The Jarzynski identity derived from general Hamiltonian or non-Hamiltonian dynamics reproducing NVT or NPT ensembles

NASA Astrophysics Data System (ADS)

Cuendet, Michel A.

2006-10-01

The Jarzynski identity (JI) relates nonequilibrium work averages to thermodynamic free energy differences. It was shown in a recent contribution [M. A. Cuendet, Phys. Rev. Lett. 96, 120602 (2006)] that the JI can, in particular, be derived directly from the Nosé-Hoover thermostated dynamics. This statistical mechanical derivation is particularly relevant in the framework of molecular dynamics simulation, because it is based solely on the equations of motion considered and is free of any additional assumptions on system size or bath coupling. Here, this result is generalized to a variety of dynamics, along two directions. On the one hand, specific improved thermostating schemes used in practical applications are treated. These include Nosé-Hoover chains, higher moment thermostats, as well as an isothermal-isobaric scheme yielding the JI in the NPT ensemble. On the other hand, the theoretical generality of the new derivation is explored. Generic dynamics with arbitrary coupling terms and an arbitrary number of thermostating variables, both non-Hamiltonian and Hamiltonian, are shown to imply the JI. In particular, a nonautonomous formulation of the generalized Nosé-Poincaré thermostat is proposed. Finally, general conditions required for the JI derivation are briefly discussed.

Exploring Hamiltonian dielectric solvent molecular dynamics

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Tavan, Paul; Mathias, Gerald

2014-09-01

Hamiltonian dielectric solvent (HADES) is a recent method [7,25], which enables Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric continua. Sample simulations of an α-helical decapeptide with and without explicit solvent demonstrate the high efficiency of HADES-MD. Addressing the folding of this peptide by replica exchange MD we study the properties of HADES by comparing melting curves, secondary structure motifs and salt bridges with explicit solvent results. Despite the unoptimized ad hoc parametrization of HADES, calculated reaction field energies correlate well with numerical grid solutions of the dielectric Poisson equation.

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

NASA Astrophysics Data System (ADS)

Kowalski, A. M.; Rossignoli, R.

2018-04-01

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

Multiple Time-Step Dual-Hamiltonian Hybrid Molecular Dynamics — Monte Carlo Canonical Propagation Algorithm

PubMed Central

Weare, Jonathan; Dinner, Aaron R.; Roux, Benoît

2016-01-01

A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method. PMID:26918826

Hamiltonian description and quantization of dissipative systems

NASA Astrophysics Data System (ADS)

Enz, Charles P.

1994-09-01

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

A partial Hamiltonian approach for current value Hamiltonian systems

NASA Astrophysics Data System (ADS)

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

2014-10-01

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

Hamiltonian quantum simulation with bounded-strength controls

NASA Astrophysics Data System (ADS)

Bookatz, Adam D.; Wocjan, Pawel; Viola, Lorenza

2014-04-01

We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed.

Hamiltonian dynamics of extended objects

NASA Astrophysics Data System (ADS)

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

2004-12-01

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

Steepest entropy ascent for two-state systems with slowly varying Hamiltonians

NASA Astrophysics Data System (ADS)

Militello, Benedetto

2018-05-01

The steepest entropy ascent approach is considered and applied to two-state systems. When the Hamiltonian of the system is time-dependent, the principle of maximum entropy production can still be exploited; arguments to support this fact are given. In the limit of slowly varying Hamiltonians, which allows for the adiabatic approximation for the unitary part of the dynamics, the system exhibits significant robustness to the thermalization process. Specific examples such as a spin in a rotating field and a generic two-state system undergoing an avoided crossing are considered.

Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects

NASA Astrophysics Data System (ADS)

Smith, Brendan; Akimov, Alexey V.

2018-04-01

A simple and robust methodology, dubbed Entangled Trajectories Hamiltonian Dynamics (ETHD), is developed to capture quantum nuclear effects such as tunneling and zero-point energy through the coupling of multiple classical trajectories. The approach reformulates the classically mapped second-order Quantized Hamiltonian Dynamics (QHD-2) in terms of coupled classical trajectories. The method partially enforces the uncertainty principle and facilitates tunneling. The applicability of the method is demonstrated by studying the dynamics in symmetric double well and cubic metastable state potentials. The methodology is validated using exact quantum simulations and is compared to QHD-2. We illustrate its relationship to the rigorous Bohmian quantum potential approach, from which ETHD can be derived. Our simulations show a remarkable agreement of the ETHD calculation with the quantum results, suggesting that ETHD may be a simple and inexpensive way of including quantum nuclear effects in molecular dynamics simulations.

Branched Hamiltonians and supersymmetry

DOE PAGES

Curtright, Thomas L.; Zachos, Cosmas K.

2014-03-21

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

The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems

NASA Astrophysics Data System (ADS)

Koon, Wang Sang; Marsden, Jerrold E.

1997-08-01

This paper compares the Hamiltonian approach to systems with nonholonomic constraints (see [31, 2, 4, 29] and references therein) with the Lagrangian approach (see [16, 27, 9]). There are many differences in the approaches and each has its own advantages; some structures have been discovered on one side and their analogues on the other side are interesting to clarify. For example, the momentum equation and the reconstruction equation were first found on the Lagrangian side and are useful for the control theory of these systems, while the failure of the reduced two-form to be closed (i.e., the failure of the Poisson bracket to satisfy the Jacobi identity) was first noticed on the Hamiltonian side. Clarifying the relation between these approaches is important for the future development of the control theory and stability and bifurcation theory for such systems. In addition to this work, we treat, in this unified framework, a simplified model of the bicycle (see [12, 13]), which is an important underactuated (nonminimum phase) control system.

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

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

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

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

Singular reduction of resonant Hamiltonians

NASA Astrophysics Data System (ADS)

Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia

2018-06-01

We investigate the dynamics of resonant Hamiltonians with n degrees of freedom to which we attach a small perturbation. Our study is based on the geometric interpretation of singular reduction theory. The flow of the Hamiltonian vector field is reconstructed from the cross sections corresponding to an approximation of this vector field in an energy surface. This approximate system is also built using normal forms and applying reduction theory obtaining the reduced Hamiltonian that is defined on the orbit space. Generically, the reduction is of singular character and we classify the singularities in the orbit space, getting three different types of singular points. A critical point of the reduced Hamiltonian corresponds to a family of periodic solutions in the full system whose characteristic multipliers are approximated accordingly to the nature of the critical point.

Linear transformation and oscillation criteria for Hamiltonian systems

NASA Astrophysics Data System (ADS)

Zheng, Zhaowen

2007-08-01

Using a linear transformation similar to the Kummer transformation, some new oscillation criteria for linear Hamiltonian systems are established. These results generalize and improve the oscillation criteria due to I.S. Kumari and S. Umanaheswaram [I. Sowjaya Kumari, S. Umanaheswaram, Oscillation criteria for linear matrix Hamiltonian systems, J. Differential Equations 165 (2000) 174-198], Q. Yang et al. [Q. Yang, R. Mathsen, S. Zhu, Oscillation theorems for self-adjoint matrix Hamiltonian systems, J. Differential Equations 190 (2003) 306-329], and S. Chen and Z. Zheng [Shaozhu Chen, Zhaowen Zheng, Oscillation criteria of Yan type for linear Hamiltonian systems, Comput. Math. Appl. 46 (2003) 855-862]. These criteria also unify many of known criteria in literature and simplify the proofs.

Uncertainty relation for non-Hamiltonian quantum systems

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

Tarasov, Vasily E.

2013-01-15

General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.

Contact Hamiltonian systems and complete integrability

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2017-12-01

We summarize recent results on the integrability of Hamiltonian systems on contact manifolds. We explain how to extend the classical formulation of action-angle variables to contact integrable systems. Using the Jacobi brackets defined on contact manifolds, we discuss the commutativity of first integrals for contact Hamiltonian systems and present the construction of generalized contact action-angle variables. We illustrate the integrability in the contact geometry on the five-dimensional Sasaki-Einstein spaces T1,1 and Yp,q.

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

PubMed

Ben Zion, Yossi; Horwitz, Lawrence

2010-04-01

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

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

PubMed

Hoover, Wm G; Hoover, Carol G

2007-04-28

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

Experimental quantification of decoherence via the Loschmidt echo in a many spin system with scaled dipolar Hamiltonians

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

Buljubasich, Lisandro; Dente, Axel D.; Levstein, Patricia R.

2015-10-28

We performed Loschmidt echo nuclear magnetic resonance experiments to study decoherence under a scaled dipolar Hamiltonian by means of a symmetrical time-reversal pulse sequence denominated Proportionally Refocused Loschmidt (PRL) echo. The many-spin system represented by the protons in polycrystalline adamantane evolves through two steps of evolution characterized by the secular part of the dipolar Hamiltonian, scaled down with a factor |k| and opposite signs. The scaling factor can be varied continuously from 0 to 1/2, giving access to a range of complexity in the dynamics. The experimental results for the Loschmidt echoes showed a spreading of the decay rates thatmore » correlate directly to the scaling factors |k|, giving evidence that the decoherence is partially governed by the coherent dynamics. The average Hamiltonian theory was applied to give an insight into the spin dynamics during the pulse sequence. The calculations were performed for every single radio frequency block in contrast to the most widely used form. The first order of the average Hamiltonian numerically computed for an 8-spin system showed decay rates that progressively decrease as the secular dipolar Hamiltonian becomes weaker. Notably, the first order Hamiltonian term neglected by conventional calculations yielded an explanation for the ordering of the experimental decoherence rates. However, there is a strong overall decoherence observed in the experiments which is not reflected by the theoretical results. The fact that the non-inverted terms do not account for this effect is a challenging topic. A number of experiments to further explore the relation of the complete Hamiltonian with this dominant decoherence rate are proposed.« less

On the chaotic diffusion in multidimensional Hamiltonian systems

NASA Astrophysics Data System (ADS)

Cincotta, P. M.; Giordano, C. M.; Martí, J. G.; Beaugé, C.

2018-01-01

We present numerical evidence that diffusion in the herein studied multidimensional near-integrable Hamiltonian systems departs from a normal process, at least for realistic timescales. Therefore, the derivation of a diffusion coefficient from a linear fit on the variance evolution of the unperturbed integrals fails. We review some topics on diffusion in the Arnold Hamiltonian and yield numerical and theoretical arguments to show that in the examples we considered, a standard coefficient would not provide a good estimation of the speed of diffusion. However, numerical experiments concerning diffusion would provide reliable information about the stability of the motion within chaotic regions of the phase space. In this direction, we present an extension of previous results concerning the dynamical structure of the Laplace resonance in Gliese-876 planetary system considering variations of the orbital parameters accordingly to the error introduced by the radial velocity determination. We found that a slight variation of the eccentricity of planet c would destabilize the inner region of the resonance that, though chaotic, shows stable when adopting the best fit values for the parameters.

