponding quantum correlations, and find that the quantities are determined by the control qubit only when the freezing phenomena occur.

Three flavor neutrino oscillations in matter: Flavor diagonal potentials, the adiabatic basis, and the CP phase

NASA Astrophysics Data System (ADS)

Kneller, James P.; McLaughlin, Gail C.

2009-09-01

We discuss the three neutrino flavor evolution problem with general, flavor-diagonal, matter potentials and a fully parametrized mixing matrix that includes CP violation, and derive expressions for the eigenvalues, mixing angles, and phases. We demonstrate that, in the limit that the mu and tau potentials are equal, the eigenvalues and matter mixing angles θ˜12 and θ˜13 are independent of the CP phase, although θ˜23 does have CP dependence. Since we are interested in developing a framework that can be used for S matrix calculations of neutrino flavor transformation, it is useful to work in a basis that contains only off-diagonal entries in the Hamiltonian. We derive the “nonadiabaticity” parameters that appear in the Hamiltonian in this basis. We then introduce the neutrino S matrix, derive its evolution equation and the integral solution. We find that this new Hamiltonian, and therefore the S matrix, in the limit that the μ and τ neutrino potentials are the same, is independent of both θ˜23 and the CP violating phase. In this limit, any CP violation in the flavor basis can only be introduced via the rotation matrices, and so effects which derive from the CP phase are then straightforward to determine. We then show explicitly that the electron neutrino and electron antineutrino survival probability is independent of the CP phase in this limit. Conversely, if the CP phase is nonzero and mu and tau matter potentials are not equal, then the electron neutrino survival probability cannot be independent of the CP phase.

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

PubMed

Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K

2007-07-07

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

Iterating the Number of Intersection Points of the Diagonals of Irregular Convex Polygons, or C (n, 4) the Hard Way!

ERIC Educational Resources Information Center

Hathout, Leith

2007-01-01

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…

Asymmetric rotor-like probes to polarized fluorescence study of the macroscopically oriented uniaxial media: Model parameters recognition

NASA Astrophysics Data System (ADS)

Buczkowski, M.; Fisz, J. J.

2008-07-01

In this paper the possibility of the numerical data modelling in the case of angle- and time-resolved fluorescence spectroscopy is investigated. The asymmetric fluorescence probes are assumed to undergo the restricted rotational diffusion in a hosting medium. This process is described quantitatively by the diffusion tensor and the aligning potential. The evolution of the system is expressed in terms of the Smoluchowski equation with an appropriate time-developing operator. A matrix representation of this operator is calculated, then symmetrized and diagonalized. The resulting propagator is used to generate the synthetic noisy data set that imitates results of experimental measurements. The data set serves as a groundwork to the χ2 optimization, performed by the genetic algorithm followed by the gradient search, in order to recover model parameters, which are diagonal elements of the diffusion tensor, aligning potential expansion coefficients and directions of the electronic dipole moments. This whole procedure properly identifies model parameters, showing that the outlined formalism should be taken in the account in the case of analysing real experimental data.

Combination of COFRADIC and high temperature-extended column length conventional liquid chromatography: a very efficient way to tackle complex protein samples, such as serum.

PubMed

Sandra, Koen; Verleysen, Katleen; Labeur, Christine; Vanneste, Lies; D'Hondt, Filip; Thomas, Grégoire; Kas, Koen; Gevaert, Kris; Vandekerckhove, Joël; Sandra, Pat

2007-03-01

The previously reported COmbined FRActional DIagonal Chromatography (COFRA-DIC) methodology, in which a subset of peptides representative for their parent proteins are sorted, is particularly powerful for whole proteome analysis. This peptide-centric technology is built around diagonal chromatography, where peptide separations are crucial. This paper presents high efficiency peptide separations, in which four 250 x 2.1 mm, 5 microm Zorbax 300SB-C18 columns (total length 1 m) were coupled at operating temperatures of 60'C using a dedicated LC oven and conventional LC equipment. The high efficiency separations were combined with the COFRADIC procedure. This extremely powerful combination resulted, for the analysis of serum, in an increase in the uniquely identified peptide sequences by a factor of 2.6, compared to the COFRADIC procedure on a 25 cm column. This is a reflection of the increased peak capacity obtained on the 1 m column, which was calculated to be a factor 2.7 higher than on the 25 cm column. Besides more efficient sorting, less ion suppression was noticed.

Efficient Numerical Diagonalization of Hermitian 3 × 3 Matrices

NASA Astrophysics Data System (ADS)

Kopp, Joachim

A very common problem in science is the numerical diagonalization of symmetric or hermitian 3 × 3 matrices. Since standard "black box" packages may be too inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with an alytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. The analytical algorithm outperforms the others by more than a factor of 2, but becomes inaccurate or may even fail completely if the matrix entries differ greatly in magnitude. This can mostly be circumvented by using a hybrid method, which falls back to QL if conditions are such that the analytical calculation might become too inaccurate. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from .

Influence of the sign of the coupling on the temperature dependence of optical properties of one-dimensional exciton models

NASA Astrophysics Data System (ADS)

Cruzeiro, L.

2008-10-01

A new physical cause for a temperature-dependent double peak in exciton systems is put forward within a thermal equilibrium approach for the calculation of optical properties of exciton systems. Indeed, it is found that one-dimensional exciton systems with only one molecule per unit cell can have an absorption spectrum characterized by a double peak provided that the coupling between excitations in different molecules is positive. The two peaks, whose relative intensities vary with temperature, are located around the exciton band edges, being separated by an energy of approximately 4V, where V is the average coupling between nearest neighbours. For small amounts of diagonal and off-diagonal disorder, the contributions from the intermediate states in the band are also visible as intermediate structure between the two peaks, this being enhanced for systems with periodic boundary conditions. At a qualitative level, these results correlate well with experimental observations in the molecular aggregates of the thiacarbocyanine dye THIATS and in the organic crystals of acetanilide and N-methylacetamide.

Empirical Bayes method for reducing false discovery rates of correlation matrices with block diagonal structure.

PubMed

Pacini, Clare; Ajioka, James W; Micklem, Gos

2017-04-12

Correlation matrices are important in inferring relationships and networks between regulatory or signalling elements in biological systems. With currently available technology sample sizes for experiments are typically small, meaning that these correlations can be difficult to estimate. At a genome-wide scale estimation of correlation matrices can also be computationally demanding. We develop an empirical Bayes approach to improve covariance estimates for gene expression, where we assume the covariance matrix takes a block diagonal form. Our method shows lower false discovery rates than existing methods on simulated data. Applied to a real data set from Bacillus subtilis we demonstrate it's ability to detecting known regulatory units and interactions between them. We demonstrate that, compared to existing methods, our method is able to find significant covariances and also to control false discovery rates, even when the sample size is small (n=10). The method can be used to find potential regulatory networks, and it may also be used as a pre-processing step for methods that calculate, for example, partial correlations, so enabling the inference of the causal and hierarchical structure of the networks.

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion

NASA Astrophysics Data System (ADS)

Olšina, Jan; Kramer, Tobias; Kreisbeck, Christoph; Mančal, Tomáš

2014-10-01

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Detailed noise statistics for an optically preamplified direct detection receiver

NASA Astrophysics Data System (ADS)

Danielsen, Soeren Lykke; Mikkelsen, Benny; Durhuus, Terji; Joergensen, Carsten; Stubkjaer, Kristian E.

We describe the exact statistics of an optically preamplified direct detection receiver by means of the moment generating function. The theory allows an arbitrary shaped electrical filter in the receiver circuit. The moment generating function (MGF) allows for a precise calculation of the error rate by using the inverse Fast Fourier transform (FFT). The exact results are compared with the usual Gaussian approximation (GA), the saddlepoint approximation (SAP) and the modified Chernoff bound (MCB). This comparison shows that the noise is not Gaussian distributed for all values of the optical amplifier gain. In the region from 20-30 dB gain, calculations shows that the GA underestimates the receiver sensitivity while the SAP is very close to the results of our exact model. Using the MGF derived in the article we then find the optimal bandwidth of the electrical filter in the receiver circuit and calculate the sensitivity degradation due to inter symbol interference (ISI).

Complete devil's staircase and crystal-superfluid transitions in a dipolar XXZ spin chain: a trapped ion quantum simulation

NASA Astrophysics Data System (ADS)

Hauke, Philipp; Cucchietti, Fernando M.; Müller-Hermes, Alexander; Bañuls, Mari-Carmen; Cirac, J. Ignacio; Lewenstein, Maciej

2010-11-01

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many metastable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional (1D) model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization and quasi-exact numerical techniques (density-matrix renormalization group and infinite time-evolving block decimation). We find that the complete devil's staircase—an infinite sequence of crystal states existing at vanishing tunneling—spreads to a succession of lobes similar to the Mott lobes found in Bose-Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar 2D models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long-range (algebraic) correlations, as opposed to models with nearest-neighbor tunneling, that show exponential decay of correlations.