Quasi-Hamiltonian structure and Hojman construction

NASA Astrophysics Data System (ADS)

Carinena, Jose F.; Guha, Partha; Ranada, Manuel F.

2007-08-01

Given a smooth vector field [Gamma] and assuming the knowledge of an infinitesimal symmetry X, Hojman [S. Hojman, The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system, J. Phys. A Math. Gen. 29 (1996) 667-674] proposed a method for finding both a Poisson tensor and a function H such that [Gamma] is the corresponding Hamiltonian system. In this paper, we approach the problem from geometrical point of view. The geometrization leads to the clarification of several concepts and methods used in Hojman's paper. In particular, the relationship between the nonstandard Hamiltonian structure proposed by Hojman and the degenerate quasi-Hamiltonian structures introduced by Crampin and Sarlet [M. Crampin, W. Sarlet, Bi-quasi-Hamiltonian systems, J. Math. Phys. 43 (2002) 2505-2517] is unveiled in this paper. We also provide some applications of our construction.

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

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, Diego

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

Hamiltonian structure of classical N-body systems of finite-size particles subject to EM interactions

NASA Astrophysics Data System (ADS)

Cremaschini, C.; Tessarotto, M.

2012-01-01

An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical N-body systems of mutually interacting particles. This refers, in particular, to charged particles subject to EM interactions, including both binary interactions and self-interactions ( EM-interacting N- body systems). The correct solution to the question represents an overriding prerequisite for the consistency between classical and quantum mechanics. In this paper it is shown that such a description can be consistently obtained in the context of classical electrodynamics, for the case of a N-body system of classical finite-size charged particles. A variational formulation of the problem is presented, based on the N -body hybrid synchronous Hamilton variational principle. Covariant Lagrangian and Hamiltonian equations of motion for the dynamics of the interacting N-body system are derived, which are proved to be delay-type ODEs. Then, a representation in both standard Lagrangian and Hamiltonian forms is proved to hold, the latter expressed by means of classical Poisson Brackets. The theory developed retains both the covariance with respect to the Lorentz group and the exact Hamiltonian structure of the problem, which is shown to be intrinsically non-local. Different applications of the theory are investigated. The first one concerns the development of a suitable Hamiltonian approximation of the exact equations that retains finite delay-time effects characteristic of the binary interactions and self-EM-interactions. Second, basic consequences concerning the validity of Dirac generator formalism are pointed out, with particular reference to the instant-form representation of Poincaré generators. Finally, a discussion is presented both on the validity and possible extension of the Dirac generator formalism as well as the failure of the so-called Currie "no-interaction" theorem for the non-local Hamiltonian system considered here.

Effective Hamiltonian for travelling discrete breathers

NASA Astrophysics Data System (ADS)

MacKay, Robert S.; Sepulchre, Jacques-Alexandre

2002-05-01

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

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

NASA Astrophysics Data System (ADS)

Bukov, Marin; Polkovnikov, Anatoli

2014-10-01

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

Open quantum systems, effective Hamiltonians, and device characterization

NASA Astrophysics Data System (ADS)

Duffus, S. N. A.; Dwyer, V. M.; Everitt, M. J.

2017-10-01

High fidelity models, which are able to both support accurate device characterization and correctly account for environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity of the density matrix, one preferred model of open systems describes the dynamics with a master equation in Lindblad form. In practice, Linblad operators are rarely derived from first principles, and often a particular form of annihilator is assumed. This results in dynamical models that miss those additional terms which must generally be added for the master equation to assume the Lindblad form, together with the other concomitant terms that must be assimilated into an effective Hamiltonian to produce the correct free evolution. In first principles derivations, such additional terms are often canceled (or countered), frequently in a somewhat ad hoc manner, leading to a number of competing models. Whilst the implications of this paper are quite general, to illustrate the point we focus here on an example anharmonic system; specifically that of a superconducting quantum interference device (SQUID) coupled to an Ohmic bath. The resulting master equation implies that the environment has a significant impact on the system's energy; we discuss the prospect of keeping or canceling this impact and note that, for the SQUID, monitoring the magnetic susceptibility under control of the capacitive coupling strength and the externally applied flux results in experimentally measurable differences between a number of these models. In particular, one should be able to determine whether a squeezing term of the form X ̂P ̂+P ̂X ̂ should be present in the effective Hamiltonian or not. If model generation is not performed correctly, device characterization will be prone to systemic errors.

Quantum Dynamics of Multi Harmonic Oscillators Described by Time Variant Conic Hamiltonian and their Use in Contemporary Sciences

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

Demiralp, Metin

This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if themore » dynamic of the system is related to a set of ODEs.« less

Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems

NASA Astrophysics Data System (ADS)

Vogl, M.; Pankratov, O.; Shallcross, S.

2017-07-01

We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

Hamiltonian description of closed configurations of the vacuum magnetic field

NASA Astrophysics Data System (ADS)

Skovoroda, A. A.

2015-05-01

Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov'ev, and V.D. Shafranov.

Parallel dynamics between non-Hermitian and Hermitian systems

NASA Astrophysics Data System (ADS)

Wang, P.; Lin, S.; Jin, L.; Song, Z.

2018-06-01

We reveals a connection between non-Hermitian and Hermitian systems by studying the connection between a family of non-Hermitian and Hermitian Hamiltonians based on exact solutions. In general, for a dynamic process in a non-Hermitian system H , there always exists a parallel dynamic process governed by the corresponding Hermitian conjugate system H†. We show that a linear superposition of the two parallel dynamics is exactly equivalent to the time evolution of a state under a Hermitian Hamiltonian H , and we present the relations between {H ,H ,H†} .

Conformal killing tensors and covariant Hamiltonian dynamics

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

Cariglia, M., E-mail: marco@iceb.ufop.br; Gibbons, G. W., E-mail: G.W.Gibbons@damtp.cam.ac.uk; LE STUDIUM, Loire Valley Institute for Advanced Studies, Tours and Orleans

2014-12-15

A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector formore » planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.« less

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

PubMed

Pang, Shengshi; Jordan, Andrew N

2017-03-09

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

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

PubMed Central

Pang, Shengshi; Jordan, Andrew N.

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-11-01

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

Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

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

Cruz, Hans, E-mail: hans@ciencias.unam.mx; Schuch, Dieter; Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx

2015-09-15

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.

Origin of Diffusion in Hamiltonian Dynamics

NASA Astrophysics Data System (ADS)

Benisti, Didier

1996-11-01

Without making any kind of ``loss of memory'' hypothesis, a diffusion equation is derived for the Hamiltonian dynamics defined by H = p^2 / 2 + A summ = -M^M \\cos (q - mt + \\varphi_m), where the \\varphi_m's are fixed random phases. The key point of the derivation is a property of locality for the waves inducing transport. Using perturbation theory, it is shown that only waves whose phase velocities meet the condition mid v_\\varphi - p (t) mid <= α A^2/3, where α is a constant close to 5, play a relevant role for the statistical properties of the dynamics. This implies that, at each time, a particle can be considered as being acted upon only by these nearby waves. Thus, after a shift of momentum of 2 α A^2/3, a particle feels the influence of different waves, with different phases \\varphi_m's, from the ones it initially experienced. Because the phases \\varphi_m's are random, a shift of momentum of 2 α A^2/3 then corresponds to the visit of a dynamical system independent from the previous one. This is what is regarded as being the cause of diffusion. Following this idea, one can predict that the force decorrelation, respectively the Gaussianity of the momentum distribution function, is well established after an average change of momentum close to 2 α A^2/3, respectively 4 α A^2/3. These predictions are in total agreement with the results of the numerical computations. Finally, a careful investigation of the initial behavior of < Δ p^2 (t) > enables one to prove the convergence of the diffusion coefficient to its quasilinear value when the amplitude A of the waves goes to infinity. The author gratefully acknowledges the collaboration of Dominique Escande, under whose supervision this work was carried out.

On time-dependent Hamiltonian realizations of planar and nonplanar systems

NASA Astrophysics Data System (ADS)

Esen, Oğul; Guha, Partha

2018-04-01

In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems in 2 D. We generalize the cosymplectic structures to time-dependent Nambu-Poisson Hamiltonian systems and corresponding Jacobi's last multiplier for 3 D systems. We illustrate our constructions with various examples.

Phase space flows for non-Hamiltonian systems with constraints

NASA Astrophysics Data System (ADS)

Sergi, Alessandro

2005-09-01

In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac’s formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nosé-Dirac bracket is introduced as an example. In the second one, Dirac’s recipe for projecting out constrained variables from time translation operators is generalized and then applied to non-Hamiltonian linear response. Dirac’s formalism avoids spurious terms in the response function of constrained systems. However, corrections coming from phase space measure must be considered for general perturbations.

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

NASA Astrophysics Data System (ADS)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

Relativistic Hamiltonian dynamics for N point particles

NASA Astrophysics Data System (ADS)

King, M. J.

1980-08-01

The theory is quantized canonically to give a relativistic quantum mechanics for N particles. The existence of such a theory has been in doubt since the proof of the No-interaction theorem. However, such a theory does exist and was generalized. This dynamics is expressed in terms of N + 1 pairs of canonical fourvectors (center-of-momentum variables or CMV). A gauge independent reduction due to N + 3 first class kinematic constraints leads to a 6N + 2 dimensional minimum kinematic phase space, K. The kinematics and dynamics of particles with intrinsic spin were also considered. To this end known constraint techniques were generalized to make use of graded Lie algebras. The (Poincare) invariant Hamiltonian is specified in terms of the gauge invarient variables of K. The covariant worldline variables of each particle were found to be gauge dependent. As such they will usually not satisfy a canonical algebra. An exception exists for free particles. The No-interaction theorem therefore is not violated.

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

PubMed

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

2017-09-12

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

Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

NASA Astrophysics Data System (ADS)

Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul

2015-11-01

Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

Evaluation of enhanced sampling provided by accelerated molecular dynamics with Hamiltonian replica exchange methods.

PubMed

Roe, Daniel R; Bergonzo, Christina; Cheatham, Thomas E

2014-04-03

Many problems studied via molecular dynamics require accurate estimates of various thermodynamic properties, such as the free energies of different states of a system, which in turn requires well-converged sampling of the ensemble of possible structures. Enhanced sampling techniques are often applied to provide faster convergence than is possible with traditional molecular dynamics simulations. Hamiltonian replica exchange molecular dynamics (H-REMD) is a particularly attractive method, as it allows the incorporation of a variety of enhanced sampling techniques through modifications to the various Hamiltonians. In this work, we study the enhanced sampling of the RNA tetranucleotide r(GACC) provided by H-REMD combined with accelerated molecular dynamics (aMD), where a boosting potential is applied to torsions, and compare this to the enhanced sampling provided by H-REMD in which torsion potential barrier heights are scaled down to lower force constants. We show that H-REMD and multidimensional REMD (M-REMD) combined with aMD does indeed enhance sampling for r(GACC), and that the addition of the temperature dimension in the M-REMD simulations is necessary to efficiently sample rare conformations. Interestingly, we find that the rate of convergence can be improved in a single H-REMD dimension by simply increasing the number of replicas from 8 to 24 without increasing the maximum level of bias. The results also indicate that factors beyond replica spacing, such as round trip times and time spent at each replica, must be considered in order to achieve optimal sampling efficiency.

Evaluation of Enhanced Sampling Provided by Accelerated Molecular Dynamics with Hamiltonian Replica Exchange Methods

PubMed Central

2015-01-01

Many problems studied via molecular dynamics require accurate estimates of various thermodynamic properties, such as the free energies of different states of a system, which in turn requires well-converged sampling of the ensemble of possible structures. Enhanced sampling techniques are often applied to provide faster convergence than is possible with traditional molecular dynamics simulations. Hamiltonian replica exchange molecular dynamics (H-REMD) is a particularly attractive method, as it allows the incorporation of a variety of enhanced sampling techniques through modifications to the various Hamiltonians. In this work, we study the enhanced sampling of the RNA tetranucleotide r(GACC) provided by H-REMD combined with accelerated molecular dynamics (aMD), where a boosting potential is applied to torsions, and compare this to the enhanced sampling provided by H-REMD in which torsion potential barrier heights are scaled down to lower force constants. We show that H-REMD and multidimensional REMD (M-REMD) combined with aMD does indeed enhance sampling for r(GACC), and that the addition of the temperature dimension in the M-REMD simulations is necessary to efficiently sample rare conformations. Interestingly, we find that the rate of convergence can be improved in a single H-REMD dimension by simply increasing the number of replicas from 8 to 24 without increasing the maximum level of bias. The results also indicate that factors beyond replica spacing, such as round trip times and time spent at each replica, must be considered in order to achieve optimal sampling efficiency. PMID:24625009

Towards investigation of evolution of dynamical systems with independence of time accuracy: more classes of systems

NASA Astrophysics Data System (ADS)

Gurzadyan, V. G.; Kocharyan, A. A.

2015-07-01

The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are much extended, now including systems that are: (1) non-Hamiltonian, conservative; (2) Hamiltonian with time-dependent perturbation; (3) non-conservative (with dissipation). These systems cover various types of N-body gravitating systems of astrophysical and cosmological interest, such as the orbital evolution of planets, minor planets, artificial satellites due to tidal, non-tidal perturbations and thermal thrust, evolving close binary stellar systems, and the dynamics of accretion disks.

Hamiltonian flows with random-walk behaviour originating from zero-sum games and fictitious play

NASA Astrophysics Data System (ADS)

van Strien, Sebastian

2011-06-01

In this paper we introduce Hamiltonian dynamics, inspired by zero-sum games (best response and fictitious play dynamics). The Hamiltonian functions we consider are continuous and piecewise affine (and of a very simple form). It follows that the corresponding Hamiltonian vector fields are discontinuous and multi-valued. Differential equations with discontinuities along a hyperplane are often called 'Filippov systems', and there is a large literature on such systems, see for example (di Bernardo et al 2008 Theory and applications Piecewise-Smooth Dynamical Systems (Applied Mathematical Sciences vol 163) (London: Springer); Kunze 2000 Non-Smooth Dynamical Systems (Lecture Notes in Mathematics vol 1744) (Berlin: Springer); Leine and Nijmeijer 2004 Dynamics and Bifurcations of Non-smooth Mechanical Systems (Lecture Notes in Applied and Computational Mechanics vol 18) (Berlin: Springer)). The special feature of the systems we consider here is that they have discontinuities along a large number of intersecting hyperplanes. Nevertheless, somewhat surprisingly, the flow corresponding to such a vector field exists, is unique and continuous. We believe that these vector fields deserve attention, because it turns out that the resulting dynamics are rather different from those found in more classically defined Hamiltonian dynamics. The vector field is extremely simple: outside codimension-one hyperplanes it is piecewise constant and so the flow phit piecewise a translation (without stationary points). Even so, the dynamics can be rather rich and complicated as a detailed study of specific examples show (see for example theorems 7.1 and 7.2 and also (Ostrovski and van Strien 2011 Regular Chaotic Dynf. 16 129-54)). In the last two sections of the paper we give some applications to game theory, and finish with posing a version of the Palis conjecture in the context of the class of non-smooth systems studied in this paper. To Jacob Palis on his 70th birthday.

Iterated Hamiltonian type systems and applications

NASA Astrophysics Data System (ADS)

Tiba, Dan

2018-04-01

We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.

Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

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

Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul, E-mail: tavan@physik.uni-muenchen.de

2015-11-14

Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADESmore » can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.« less

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

Effective Hamiltonian Approach to Optical Activity in Weyl Spin–Orbit System

NASA Astrophysics Data System (ADS)

Kawaguchi, Hideo; Tatara, Gen

2018-06-01

Chirality or handedness in condensed matter induces anomalous optical responses such as natural optical activity, rotation of the plane of light polarization, as a result of breaking of spatial-inversion symmetry. In this study, optical properties of a Weyl spin-orbit system with quadratic dispersion, a typical chiral system invariant under time-reversal, are investigated theoretically by deriving an effective Hamiltonian based on an imaginary-time path-integral formalism. We show that the effective Hamiltonian can indeed be written in terms of an optical chirality order parameter suggested by Lipkin. The natural optical activity is discussed on the basis of the Hamiltonian.

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.

Nonholonomic Hamiltonian Method for Molecular Dynamics Simulations of Reacting Shocks

NASA Astrophysics Data System (ADS)

Fahrenthold, Eric; Bass, Joseph

2015-06-01

Conventional molecular dynamics simulations of reacting shocks employ a holonomic Hamiltonian formulation: the breaking and forming of covalent bonds is described by potential functions. In general these potential functions: (a) are algebraically complex, (b) must satisfy strict smoothness requirements, and (c) contain many fitted parameters. In recent research the authors have developed a new noholonomic formulation of reacting molecular dynamics. In this formulation bond orders are determined by rate equations and the bonding-debonding process need not be described by differentiable functions. This simplifies the representation of complex chemistry and reduces the number of fitted model parameters. Example applications of the method show molecular level shock to detonation simulations in nitromethane and RDX. Research supported by the Defense Threat Reduction Agency.

Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems

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

Abedi-Fardad, J., E-mail: j.abedifardad@bonabu.ac.ir; Rezaei-Aghdam, A., E-mail: rezaei-a@azaruniv.edu; Haghighatdoost, Gh., E-mail: gorbanali@azaruniv.edu

2014-05-15

We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R{sup 4} and R{sup 6}. Furthermore, we construct some integrable and superintegrable Hamiltonian systems for which the symmetry Lie group is also the phase space of the system.

Tsallis thermostatistics for finite systems: a Hamiltonian approach

NASA Astrophysics Data System (ADS)

Adib, Artur B.; Moreira, Andrã© A.; Andrade, José S., Jr.; Almeida, Murilo P.

2003-05-01

The derivation of the Tsallis generalized canonical distribution from the traditional approach of the Gibbs microcanonical ensemble is revisited (Phys. Lett. A 193 (1994) 140). We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi-Pasta-Ulam chain of anharmonic oscillators.

Continuation of periodic orbits in symmetric Hamiltonian and conservative systems

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Dynamics of Axially Symmetric Perturbed Hamiltonians in 1:1:1 Resonance

NASA Astrophysics Data System (ADS)

Carrasco, D.; Palacián, J. F.; Vidal, C.; Vidarte, J.; Yanguas, P.

2018-03-01

We study the dynamics of a family of perturbed three-degree-of-freedom Hamiltonian systems which are in 1:1:1 resonance. The perturbation consists of axially symmetric cubic and quartic arbitrary polynomials. Our analysis is performed by normalisation, reduction and KAM techniques. Firstly, the system is reduced by the axial symmetry, and then, periodic solutions and KAM 3-tori of the full system are determined from the relative equilibria. Next, the oscillator symmetry is extended by normalisation up to terms of degree 4 in rectangular coordinates; after truncation of higher orders and reduction to the orbit space, some relative equilibria are established and periodic solutions and KAM 3-tori of the original system are obtained. As a third step, the reduction in the two symmetries leads to a one-degree-of-freedom system that is completely analysed in the twice reduced space. All the relative equilibria together with the stability and parametric bifurcations are determined. Moreover, the invariant 2-tori (related to the critical points of the twice reduced space), some periodic solutions and the KAM 3-tori, all corresponding to the full system, are established. Additionally, the bifurcations of equilibria occurring in the twice reduced space are reconstructed as quasi-periodic bifurcations involving 2-tori and periodic solutions of the full system.

Hamiltonian dynamics of vortex and magnetic lines in hydrodynamic type systems

NASA Astrophysics Data System (ADS)

Kuznetsov, E. A.; Ruban, V. P.

2000-01-01

Vortex line and magnetic line representations are introduced for a description of flows in ideal hydrodynamics and magnetohydrodynamics (MHD), respectively. For incompressible fluids, it is shown with the help of this transformation that the equations of motion for vorticity Ω and magnetic field follow from a variational principle. By means of this representation, it is possible to integrate the hydrodynamic type system with the Hamiltonian H=∫\\|Ω\\|dr and some other systems. It is also demonstrated that these representations allow one to remove from the noncanonical Poisson brackets, defined in the space of divergence-free vector fields, the degeneracy connected with the vorticity frozenness for the Euler equation and with magnetic field frozenness for ideal MHD. For MHD, a new Weber-type transformation is found. It is shown how this transformation can be obtained from the two-fluid model when electrons and ions can be considered as two independent fluids. The Weber-type transformation for ideal MHD gives the whole Lagrangian vector invariant. When this invariant is absent, this transformation coincides with the Clebsch representation analog introduced by V.E. Zakharov and E. A. Kuznetsov [Dokl. Ajad. Nauk 194, 1288 (1970) [Sov. Phys. Dokl. 15, 913 (1971)

Hamiltonian purification

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

Orsucci, Davide; Burgarth, Daniel; Facchi, Paolo

The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purificationmore » and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.« less

A Symbolic and Graphical Computer Representation of Dynamical Systems

NASA Astrophysics Data System (ADS)

Gould, Laurence I.