Ramp and periodic dynamics across non-Ising critical points

NASA Astrophysics Data System (ADS)

Ghosh, Roopayan; Sen, Arnab; Sengupta, K.

2018-01-01

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a Z3 or Z4 symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with L ≤24 using exact diagonalization (ED), of the excitation density D , the wave function overlap F , and the excess energy Q at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which D and Q show Kibble-Zurek scaling. We find, based on numerical analysis with L ≤24 , that such scaling is consistent with that expected from critical exponents of the q -state Potts universality class with q =3 ,4 . For the periodic protocol, we show that the model displays near-perfect dynamical freezing at specific frequencies; at these frequencies D ,Q →0 and |F |→1 . We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

Frustrated S = 1/2 Two-Leg Ladder with Different Leg Interactions

NASA Astrophysics Data System (ADS)

Tonegawa, Takashi; Okamoto, Kiyomi; Hikihara, Toshiya; Sakai, Tôru

2017-04-01

We explore the ground-state phase diagram of the S = 1/2 two-leg ladder. The isotropic leg interactions J1,a and J1,b between nearest neighbor spins in the legs a and b, respectively, are different from each other. The xy and z components of the uniform rung interactions are denoted by Jr and ΔJr, respectively, where Δ is the XXZ anisotropy parameter. This system has a frustration when J1,aJ1,b < 0 irrespective of the sign of Jr. The phase diagrams on the Δ (0≤Δ<1) versus J1,b plane in the cases of J1,a = - 0.2 and J1,a = 0.2 with Jr = -1 are determined numerically. We employ the physical consideration, the level spectroscopy analysis of the results obtained by the exact diagonalization method and also the density-matrix renormalization-group method. It is found that the non-collinear ferrimagnetic (NCFR) state appears as the ground state in the frustrated region of the parameters. Furthermore, the direct-product triplet-dimer (TD) state in which all rungs form the TD pair is the exact ground state, when J1,a + J1,b = 0 and 0≤ Δ ≲ 0.83. The obtained phase diagrams consist of the TD, XY and Haldane phases as well as the NCFR phase.

Abelian and non-Abelian states in ν = 2 / 3 bilayer fractional quantum Hall systems

NASA Astrophysics Data System (ADS)

Peterson, Michael; Wu, Yang-Le; Cheng, Meng; Barkeshli, Maissam; Wang, Zhenghan

There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two-component FQH systems at total filling fraction ν = n + 2 / 3 , for integer n. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction ν = n + 2 / 3 , including in particular the possibility of the non-Abelian Z4 parafermion state. In ν = 2 / 3 bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the Z4 state. On the other hand, in single-component systems at ν = 8 / 3 , we find that the Z4 parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed ν = 8 / 3 state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively. We acknowledge the Office of Research and Sponsored Programs at California State University Long Beach and Microsoft Station Q.

Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk.

PubMed

Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias

2018-01-22

Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

Atomistic absorption spectra and non-adiabatic dynamics of the LH2 complex with a GPU-accelerated ab initio exciton model

NASA Astrophysics Data System (ADS)

Glowacki, David

Recently, we outlined an efficient multi-tiered parallel excitonic framework that utilizes time dependent density functional theory (TDDFT) to calculate ground/excited state energies and gradients of large supramolecular complexes in atomistic detail. In this paper, we apply our ab initioexciton framework to the 27 coupled bacteriocholorophyll-a chromophores which make up the LH2 complex, using it to compute linear absorption spectra and short-time, on-the-fly nonadiabatic surface-hopping (SH) dynamics of electronically excited LH2. Our ab initio exciton model includes two key parameters whose values are determined by fitting to experiment: d, which is added to the diagonal elements, corrects for the error in TDDFT vertical excitation energies on a single chromophore; and e, which occurs on the off-diagonal matrix elements, describes the average dielectric screening of the inter-chromophore transition-dipole coupling. Using snapshots obtained from equilibrium molecular dynamics simulations (MD) of LH2, best-fit values of both d and e were obtained by fitting to the thermally broadened experimental absorption spectrum within the Frank-Condon approximation, providing a linear absorption spectrum that agrees reasonably well with the experimental observations. We follow the nonadiabatic dynamics using surface hopping to construct time-resolved visualizations of the EET dynamics in the sub-picosecond regime following photoexcitation. This provides some qualitative insight into the excitonic energy transfer (EET) that results from atomically resolved vibrational fluctuations of the chromophores. The dynamical picture that emerges is one of rapidly fluctuating eigenstates that are delocalized over multiple chromophores and undergo frequent crossing on a femtosecond timescale as a result of the underlying chromophore vibrational dynamics. The eigenstate fluctuations arise from disorder in both the diagonal chromophore site energies and the off-diagonal inter-chromophore couplings. The scalability of our excitonic computational framework across massively parallel architectures opens up the possibility of addressing a wide range of questions, including how specific dynamical motions impact both the pathways and efficiency of electronic energy-transfer within large supramolecular systems.