2005-04-01

AUTONO is a Macsyma/Maxima program, designed at the University of Hartford, for solving autonomous systems of differential equations as well as for relating Lagrangians and Hamiltonians to their associated dynamical equations. AUTONO can be used in a number of fields to decipher a variety of complex dynamical systems with ease, producing their Lagrangian and Hamiltonian equations in seconds. These equations can then be incorporated into VisSim, a modeling and simulation program, which yields graphical representations of motion in a given system through easily chosen input parameters. The program, along with the VisSim differential-equations graphical package, allows for resolution and easy understanding of complex problems in a relatively short time; thus enabling quicker and more advanced computing of dynamical systems on any number of platforms---from a network of sensors on a space probe, to the behavior of neural networks, to the effects of an electromagnetic field on components in a dynamical system. A flowchart of AUTONO, along with some simple applications and VisSim output, will be shown.

Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Tavan, Paul; Mathias, Gerald

2014-03-01

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call "Hamiltonian dielectric solvent" (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

Trojan dynamics well approximated by a new Hamiltonian normal form

NASA Astrophysics Data System (ADS)

Páez, Rocío Isabel; Locatelli, Ugo

2015-10-01

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

Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems.

PubMed

Zanardi, Paolo; Campos Venuti, Lorenzo

2014-12-12

Recently, it has been realized that dissipative processes can be harnessed and exploited to the end of coherent quantum control and information processing. In this spirit, we consider strongly dissipative quantum systems admitting a nontrivial manifold of steady states. We show how one can enact adiabatic coherent unitary manipulations, e.g., quantum logical gates, inside this steady-state manifold by adding a weak, time-rescaled, Hamiltonian term into the system's Liouvillian. The effective long-time dynamics is governed by a projected Hamiltonian which results from the interplay between the weak unitary control and the fast relaxation process. The leakage outside the steady-state manifold entailed by the Hamiltonian term is suppressed by an environment-induced symmetrization of the dynamics. We present applications to quantum-computation in decoherence-free subspaces and noiseless subsystems and numerical analysis of nonadiabatic errors.

Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system

NASA Astrophysics Data System (ADS)

Gong, Z. R.; Ian, H.; Liu, Yu-Xi; Sun, C. P.; Nori, Franco

2009-12-01

Using the Born-Oppenheimer approximation, we derive an effective Hamiltonian for an optomechanical system that leads to a nonlinear Kerr effect in the system’s vacuum. The oscillating mirror at one edge of the optomechanical system induces a squeezing effect in the intensity spectrum of the cavity field. A near-resonant laser field is applied at the other edge to drive the cavity field in order to enhance the Kerr effect. We also propose a quantum-nondemolition-measurement setup to monitor a system with two cavities separated by a common oscillating mirror based on our effective Hamiltonian approach.

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

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

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

2014-05-14

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

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

NASA Astrophysics Data System (ADS)

Ghosh, Pijush K.; Sinha, Debdeep

2018-01-01

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

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

Upon Generating (2+1)-dimensional Dynamical Systems

NASA Astrophysics Data System (ADS)

Zhang, Yufeng; Bai, Yang; Wu, Lixin

2016-06-01

Under the framework of the Adler-Gel'fand-Dikii(AGD) scheme, we first propose two Hamiltonian operator pairs over a noncommutative ring so that we construct a new dynamical system in 2+1 dimensions, then we get a generalized special Novikov-Veselov (NV) equation via the Manakov triple. Then with the aid of a special symmetric Lie algebra of a reductive homogeneous group G, we adopt the Tu-Andrushkiw-Huang (TAH) scheme to generate a new integrable (2+1)-dimensional dynamical system and its Hamiltonian structure, which can reduce to the well-known (2+1)-dimensional Davey-Stewartson (DS) hierarchy. Finally, we extend the binormial residue representation (briefly BRR) scheme to the super higher dimensional integrable hierarchies with the help of a super subalgebra of the super Lie algebra sl(2/1), which is also a kind of symmetric Lie algebra of the reductive homogeneous group G. As applications, we obtain a super 2+1 dimensional MKdV hierarchy which can be reduced to a super 2+1 dimensional generalized AKNS equation. Finally, we compare the advantages and the shortcomings for the three schemes to generate integrable dynamical systems.

Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

NASA Astrophysics Data System (ADS)

Bianucci, Marco

2018-05-01

Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Niño, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere.

Hamiltonian thermostats fail to promote heat flow

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Stickiness in Hamiltonian systems: From sharply divided to hierarchical phase space

NASA Astrophysics Data System (ADS)

Altmann, Eduardo G.; Motter, Adilson E.; Kantz, Holger

2006-02-01

We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with nonhierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one-parameter families of marginally unstable periodic orbits and is characterized by an exponent γ=2 for the asymptotic power-law decay of the distribution of recurrence times. Generic perturbations lead to systems with hierarchical phase space, where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and Cantori. In this case, we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power laws, depending on the relative contribution of the primary and secondary structures of the hierarchy. Numerical verification of our main results are provided for area-preserving maps, mushroom billiards, and the newly defined magnetic mushroom billiards.

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

NASA Astrophysics Data System (ADS)

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

2002-11-01

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

An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

NASA Astrophysics Data System (ADS)

Turkington, Bruce

2013-08-01

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter.

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

Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

NASA Astrophysics Data System (ADS)

Evans, Denis J.; Searles, Debra J.; Mittag, Emil

2001-05-01

For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

Extended Hamiltonian approach to continuous tempering

NASA Astrophysics Data System (ADS)

Gobbo, Gianpaolo; Leimkuhler, Benedict J.

2015-06-01

We introduce an enhanced sampling simulation technique based on continuous tempering, i.e., on continuously varying the temperature of the system under investigation. Our approach is mathematically straightforward, being based on an extended Hamiltonian formulation in which an auxiliary degree of freedom, determining the effective temperature, is coupled to the physical system. The physical system and its temperature evolve continuously in time according to the equations of motion derived from the extended Hamiltonian. Due to the Hamiltonian structure, it is easy to show that a particular subset of the configurations of the extended system is distributed according to the canonical ensemble for the physical system at the correct physical temperature.

Hamiltonian structure of the Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-03-01

The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

Hamiltonian analysis of higher derivative scalar-tensor theories

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

Langlois, David; Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr

2016-07-01

We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of themore » dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.« less

Hamiltonian modelling of relative motion.

PubMed

Kasdin, N Jeremy; Gurfil, Pini

2004-05-01

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

On non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2015-04-01

In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass.

Focal points and principal solutions of linear Hamiltonian systems revisited

NASA Astrophysics Data System (ADS)

Šepitka, Peter; Šimon Hilscher, Roman

2018-05-01

In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians

NASA Astrophysics Data System (ADS)

Subasi, Yigit; Jarzynski, Christopher

The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary k-body interactions, their use is limited to small k because the strength of interaction is k'th order in perturbation theory. Here we develop a nonperturbative technique for obtaining effective k-body interactions using Hamiltonians consisting of at most l-body interactions with l < k . This technique works best for Hamiltonians with a few interactions with very large k and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme. We gratefully acknowledge financial support from the Lockheed Martin Corporation under Contract U12001C.

A theorem about Hamiltonian systems.

PubMed

Case, K M

1984-09-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation.

Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Schwörer, Magnus; Breitenfeld, Benedikt; Tröster, Philipp; Bauer, Sebastian; Lorenzen, Konstantin; Tavan, Paul; Mathias, Gerald

2013-06-01

Hybrid molecular dynamics (MD) simulations, in which the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 103-105 molecules, pose a challenge. A corresponding computational approach should guarantee energy conservation, exclude artificial distortions of the electron density at the interface between the DFT and PMM fragments, and should treat the long-range electrostatic interactions within the hybrid simulation system in a linearly scaling fashion. Here we describe a corresponding Hamiltonian DFT/(P)MM implementation, which accounts for inducible atomic dipoles of a PMM environment in a joint DFT/PMM self-consistency iteration. The long-range parts of the electrostatics are treated by hierarchically nested fast multipole expansions up to a maximum distance dictated by the minimum image convention of toroidal boundary conditions and, beyond that distance, by a reaction field approach such that the computation scales linearly with the number of PMM atoms. Short-range over-polarization artifacts are excluded by using Gaussian inducible dipoles throughout the system and Gaussian partial charges in the PMM region close to the DFT fragment. The Hamiltonian character, the stability, and efficiency of the implementation are investigated by hybrid DFT/PMM-MD simulations treating one molecule of the water dimer and of bulk water by DFT and the respective remainder by PMM.

A theorem about Hamiltonian systems

PubMed Central

Case, K. M.

1984-01-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation. PMID:16593515

Hamiltonian adaptive resolution molecular dynamics simulation of infrared dielectric functions of liquids

NASA Astrophysics Data System (ADS)

Wang, C. C.; Tan, J. Y.; Liu, L. H.

2018-05-01

Hamiltonian adaptive resolution scheme (H-AdResS), which allows to simulate materials by treating different domains of the system at different levels of resolution, is a recently proposed atomistic/coarse-grained multiscale model. In this work, a scheme to calculate the dielectric functions of liquids on account of H-AdResS is presented. In the proposed H-AdResS dielectric-function calculation scheme (DielectFunctCalS), the corrected molecular dipole moments are calculated by multiplying molecular dipole moment by the weighting fraction of the molecular mapping point. As the widths of all-atom and hybrid regions show different degrees of influence on the dielectric functions, a prefactor is multiplied to eliminate the effects of all-atom and hybrid region widths. Since one goal of using the H-AdResS method is to reduce computational costs, widths of the all-atom region and the hybrid region can be reduced considering that the coarse-grained simulation is much more timesaving compared to atomistic simulation. Liquid water and ethanol are taken as test cases to validate the DielectFunctCalS. The H-AdResS DielectFunctCalS results are in good agreement with all-atom molecular dynamics simulations. The accuracy of the H-AdResS results, together with all-atom molecular dynamics results, depends heavily on the choice of the force field and force field parameters. The H-AdResS DielectFunctCalS allows us to calculate the dielectric functions of macromolecule systems with high efficiency and makes the dielectric function calculations of large biomolecular systems possible.

Collective coordinates and constrained hamiltonian systems

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

Dayi, O.F.

1992-07-01

A general method of incorporating collective coordinates (transformation of fields into an overcomplete basis) with constrained hamiltonian systems is given where the original phase space variables and collective coordinates can be bosonic or/and fermionic. This method is illustrated by applying it to the SU(2) Yang-Mills-Higgs theory and its BFV-BRST quantization is discussed. Moreover, this formalism is used to give a systematic way of converting second class constraints into effectively first class ones, by considering second class constraints as first class constraints and gauge fixing conditions. This approach is applied to the massive superparticle. Proca lagrangian, and some topological quantum fieldmore » theories.« less

From classical to quantum and back: Hamiltonian adaptive resolution path integral, ring polymer, and centroid molecular dynamics

NASA Astrophysics Data System (ADS)

Kreis, Karsten; Kremer, Kurt; Potestio, Raffaello; Tuckerman, Mark E.

2017-12-01

Path integral-based methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art path integral simulation techniques, including path-integral molecular dynamics, which allows for the calculation of quantum statistical properties, and ring-polymer and centroid molecular dynamics, which allow the calculation of approximate quantum dynamical properties. To this end, we derive a new integration algorithm that also makes use of multiple time-stepping. The scheme is validated via adaptive classical-path-integral simulations of liquid water. Potential applications of the proposed multiresolution method are diverse and include efficient quantum simulations of interfaces as well as complex biomolecular systems such as membranes and proteins.

Bifurcation of solutions to Hamiltonian boundary value problems

NASA Astrophysics Data System (ADS)

McLachlan, R. I.; Offen, C.

2018-06-01

A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples.

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

NASA Astrophysics Data System (ADS)

Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

2018-05-01

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

Hamiltonian closures in fluid models for plasmas

NASA Astrophysics Data System (ADS)

Tassi, Emanuele

2017-11-01

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

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

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

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

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

Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches

NASA Astrophysics Data System (ADS)

Antonowicz, Marek; Szczyrba, Wiktor

1985-06-01

We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.

Reduction and reconstruction of the dynamics of nonholonomic systems

NASA Astrophysics Data System (ADS)

Cortés, Jorge; de León, Manuel

1999-12-01

The reduction and reconstruction of the dynamics of nonholonomic mechanical systems with symmetry are investigated. We have considered a more general framework of constrained Hamiltonian systems since they appear in the reduction procedure. A reduction scheme in terms of the nonholonomic momentum mapping is developed. The reduction of the nonholonomic brackets is also discussed. The theory is illustrated with several examples.

Statistical Mechanical Derivation of Jarzynski's Identity for Thermostated Non-Hamiltonian Dynamics

NASA Astrophysics Data System (ADS)

Cuendet, Michel A.

2006-03-01

The recent Jarzynski identity (JI) relates thermodynamic free energy differences to nonequilibrium work averages. Several proofs of the JI have been provided on the thermodynamic level. They rely on assumptions such as equivalence of ensembles in the thermodynamic limit or weakly coupled infinite heat baths. However, the JI is widely applied to NVT computer simulations involving finite numbers of particles, whose equations of motion are strongly coupled to a few extra degrees of freedom modeling a thermostat. In this case, the above assumptions are no longer valid. We propose a statistical mechanical approach to the JI solely based on the specific equations of motion, without any further assumption. We provide a detailed derivation for the non-Hamiltonian Nosé-Hoover dynamics, which is routinely used in computer simulations to produce canonical sampling.

Hamiltonian flow over saddles for exploring molecular phase space structures

NASA Astrophysics Data System (ADS)

Farantos, Stavros C.

2018-03-01

Despite using potential energy surfaces, multivariable functions on molecular configuration space, to comprehend chemical dynamics for decades, the real happenings in molecules occur in phase space, in which the states of a classical dynamical system are completely determined by the coordinates and their conjugate momenta. Theoretical and numerical results are presented, employing alanine dipeptide as a model system, to support the view that geometrical structures in phase space dictate the dynamics of molecules, the fingerprints of which are traced by following the Hamiltonian flow above saddles. By properly selecting initial conditions in alanine dipeptide, we have found internally free rotor trajectories the existence of which can only be justified in a phase space perspective. This article is part of the theme issue `Modern theoretical chemistry'.

EPR & Klein Paradoxes in Complex Hamiltonian Dynamics and Krein Space Quantization

NASA Astrophysics Data System (ADS)

Payandeh, Farrin

2015-07-01

Negative energy states are applied in Krein space quantization approach to achieve a naturally renormalized theory. For example, this theory by taking the full set of Dirac solutions, could be able to remove the propagator Green function's divergences and automatically without any normal ordering, to vanish the expected value for vacuum state energy. However, since it is a purely mathematical theory, the results are under debate and some efforts are devoted to include more physics in the concept. Whereas Krein quantization is a pure mathematical approach, complex quantum Hamiltonian dynamics is based on strong foundations of Hamilton-Jacobi (H-J) equations and therefore on classical dynamics. Based on complex quantum Hamilton-Jacobi theory, complex spacetime is a natural consequence of including quantum effects in the relativistic mechanics, and is a bridge connecting the causality in special relativity and the non-locality in quantum mechanics, i.e. extending special relativity to the complex domain leads to relativistic quantum mechanics. So that, considering both relativistic and quantum effects, the Klein-Gordon equation could be derived as a special form of the Hamilton-Jacobi equation. Characterizing the complex time involved in an entangled energy state and writing the general form of energy considering quantum potential, two sets of positive and negative energies will be realized. The new states enable us to study the spacetime in a relativistic entangled “space-time” state leading to 12 extra wave functions than the four solutions of Dirac equation for a free particle. Arguing the entanglement of particle and antiparticle leads to a contradiction with experiments. So, in order to correct the results, along with a previous investigation [1], we realize particles and antiparticles as physical entities with positive energy instead of considering antiparticles with negative energy. As an application of modified descriptions for entangled (space

Normalization of Hamiltonian and nonlinear stability of the triangular equilibrium points in non-resonance case with perturbations

NASA Astrophysics Data System (ADS)

Kishor, Ram; Kushvah, Badam Singh

2017-09-01

For the study of nonlinear stability of a dynamical system, normalized Hamiltonian of the system is very important to discuss the dynamics in the vicinity of invariant objects. In general, it represents a nonlinear approximation to the dynamics, which is very helpful to obtain the information as regards a realistic solution of the problem. In the present study, normalization of the Hamiltonian and analysis of nonlinear stability in non-resonance case, in the Chermnykh-like problem under the influence of perturbations in the form of radiation pressure, oblateness, and a disc is performed. To describe nonlinear stability, initially, quadratic part of the Hamiltonian is normalized in the neighborhood of triangular equilibrium point and then higher order normalization is performed by computing the fourth order normalized Hamiltonian with the help of Lie transforms. In non-resonance case, nonlinear stability of the system is discussed using the Arnold-Moser theorem. Again, the effects of radiation pressure, oblateness and the presence of the disc are analyzed separately and it is observed that in the absence as well as presence of perturbation parameters, triangular equilibrium point is unstable in the nonlinear sense within the stability range 0<μ<μ1=\\bar{μc} due to failure of the Arnold-Moser theorem. However, perturbation parameters affect the values of μ at which D4=0, significantly. This study may help to analyze more generalized cases of the problem in the presence of some other types of perturbations such as P-R drag and solar wind drag. The results are limited to the regular symmetric disc but it can be extended in the future.

Hamiltonian identifiability assisted by single-probe measurement

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Enhanced conformational sampling of nucleic acids by a new Hamiltonian replica exchange molecular dynamics approach.

PubMed

Curuksu, Jeremy; Zacharias, Martin

2009-03-14

Although molecular dynamics (MD) simulations have been applied frequently to study flexible molecules, the sampling of conformational states separated by barriers is limited due to currently possible simulation time scales. Replica-exchange (Rex)MD simulations that allow for exchanges between simulations performed at different temperatures (T-RexMD) can achieve improved conformational sampling. However, in the case of T-RexMD the computational demand grows rapidly with system size. A Hamiltonian RexMD method that specifically enhances coupled dihedral angle transitions has been developed. The method employs added biasing potentials as replica parameters that destabilize available dihedral substates and was applied to study coupled dihedral transitions in nucleic acid molecules. The biasing potentials can be either fixed at the beginning of the simulation or optimized during an equilibration phase. The method was extensively tested and compared to conventional MD simulations and T-RexMD simulations on an adenine dinucleotide system and on a DNA abasic site. The biasing potential RexMD method showed improved sampling of conformational substates compared to conventional MD simulations similar to T-RexMD simulations but at a fraction of the computational demand. It is well suited to study systematically the fine structure and dynamics of large nucleic acids under realistic conditions including explicit solvent and ions and can be easily extended to other types of molecules.

Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction

NASA Astrophysics Data System (ADS)

Fehér, L.; Klimčík, C.

2012-07-01

The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars-Schneider IIIb system from a quasi-Hamiltonian reduction of the internally fused double SU(n)×SU(n). In particular, the reduced spectral functions depending respectively on the first and second SU(n) factor of the double engender two toric moment maps on the IIIb phase space CP(n-1) that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z) mapping class group of the torus with one boundary component is shown to act on the quasi-Hamiltonian double by automorphisms and, upon reduction, the standard generator S of the mapping class group is proved to descend to the Ruijsenaars self-duality symplectomorphism that exchanges the toric moment maps. We give also two new presentations of this duality map: one as the composition of two Delzant symplectomorphisms and the other as the composition of three Dehn twist symplectomorphisms realized by Goldman twist flows. Through the well-known relation between quasi-Hamiltonian manifolds and moduli spaces, our results rigorously establish the validity of the interpretation [going back to Gorsky and Nekrasov] of the IIIb system in terms of flat SU(n) connections on the one-holed torus.

Systems of conservation laws with third-order Hamiltonian structures

NASA Astrophysics Data System (ADS)

Ferapontov, Evgeny V.; Pavlov, Maxim V.; Vitolo, Raffaele F.

2018-06-01

We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in P^{n+2} satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension n+2, classify n-tuples of skew-symmetric 2-forms A^{α } \\in Λ^2(W) such that φ _{β γ }A^{β }\\wedge A^{γ }=0, for some non-degenerate symmetric φ.

Symplectic semiclassical wave packet dynamics II: non-Gaussian states

NASA Astrophysics Data System (ADS)

Ohsawa, Tomoki

2018-05-01

We generalize our earlier work on the symplectic/Hamiltonian formulation of the dynamics of the Gaussian wave packet to non-Gaussian semiclassical wave packets. We find the symplectic forms and asymptotic expansions of the Hamiltonians associated with these semiclassical wave packets, and obtain Hamiltonian systems governing their dynamics. Numerical experiments demonstrate that the dynamics give a very good approximation to the short-time dynamics of the expectation values computed by a method based on Egorov’s theorem or the initial value representation.