HYPERFINE-DEPENDENT gf-VALUES OF Mn I LINES IN THE 1.49-1.80 μm H BAND

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

Andersson, M.; Hutton, R.; Zou, Y.

2015-01-01

The three Mn I lines at 17325, 17339, and 17349 Å are among the 25 strongest lines (log (gf) > 0.5) in the H band. They are all heavily broadened due to hyperfine structure, and the profiles of these lines have so far not been understood. Earlier studies of these lines even suggested that they were blended. In this work, the profiles of these three infrared (IR) lines have been studied theoretically and compared to experimental spectra to assist in the complete understanding of the solar spectrum in the IR. It is shown that the structure of these lines cannot be describedmore » in the conventional way using the diagonal A and B hyperfine interaction constants. The off-diagonal hyperfine interaction not only has a large impact on the energies of the hyperfine levels, but also introduces a large intensity redistribution among the hyperfine lines, changing the line profiles dramatically. By performing large-scale calculations of the diagonal and off-diagonal hyperfine interaction and the gf-values between the upper and lower hyperfine levels and using a semi-empirical fitting procedure, we achieved agreement between our synthetic and experimental spectra. Furthermore, we compare our results with observations of stellar spectra. The spectra of the Sun and the K1.5 III red giant star Arcturus were modeled in the relevant region, 1.73-1.74 μm, using our theoretically predicted gf-values and energies for each individual hyperfine line. Satisfactory fits were obtained and clear improvements were found using our new data compared with the old available Mn I data. A complete list of energies and gf-values for all the 3d {sup 5}4s({sup 7} S)4d e{sup 6}D - 3d {sup 5}4s({sup 7} S)4f w{sup 6}F hyperfine lines are available as supporting material, whereas only the stronger lines are presented and discussed in detail in this paper.« less

Born-Oppenheimer and Renner-Teller coupled-channel quantum reaction dynamics of O((3)P) + H2(+)(X(2)Σg(+)) collisions.

PubMed

Gamallo, Pablo; Defazio, Paolo; González, Miguel; Paniagua, Miguel; Petrongolo, Carlo

2015-09-28

We present Born-Oppenheimer (BO) and Renner-Teller (RT) time dependent quantum dynamics studies of the reactions O((3)P) + H2(+)(X(2)Σg(+)) → OH(+)(X(3)Σ(-)) + H((2)S) and OH(X(2)Π) + H(+). We consider the OH2(+) X[combining tilde](2)A'' and Ã(2)A' electronic states that correlate with a linear (2)Π species. The electronic angular momenta operators L[combining circumflex] and L[combining circumflex](2) are considered in nonadiabatic coupled-channel calculations, where the associated RT effects are due to diagonal V(RT) potentials that add up to the PESs and to off-diagonal C(RT) couplings between the potential energy surfaces (PESs). Initial-state-resolved reaction probabilities PI, integral cross sections σI, and rate constants kI are obtained using recent ab initio PESs and couplings and the real wavepacket formalism. Because the PESs are strongly attractive, PI have no threshold energy and are large, σI decrease with collision energy, and kI depend little on the temperature. The X[combining tilde](2)A'' PES is up to three times more reactive than the Ã(2)A' PES and H2(+) rotational effects (j0 = 0, 1) are negligible. The diagonal V(RT) potentials are strongly repulsive at the collinearity and nearly halve all low-energy observables with respect to the BO ones. The off-diagonal C(RT) couplings are important at low partial waves, where they mix the X[combining tilde](2)A'' and Ã(2)A' states up to ∼20%. However, V(RT) effects predominate over the C(RT) ones that change at most by ∼19% the BO values of σI and kI. The reaction O((3)P) + H2(+)(X(2)Σg(+)) → OH(+)(X(3)Σ(-)) + H((2)S) is probably one of the most reactive atom + diatom collisions because its RT rate constant at room temperature is equal to 2.26 × 10(-10) cm(3) s(-1). Within the BO approximation, the present results agree rather well with recent quasiclassical and centrifugal-sudden data using the same PESs.

A k-space method for acoustic propagation using coupled first-order equations in three dimensions.

PubMed

Tillett, Jason C; Daoud, Mohammad I; Lacefield, James C; Waag, Robert C

2009-09-01

A previously described two-dimensional k-space method for large-scale calculation of acoustic wave propagation in tissues is extended to three dimensions. The three-dimensional method contains all of the two-dimensional method features that allow accurate and stable calculation of propagation. These features are spectral calculation of spatial derivatives, temporal correction that produces exact propagation in a homogeneous medium, staggered spatial and temporal grids, and a perfectly matched boundary layer. Spectral evaluation of spatial derivatives is accomplished using a fast Fourier transform in three dimensions. This computational bottleneck requires all-to-all communication; execution time in a parallel implementation is therefore sensitive to node interconnect latency and bandwidth. Accuracy of the three-dimensional method is evaluated through comparisons with exact solutions for media having spherical inhomogeneities. Large-scale calculations in three dimensions were performed by distributing the nearly 50 variables per voxel that are used to implement the method over a cluster of computers. Two computer clusters used to evaluate method accuracy are compared. Comparisons of k-space calculations with exact methods including absorption highlight the need to model accurately the medium dispersion relationships, especially in large-scale media. Accurately modeled media allow the k-space method to calculate acoustic propagation in tissues over hundreds of wavelengths.

Calculation of electronic coupling matrix elements for ground and excited state electron transfer reactions: Comparison of the generalized Mulliken{endash}Hush and block diagonalization methods

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

Cave, R.J.; Newton, M.D.

1997-06-01

Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (H{sub ab}) for electron transfer reactions using {ital ab initio} electronic structure theory. The first is based on the generalized Mulliken{endash}Hush (GMH) model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization (BD) approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for (a) several states of the system Zn{sub 2}OH{sub 2}{sup +} and (b) the low-lying states of the benzene{endash}Cl atom complex andmore » its contact ion pair. Generally good agreement between the two methods is obtained over a range of geometries. Either method can be applied at an arbitrary nuclear geometry and, as a result, may be used to test the validity of the Condon approximation. Examples of nonmonotonic behavior of the electronic coupling as a function of nuclear coordinates are observed for Zn{sub 2}OH{sub 2}{sup +}. Both methods also yield a natural definition of the effective distance (r{sub DA}) between donor (D) and acceptor (A) sites, in contrast to earlier approaches which required independent estimates of r{sub DA}, generally based on molecular structure data. {copyright} {ital 1997 American Institute of Physics.}« less

186 K Operation of Terahertz Quantum-Cascade Lasers Based on a Diagonal Design

NASA Technical Reports Server (NTRS)

Kumar, Sushil; Hu, Qing; Reno, John L.

2009-01-01

Resonant-phonon terahertz quantum-cascade lasers operating up to a heat-sink temperature of 186 K are demonstrated. This record temperature performance is achieved based on a diagonal design, with the objective to increase the upper-state lifetime and therefore the gain at elevated temperatures. The increased diagonality also lowers the operating current densities by limiting the flow of parasitic leakage current. Quantitatively, the diagonality is characterized by a radiative oscillator strength that is smaller by a factor of two from the least of any previously published designs. At the lasing frequency of 3.9 THz, 63 mW of peak optical power was measured at 5 K, and approximately 5 mW could still be detected at 180 K.

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory

NASA Astrophysics Data System (ADS)

Jia, Weile; Lin, Lin

2017-10-01

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory.

PubMed

Jia, Weile; Lin, Lin

2017-10-14

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

Quantum mechanical calculations of vibrational population inversion in chemical reactions - Numerically exact L-squared-amplitude-density study of the H2Br reactive system

NASA Technical Reports Server (NTRS)

Zhang, Y. C.; Zhang, J. Z. H.; Kouri, D. J.; Haug, K.; Schwenke, D. W.

1988-01-01

Numerically exact, fully three-dimensional quantum mechanicl reactive scattering calculations are reported for the H2Br system. Both the exchange (H + H-prime Br to H-prime + HBr) and abstraction (H + HBR to H2 + Br) reaction channels are included in the calculations. The present results are the first completely converged three-dimensional quantum calculations for a system involving a highly exoergic reaction channel (the abstraction process). It is found that the production of vibrationally hot H2 in the abstraction reaction, and hence the extent of population inversion in the products, is a sensitive function of initial HBr rotational state and collision energy.