Contact symmetries and Hamiltonian thermodynamics

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

Bravetti, A., E-mail: bravetti@correo.nucleares.unam.mx; Lopez-Monsalvo, C.S., E-mail: cesar.slm@correo.nucleares.unam.mx; Nettel, F., E-mail: Francisco.Nettel@roma1.infn.it

It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendremore » symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.« less

Chain representations of Open Quantum Systems and Lieb-Robinson like bounds for the dynamics

NASA Astrophysics Data System (ADS)

Woods, Mischa

2013-03-01

This talk is concerned with the mapping of the Hamiltonian of open quantum systems onto chain representations, which forms the basis for a rigorous theory of the interaction of a system with its environment. This mapping progresses as an interaction which gives rise to a sequence of residual spectral densities of the system. The rigorous mathematical properties of this mapping have been unknown so far. Here we develop the theory of secondary measures to derive an analytic, expression for the sequence solely in terms of the initial measure and its associated orthogonal polynomials of the first and second kind. These mappings can be thought of as taking a highly nonlocal Hamiltonian to a local Hamiltonian. In the latter, a Lieb-Robinson like bound for the dynamics of the open quantum system makes sense. We develop analytical bounds on the error to observables of the system as a function of time when the semi-infinite chain in truncated at some finite length. The fact that this is possible shows that there is a finite ``Speed of sound'' in these chain representations. This has many implications of the simulatability of open quantum systems of this type and demonstrates that a truncated chain can faithfully reproduce the dynamics at shorter times. These results make a significant and mathematically rigorous contribution to the understanding of the theory of open quantum systems; and pave the way towards the efficient simulation of these systems, which within the standard methods, is often an intractable problem. EPSRC CDT in Controlled Quantum Dynamics, EU STREP project and Alexander von Humboldt Foundation

Wheels within Wheels: Hamiltonian Dynamics as a Hierarchy of Action Variables

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

Perkins, Rory J.; Bellan, Paul M.

2010-09-17

In systems where one coordinate undergoes periodic oscillation, the net displacement in any other coordinate over a single period is shown to be given by differentiation of the action integral associated with the oscillating coordinate. This result is then used to demonstrate that the action integral acts as a Hamiltonian for slow coordinates providing time is scaled to the 'tick time' of the oscillating coordinate. Numerous examples, including charged particle drifts and relativistic motion, are supplied to illustrate the varied application of these results.

Hamiltonian structure of the guiding center plasma model

NASA Astrophysics Data System (ADS)

Burby, J. W.; Sengupta, W.

2018-02-01

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

Translation invariant time-dependent massive gravity: Hamiltonian analysis

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

Mourad, Jihad; Steer, Danièle A.; Noui, Karim, E-mail: mourad@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: steer@apc.univ-paris7.fr

2014-09-01

The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagating degrees of freedom are the dRGT mass terms, namely those which are linear in the lapse. We also complete the Hamiltonian analysis with the dynamical evolution of the system.

Léon Rosenfeld's general theory of constrained Hamiltonian dynamics

NASA Astrophysics Data System (ADS)

Salisbury, Donald

Léon Rosenfeld published in Annalen der Physik in 1930 a groundbreaking paper showing how to construct a Hamiltonian formalism for Lagrangian theories which admitted an underlying local gauge symmetry. The theory included both ``internal'' transformations such as the U(1) symmetry group of electromagnetism, and ``external'' symmetries typified by Einstein's general theory of relativity. His comprehensive analysis predated by two decades the formalism known as the Dirac-Bergmann approach, and I will present evidence that each of these giants were to some extent influenced by Rosenfeld's theory. Of particular significance is Rosenfeld's incorporation of arbitrary functions into the phase space generator of temporal evolution, and his construction of the phase space generator of symmetry transformations. The existing Hamiltonian formalisms have of course played a central role both in the demonstration of the renormalizability of Yang-Mills theories and current efforts in constructing a quantum theory of gravity.

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.

Finite Group Invariance and Solution of Jaynes-Cummings Hamiltonian

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

Haydargil, Derya; Koc, Ramazan

2004-10-04

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

Dynamical analysis of an orbiting three-rigid-body system

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

Pagnozzi, Daniele, E-mail: daniele.pagnozzi@strath.ac.uk, E-mail: james.biggs@strath.ac.uk; Biggs, James D., E-mail: daniele.pagnozzi@strath.ac.uk, E-mail: james.biggs@strath.ac.uk

2014-12-10

The development of multi-joint-spacecraft mission concepts calls for a deeper understanding of their nonlinear dynamics to inform and enhance system design. This paper presents a study of a three-finite-shape rigid-body system under the action of an ideal central gravitational field. The aim of this paper is to gain an insight into the natural dynamics of this system. The Hamiltonian dynamics is derived and used to identify relative attitude equilibria of the system with respect to the orbital reference frame. Then a numerical investigation of the behaviour far from the equilibria is provided using tools from modern dynamical systems theory suchmore » as energy methods, phase portraits and Poincarè maps. Results reveal a complex structure of the dynamics as well as the existence of connections between some of the equilibria. Stable equilibrium configurations appear to be surrounded by very narrow regions of regular and quasi-regular motions. Trajectories evolve on chaotic motions in the rest of the domain.« less

Local Hamiltonians for maximally multipartite-entangled states

NASA Astrophysics Data System (ADS)

Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.

2010-10-01

We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.

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

PubMed

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

2016-08-09

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

Integrated Hamiltonian sampling: a simple and versatile method for free energy simulations and conformational sampling.

PubMed

Mori, Toshifumi; Hamers, Robert J; Pedersen, Joel A; Cui, Qiang

2014-07-17

Motivated by specific applications and the recent work of Gao and co-workers on integrated tempering sampling (ITS), we have developed a novel sampling approach referred to as integrated Hamiltonian sampling (IHS). IHS is straightforward to implement and complementary to existing methods for free energy simulation and enhanced configurational sampling. The method carries out sampling using an effective Hamiltonian constructed by integrating the Boltzmann distributions of a series of Hamiltonians. By judiciously selecting the weights of the different Hamiltonians, one achieves rapid transitions among the energy landscapes that underlie different Hamiltonians and therefore an efficient sampling of important regions of the conformational space. Along this line, IHS shares similar motivations as the enveloping distribution sampling (EDS) approach of van Gunsteren and co-workers, although the ways that distributions of different Hamiltonians are integrated are rather different in IHS and EDS. Specifically, we report efficient ways for determining the weights using a combination of histogram flattening and weighted histogram analysis approaches, which make it straightforward to include many end-state and intermediate Hamiltonians in IHS so as to enhance its flexibility. Using several relatively simple condensed phase examples, we illustrate the implementation and application of IHS as well as potential developments for the near future. The relation of IHS to several related sampling methods such as Hamiltonian replica exchange molecular dynamics and λ-dynamics is also briefly discussed.

Léon Rosenfeld's general theory of constrained Hamiltonian dynamics

NASA Astrophysics Data System (ADS)

Salisbury, Donald; Sundermeyer, Kurt

2017-04-01

This commentary reflects on the 1930 general theory of Léon Rosenfeld dealing with phase-space constraints. We start with a short biography of Rosenfeld and his motivation for this article in the context of ideas pursued by W. Pauli, F. Klein, E. Noether. We then comment on Rosenfeld's General Theory dealing with symmetries and constraints, symmetry generators, conservation laws and the construction of a Hamiltonian in the case of phase-space constraints. It is remarkable that he was able to derive expressions for all phase space symmetry generators without making explicit reference to the generator of time evolution. In his Applications, Rosenfeld treated the general relativistic example of Einstein-Maxwell-Dirac theory. We show, that although Rosenfeld refrained from fully applying his general findings to this example, he could have obtained the Hamiltonian. Many of Rosenfeld's discoveries were re-developed or re-discovered by others two decades later, yet as we show there remain additional firsts that are still not recognized in the community.

Polynomial approximation of Poincare maps for Hamiltonian system

NASA Technical Reports Server (NTRS)

Froeschle, Claude; Petit, Jean-Marc

1992-01-01

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Parity-time symmetry-breaking mechanism of dynamic Mott transitions in dissipative systems

DOE PAGES

Tripathi, Vikram; Galda, Alexey; Barman, Himadri; ...

2016-07-05

Here, we describe the critical behavior of the electric field-driven (dynamic) Mott insulator-to-metal transitions in dissipative Fermi and Bose systems in terms of non-Hermitian Hamiltonians invariant under simultaneous parity (P) and time-reversal (T) operations. The dynamic Mott transition is identified as a PT symmetry-breaking phase transition, with the Mott insulating state corresponding to the regime of unbroken PT symmetry with a real energy spectrum. We also established that the imaginary part of the Hamiltonian arises from the combined effects of the driving field and inherent dissipation. We derive the renormalization and collapse of the Mott gap at the dielectric breakdownmore » and describe the resulting critical behavior of transport characteristics. The critical exponent we obtained is in an excellent agreement with experimental findings.« less

Quantum speed limits in open system dynamics.

PubMed

del Campo, A; Egusquiza, I L; Plenio, M B; Huelga, S F

2013-02-01

Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics, and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive, and trace preserving evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the role of the Hamiltonian being played by the adjoint of the generator of the dynamical semigroup. The utility of the new bound is exemplified in different scenarios, ranging from the estimation of the passage time to the determination of precision limits for quantum metrology in the presence of dephasing noise.

Improved nonorthogonal tight-binding Hamiltonian for molecular-dynamics simulations of silicon clusters

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

Ordejon, P.; Lebedenko, D.; Menon, M.

1994-08-15

We present an improvement over the nonorthogonal tight-binding molecular-dynamics scheme recently proposed by Menon and Subbaswamy [Phys. Rev. B 47, 12 754 (1993)]. The proper treatment of the nonorthogonality and its effect on the Hamiltonian matrix elements has been found to obviate the need for a bond-counting term, leaving only two adjustable parameters in the formalism. With the improved parametrization we obtain values of the energies and bonding distances which are in better agreement with the available [ital ab] [ital initio] results for clusters of size up to [ital N]=10. Additionally, we have identified a lowest energy structure for themore » Si[sub 9] cluster, which to our knowledge has not been considered to date. We show that this structure (a distorted tricapped trigonal prism with [ital C][sub 2[ital v

Finite BRST-BFV transformations for dynamical systems with second-class constraints

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2015-06-01

We study finite field-dependent BRST-BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.

Integrability and Poisson Structures of Three Dimensional Dynamical Systems and Equations of Hydrodynamic Type

NASA Astrophysics Data System (ADS)

Gumral, Hasan

Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.

Classical Coset Hamiltonian for the Electronic Motion and its Application to Anderson Localization and Hammett Equation

NASA Astrophysics Data System (ADS)

Xing, Guan; Wu, Guo-Zhen

2001-02-01

A classical coset Hamiltonian is introduced for the system of one electron in multi-sites. By this Hamiltonian, the dynamical behaviour of the electronic motion can be readily simulated. The simulation reproduces the retardation of the electron density decay in a lattice with site energies randomly distributed - an analogy with Anderson localization. This algorithm is also applied to reproduce the Hammett equation which relates the reaction rate with the property of the substitutions in the organic chemical reactions. The advantages and shortcomings of this algorithm, as contrasted with traditional quantum methods such as the molecular orbital theory, are also discussed.

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

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

Zhang, Ruili; Liu, Jian; Xiao, Jianyuan

2016-07-15

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

Dynamical systems theory for nonlinear evolution equations.

PubMed

Choudhuri, Amitava; Talukdar, B; Das, Umapada

2010-09-01

We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as K(n,m) equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated with the equations. We treat the resulting Hamiltonian equations by the dynamical systems theory and present a phase-space analysis of their stable points. The results of our study demonstrate that the equations can, in general, support both compacton and soliton solutions. For the K(2,2) and K(3,3) cases one type of solutions can be obtained from the other by continuously varying a parameter of the equations. This is not true for the K(3,2) equation for which the parameter can take only negative values. The K(2,3) equation does not have any stable point and, in the language of mechanics, represents a particle moving with constant acceleration.

The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

NASA Technical Reports Server (NTRS)

Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

1994-01-01

The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems

NASA Astrophysics Data System (ADS)

Tonni, Erik; Rodríguez-Laguna, Javier; Sierra, Germán

2018-04-01

Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.

Hamiltonian identifiability assisted by a single-probe measurement

NASA Astrophysics Data System (ADS)

Sone, Akira; Cappellaro, Paola

2017-02-01

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

Hamiltonian structure of real Monge - Ampère equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-06-01

The variational principle for the real homogeneous Monge - Ampère equation in two dimensions is shown to contain three arbitrary functions of four variables. There exist two different specializations of this variational principle where the Lagrangian is degenerate and furthermore contains an arbitrary function of two variables. The Hamiltonian formulation of these degenerate Lagrangian systems requires the use of Dirac's theory of constraints. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. Thus the real homogeneous Monge - Ampère equation in two dimensions admits two classes of infinitely many Hamiltonian operators, namely a family of local, as well as another family non-local Hamiltonian operators and symplectic 2-forms which depend on arbitrary functions of two variables. The simplest non-local Hamiltonian operator corresponds to the Kac - Moody algebra of vector fields and functions on the unit circle. Hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair. In the case of real Monge - Ampère equations with constant right-hand side this compatible pair is the only pair of Hamiltonian operators that survives. Then the complete integrability of all these real Monge - Ampère equations follows by Magri's theorem. Some of the remarkable properties we have obtained for the Hamiltonian structure of the real homogeneous Monge - Ampère equation in two dimensions turn out to be generic to the real homogeneous Monge - Ampère equation and the geodesic flow for the complex homogeneous Monge - Ampère equation in arbitrary number of dimensions. Hence among all integrable nonlinear evolution equations in one space and one time dimension, the real homogeneous Monge - Ampère equation is distinguished as one that retains its character as an integrable system in multiple dimensions.

The dynamical behaviour of our planetary system. Proceedings. 4th Alexander von Humboldt Colloquium on Celestial Mechanics, Ramsau (Austria), 17 - 23 Mar 1996.

NASA Astrophysics Data System (ADS)

Dvorak, R.; Henrard, J.

1996-03-01

The following topics were dealt with: celestial mechanics, dynamical astronomy, planetary systems, resonance scattering, Hamiltonian mechanics non-integrability, irregular periodic orbits, escape, dynamical system mapping, fast Fourier method, precession-nutation, Nekhoroshev theorem, asteroid dynamics, the Trojan problem, planet-crossing orbits, Kirkwood gaps, future research, human comprehension limitations.

On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations.

PubMed

Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio

2015-01-01

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P[Formula: see text]) equation or its fourth-order analogue P[Formula: see text]. As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

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

NASA Astrophysics Data System (ADS)

Nutku, Y.

1987-11-01

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

Hamiltonian formulation of the KdV equation

NASA Astrophysics Data System (ADS)

Nutku, Y.

1984-06-01

We consider the canonical formulation of Whitham's variational principle for the KdV equation. This Lagrangian is degenerate and we have found it necessary to use Dirac's theory of constrained systems in constructing the Hamiltonian. Earlier discussions of the Hamiltonian structure of the KdV equation were based on various different decompositions of the field which is avoided by this new approach.

Optimal feedback scheme and universal time scaling for Hamiltonian parameter estimation.

PubMed

Yuan, Haidong; Fung, Chi-Hang Fred

2015-09-11

Time is a valuable resource and it is expected that a longer time period should lead to better precision in Hamiltonian parameter estimation. However, recent studies in quantum metrology have shown that in certain cases more time may even lead to worse estimations, which puts this intuition into question. In this Letter we show that by including feedback controls this intuition can be restored. By deriving asymptotically optimal feedback controls we quantify the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit under the optimal feedback scheme. Our study reveals an intriguing connection between noncommutativity in the dynamics and the gain of feedback controls in Hamiltonian parameter estimation.

Non-stoquastic Hamiltonians in quantum annealing via geometric phases

NASA Astrophysics Data System (ADS)

Vinci, Walter; Lidar, Daniel A.

2017-09-01

We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.

Robust Online Hamiltonian Learning

NASA Astrophysics Data System (ADS)

Granade, Christopher; Ferrie, Christopher; Wiebe, Nathan; Cory, David

2013-05-01

In this talk, we introduce a machine-learning algorithm for the problem of inferring the dynamical parameters of a quantum system, and discuss this algorithm in the example of estimating the precession frequency of a single qubit in a static field. Our algorithm is designed with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online, during experimental data collection, or can be used as a tool for post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. Finally, we discuss the performance of the our algorithm by appeal to the Cramer-Rao bound. This work was financially supported by the Canadian government through NSERC and CERC and by the United States government through DARPA. NW would like to acknowledge funding from USARO-DTO.

Finite Nilpotent BRST Transformations in Hamiltonian Formulation

NASA Astrophysics Data System (ADS)

Rai, Sumit Kumar; Mandal, Bhabani Prasad

2013-10-01

We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformations in the sector of Lagrange multiplier and its corresponding momenta.

Bi-Hamiltonian Structure in 2-d Field Theory

NASA Astrophysics Data System (ADS)

Ferapontov, E. V.; Galvão, C. A. P.; Mokhov, O. I.; Nutku, Y.

We exhibit the bi-Hamiltonian structure of the equations of associativity (Witten-Dijkgraaf-Verlinde-Verlinde-Dubrovin equations) in 2-d topological field theory, which reduce to a single equation of Monge-Ampère type $ fttt}=f{xxt;;;;;2 - fxxx}f{xtt ,$ in the case of three primary fields. The first Hamiltonian structure of this equation is based on its representation as a 3-component system of hydrodynamic type and the second Hamiltonian structure follows from its formulation in terms of a variational principle with a degenerate Lagrangian.

Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states

PubMed Central

Bonet-Luz, Esther

2016-01-01

The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest’s theorem is shown to be Lie–Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie–Poisson structure associated with another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models that have previously appeared in the chemical physics literature. PMID:27279764

Explicit symplectic algorithms based on generating functions for charged particle dynamics

NASA Astrophysics Data System (ADS)

Zhang, Ruili; Qin, Hong; Tang, Yifa; Liu, Jian; He, Yang; Xiao, Jianyuan

2016-07-01

Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity. For long-term simulations with high efficiency, explicit symplectic algorithms are desirable. However, it is generally believed that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and this restriction limits the application of explicit symplectic algorithms to charged particle dynamics. To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second- and third-order explicit symplectic algorithms for dynamics of charged particle. The generating function method is designed to generate explicit symplectic algorithms for product-separable Hamiltonian with form of H (x ,p ) =pif (x ) or H (x ,p ) =xig (p ) . Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency.

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

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

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

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

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

DOE PAGES

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

2017-12-22

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

Stability of Poisson Equilibria and Hamiltonian Relative Equilibria by Energy Methods

NASA Astrophysics Data System (ADS)

Patrick, George W.; Roberts, Mark; Wulff, Claudia

2004-12-01

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum Methods. Using a topological generalisation of Lyapunov’s result that an extremal critical point of a conserved quantity is stable, we show that a Poisson equilibrium is stable if it is an isolated point in the intersection of a level set of a conserved function with a subset of the phase space that is related to the topology of the symplectic leaf space at that point. This criterion is applied to generalise the energy-momentum method to Hamiltonian systems which are invariant under non-compact symmetry groups for which the coadjoint orbit space is not Hausdorff. We also show that a G-stable relative equilibrium satisfies the stronger condition of being A-stable, where A is a specific group-theoretically defined subset of G which contains the momentum isotropy subgroup of the relative equilibrium. The results are illustrated by an application to the stability of a rigid body in an ideal irrotational fluid.

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

NASA Astrophysics Data System (ADS)

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

2015-01-01

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

BRST theory without Hamiltonian and Lagrangian

NASA Astrophysics Data System (ADS)

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

2005-03-01

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

Multi-Hamiltonian structure of the Born-Infeld equation

NASA Astrophysics Data System (ADS)

Arik, Metin; Neyzi, Fahrünisa; Nutku, Yavuz; Olver, Peter J.; Verosky, John M.

1989-06-01

The multi-Hamiltonian structure, conservation laws, and higher order symmetries for the Born-Infeld equation are exhibited. A new transformation of the Born-Infeld equation to the equations of a Chaplygin gas is presented and explored. The Born-Infeld equation is distinguished among two-dimensional hyperbolic systems by its wealth of such multi-Hamiltonian structures.

Mass segregation phenomena using the Hamiltonian Mean Field model

NASA Astrophysics Data System (ADS)

Steiner, J. R.; Zolacir, T. O.

2018-02-01

Mass segregation problem is thought to be entangled with the dynamical evolution of young stellar clusters (Olczak, 2011 [1]). This is a common sense in the astrophysical community. In this work, the Hamiltonian Mean Field (HMF) model with different masses is studied. A mass segregation phenomenon (MSP) arises from this study as a dynamical feature. The MSP in the HMF model is a consequence of the Landau damping (LD) and it appears in systems that the interactions belongs to a long range regime. Actually HMF is a toy model known to show up the main characteristics of astrophysical systems due to the mean field character of the potential and for different masses, as stellar and galaxies clusters, also exhibits MSP. It is in this sense that computational simulations focusing in what happens over the mass distribution in the phase space are performed for this system. What happens through the violent relaxation period and what stands for the quasi-stationary states (QSS) of this dynamics is analyzed. The results obtained support the fact that MSP is observed already in the violent relaxation time and is maintained during the QSS. Some structures in the mass distribution function are observed. As a result of this study the mass distribution is determined by the system dynamics and is independent of the dimensionality of the system. MSP occurs in a one dimensional system as a result of the long range forces that acts in the system. In this approach MSP emerges as a dynamical feature. We also show that for HMF with different masses, the dynamical time scale is N.