Line mixing in a N2-broadened CO2 Q branch observed with a tunable diode laser

NASA Technical Reports Server (NTRS)

Gentry, Bruce; Strow, L. Larrabee

1987-01-01

Line-mixing effects have been observed in the infrared Q branch of the (11/1/0,03/1/0)I-00/0/0 band of CO2 at 2076/cm. A tunable diode laser spectrometer was used to record spectra of CO2 broadened by N2 and O2 at total pressures ranging from 100 to 720 torr. The observed absorption coefficients are up to 65 percent lower than those calculated using an isolated Lorentzian line approximation. A simple energy gap scaling law is used to determine the off-diagonal relaxation matrix elements from the known pressure-broadening coefficients. The spectra calculated using these matrix elements reproduces the observed absorption coefficients to within several percent.

Symbolic Algebra Development for Higher-Order Electron Propagator Formulation and Implementation.

PubMed

Tamayo-Mendoza, Teresa; Flores-Moreno, Roberto

2014-06-10

Through the use of symbolic algebra, implemented in a program, the algebraic expression of the elements of the self-energy matrix for the electron propagator to different orders were obtained. In addition, a module for the software package Lowdin was automatically generated. Second- and third-order electron propagator results have been calculated to test the correct operation of the program. It was found that the Fortran 90 modules obtained automatically with our algorithm succeeded in calculating ionization energies with the second- and third-order electron propagator in the diagonal approximation. The strategy for the development of this symbolic algebra program is described in detail. This represents a solid starting point for the automatic derivation and implementation of higher-order electron propagator methods.

Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Alexander, Steven; Coldwell, R. L.

2015-03-01

The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this poster I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.

Large scale exact quantum dynamics calculations: Ten thousand quantum states of acetonitrile

NASA Astrophysics Data System (ADS)

Halverson, Thomas; Poirier, Bill

2015-03-01

'Exact' quantum dynamics (EQD) calculations of the vibrational spectrum of acetonitrile (CH3CN) are performed, using two different methods: (1) phase-space-truncated momentum-symmetrized Gaussian basis and (2) correlated truncated harmonic oscillator basis. In both cases, a simple classical phase space picture is used to optimize the selection of individual basis functions-leading to drastic reductions in basis size, in comparison with existing methods. Massive parallelization is also employed. Together, these tools-implemented into a single, easy-to-use computer code-enable a calculation of tens of thousands of vibrational states of CH3CN to an accuracy of 0.001-10 cm-1.

High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

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

Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas, E-mail: alvermann@physik.uni-greifswald.de

2016-11-15

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need formore » matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 10{sup 2} innermost eigenpairs of a topological insulator matrix with dimension 10{sup 9} derived from quantum physics applications.« less

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

PubMed

Hesselmann, Andreas; Görling, Andreas

2011-01-21

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

Correlated natural transition orbital framework for low-scaling excitation energy calculations (CorNFLEx).

PubMed

Baudin, Pablo; Kristensen, Kasper

2017-06-07

We present a new framework for calculating coupled cluster (CC) excitation energies at a reduced computational cost. It relies on correlated natural transition orbitals (NTOs), denoted CIS(D')-NTOs, which are obtained by diagonalizing generalized hole and particle density matrices determined from configuration interaction singles (CIS) information and additional terms that represent correlation effects. A transition-specific reduced orbital space is determined based on the eigenvalues of the CIS(D')-NTOs, and a standard CC excitation energy calculation is then performed in that reduced orbital space. The new method is denoted CorNFLEx (Correlated Natural transition orbital Framework for Low-scaling Excitation energy calculations). We calculate second-order approximate CC singles and doubles (CC2) excitation energies for a test set of organic molecules and demonstrate that CorNFLEx yields excitation energies of CC2 quality at a significantly reduced computational cost, even for relatively small systems and delocalized electronic transitions. In order to illustrate the potential of the method for large molecules, we also apply CorNFLEx to calculate CC2 excitation energies for a series of solvated formamide clusters (up to 4836 basis functions).

23. INCLINED END POST / VERTICAL / DIAGONAL / PORTAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

23. INCLINED END POST / VERTICAL / DIAGONAL / PORTAL BRACING DETAIL. VIEW TO SOUTHEAST. - Abraham Lincoln Memorial Bridge, Spanning Missouri River on Highway 30 between Nebraska & Iowa, Blair, Washington County, NE