Exploring corrections to the Optomechanical Hamiltonian.

PubMed

Sala, Kamila; Tufarelli, Tommaso

2018-06-14

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

A study to evaluate STS heads-up ascent trajectory performance employing a minimum-Hamiltonian optimization strategy

NASA Technical Reports Server (NTRS)

Sinha, Sujit

1988-01-01

A study was conducted to evaluate the performance implications of a heads-up ascent flight design for the Space Transportation System, as compared to the current heads-down flight mode. The procedure involved the use of the Minimum Hamiltonian Ascent Shuttle Trajectory Evaluation Program, which is a three-degree-of-freedom moment balance simulation of shuttle ascent. A minimum-Hamiltonian optimization strategy was employed to maximize injection weight as a function of maximum dynamic pressure constraint and Solid Rocket Motor burnrate. Performance Reference Mission Four trajectory groundrules were used for consistency. The major conclusions are that for heads-up ascent and a mission nominal design maximum dynamic pressure value of 680 psf, the optimum solid motor burnrate is 0.394 ips, which produces a performance enhancement of 4293 lbm relative to the baseline heads-down ascent, with 0.368 ips burnrate solid motors and a 680 psf dynamic pressure constraint. However, no performance advantage exists for heads-up flight if the current Solid Rocket Motor target burnrate of 0.368 ips is used. The advantage of heads-up ascent flight employing the current burnrate is that Space Shuttle Main Engine throttling for dynamic pressure control is not necessary.

Hamiltonian approach to second order gauge invariant cosmological perturbations

NASA Astrophysics Data System (ADS)

Domènech, Guillem; Sasaki, Misao

2018-01-01

In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian is a suitable and consistent approach to reduce the gauge degrees of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian reduction. An appropriate set of gauge invariant variables that describe the dynamical degrees of freedom may be obtained by suitable canonical transformations in the phase space. We derive a set of gauge invariant variables up to 2nd order in perturbation expansion and for the first time we reduce the 3rd order action without adding gauge fixing terms. In particular, we are able to show the relation between the uniform-ϕ and Newtonian slicings, and study the difference in the definition of tensor modes in these two slicings.

Convergence to equilibrium under a random Hamiltonian.

PubMed

Brandão, Fernando G S L; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K; Mozrzymas, Marek

2012-09-01

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

Convergence to equilibrium under a random Hamiltonian

NASA Astrophysics Data System (ADS)

Brandão, Fernando G. S. L.; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K.; Mozrzymas, Marek

2012-09-01

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems,

DTIC Science & Technology

1987-02-01

equation [18]. It should be noted that the 80 equation has more similarities [19] with the Kadomtsev - Petviashvili (KP...Cimento, 39B, 1 (1977). [31] P. Caudrey, Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation , preprint U.M.I.S.T. (1985). II ’AI D p-I 4, - -- - -- - - -w 4 ...TOM NONLINEAR STUDIES IDTIC I IELEC )// MAR 2 51988 I / \\ / Integrable Equations in Multi- dimensions (2+1) are Bi-Hamiltonian Systems by A.S.

Explicit symplectic algorithms based on generating functions for charged particle dynamics.

PubMed

Zhang, Ruili; Qin, Hong; Tang, Yifa; Liu, Jian; He, Yang; Xiao, Jianyuan

2016-07-01

Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity. For long-term simulations with high efficiency, explicit symplectic algorithms are desirable. However, it is generally believed that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and this restriction limits the application of explicit symplectic algorithms to charged particle dynamics. To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second- and third-order explicit symplectic algorithms for dynamics of charged particle. The generating function method is designed to generate explicit symplectic algorithms for product-separable Hamiltonian with form of H(x,p)=p_{i}f(x) or H(x,p)=x_{i}g(p). Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency.

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

NASA Astrophysics Data System (ADS)

dos Santos, Fabio; Vidal, Claudio

2018-04-01

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

Many-body self-localization in a translation-invariant Hamiltonian

NASA Astrophysics Data System (ADS)

Mondaini, Rubem; Cai, Zi

2017-07-01

We study the statistical and dynamical aspects of a translation-invariant Hamiltonian, without quench disorder, as an example of the manifestation of the phenomenon of many-body localization. This is characterized by the breakdown of thermalization and by information preservation of initial preparations at long times. To realize this, we use quasiperiodic long-range interactions, which are now achievable in high-finesse cavity experiments, to find evidence suggestive of a divergent time-scale in which charge inhomogeneities in the initial state survive asymptotically. This is reminiscent of a glassy behavior, which appears in the ground state of this system, being also present at infinite temperatures.

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

NASA Astrophysics Data System (ADS)

Sheftel, Mikhail; Yazıcı, Devrim

2016-09-01

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

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson.

PubMed

Miller, Michael I; Trouvé, Alain; Younes, Laurent

2015-01-01

The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

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

PubMed

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

2005-02-11

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

An electromechanical Ising Hamiltonian

PubMed Central

Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi

2016-01-01

Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling. PMID:28861469

An electromechanical Ising Hamiltonian.

PubMed

Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi

2016-06-01

Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling.

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

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

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

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

Dynamical quantum phase transitions in discrete time crystals

NASA Astrophysics Data System (ADS)

Kosior, Arkadiusz; Sacha, Krzysztof

2018-05-01

Discrete time crystals are related to nonequilibrium dynamics of periodically driven quantum many-body systems where the discrete time-translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry. Recently, the concept of phase transitions has been extended to nonequilibrium dynamics of time-independent systems induced by a quantum quench, i.e., a sudden change of some parameter of the Hamiltonian. There, the return probability of a system to the ground state reveals singularities in time which are dubbed dynamical quantum phase transitions. We show that the quantum quench in a discrete time crystal leads to dynamical quantum phase transitions where the return probability of a periodically driven system to a Floquet eigenstate before the quench reveals singularities in time. It indicates that dynamical quantum phase transitions are not restricted to time-independent systems and can be also observed in systems that are periodically driven. We discuss how the phenomenon can be observed in ultracold atomic gases.

Gapped two-body Hamiltonian for continuous-variable quantum computation.

PubMed

Aolita, Leandro; Roncaglia, Augusto J; Ferraro, Alessandro; Acín, Antonio

2011-03-04

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv) possess a constant energy gap proportional to the squared inverse of the squeezing. Their ground states are the celebrated Gaussian graph states, which are universal resources for quantum computation in the limit of infinite squeezing. These Hamiltonians constitute the basic ingredient for the adiabatic preparation of graph states and thus open new venues for the physical realization of continuous-variable quantum computing beyond the standard optical approaches. We characterize the correlations in these systems at thermal equilibrium. In particular, we prove that the correlations across any multipartition are contained exactly in its boundary, automatically yielding a correlation area law.

Explicit methods in extended phase space for inseparable Hamiltonian problems

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2015-03-01

We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator.

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

PubMed

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

Initial correlations in open-systems dynamics: The Jaynes-Cummings model

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

Smirne, Andrea; Vacchini, Bassano; INFN, Sezione di Milano, Via Celoria 16, I-20133 Milano

2010-12-15

Employing the trace distance as a measure for the distinguishability of quantum states, we study the influence of initial correlations on the dynamics of open systems. We concentrate on the Jaynes-Cummings model for which the knowledge of the exact joint dynamics of system and reservoir allows the treatment of initial states with arbitrary correlations. As a measure for the correlations in the initial state we consider the trace distance between the system-environment state and the product of its marginal states. In particular, we examine the correlations contained in the thermal equilibrium state for the total system, analyze their dependence onmore » the temperature and on the coupling strength, and demonstrate their connection to the entanglement properties of the eigenstates of the Hamiltonian. A detailed study of the time dependence of the distinguishability of the open system states evolving from the thermal equilibrium state and its corresponding uncorrelated product state shows that the open system dynamically uncovers typical features of the initial correlations.« less

A Hamiltonian approach to Thermodynamics

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

Baldiotti, M.C., E-mail: baldiotti@uel.br; Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br; Molina, C., E-mail: cmolina@usp.br

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensivelymore » used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.« less

Vlasov dynamics of periodically driven systems

NASA Astrophysics Data System (ADS)

Banerjee, Soumyadip; Shah, Kushal

2018-04-01

Analytical solutions of the Vlasov equation for periodically driven systems are of importance in several areas of plasma physics and dynamical systems and are usually approximated using ponderomotive theory. In this paper, we derive the plasma distribution function predicted by ponderomotive theory using Hamiltonian averaging theory and compare it with solutions obtained by the method of characteristics. Our results show that though ponderomotive theory is relatively much easier to use, its predictions are very restrictive and are likely to be very different from the actual distribution function of the system. We also analyse all possible initial conditions which lead to periodic solutions of the Vlasov equation for periodically driven systems and conjecture that the irreducible polynomial corresponding to the initial condition must only have squares of the spatial and momentum coordinate. The resulting distribution function for other initial conditions is aperiodic and can lead to complex relaxation processes within the plasma.

Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

PubMed

Chou, Chia-Chun; Kouri, Donald J

2013-04-25

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

Poisson structure of dynamical systems with three degrees of freedom

NASA Astrophysics Data System (ADS)

Gümral, Hasan; Nutku, Yavuz

1993-12-01

It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one-form in three dimensions. Advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability. Techniques for finding Poisson structures are presented and applied to various examples such as the Halphen system which has been studied as the two-monopole problem by Atiyah and Hitchin. It is shown that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a nontrivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of three-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the SL(2,R) structure is a quadratic unfolding of an integrable one-form in 3+1 dimensions. It is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of Poisson structure and some new techniques for incorporating arbitrary constants into the Poisson one-form are presented herein. This leads to some extensions, analogous to q extensions, of Poisson structure. The Kermack-McKendrick model and some of its generalizations describing the spread of epidemics, as well as the integrable cases of the Lorenz, Lotka-Volterra, May-Leonard, and Maxwell-Bloch systems admit globally integrable bi-Hamiltonian structure.

State transformations and Hamiltonian structures for optimal control in discrete systems

NASA Astrophysics Data System (ADS)

Sieniutycz, S.

2006-04-01

Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.

Constant pH Molecular Dynamics in Explicit Solvent with Enveloping Distribution Sampling and Hamiltonian Exchange

PubMed Central

2015-01-01

We present a new computational approach for constant pH simulations in explicit solvent based on the combination of the enveloping distribution sampling (EDS) and Hamiltonian replica exchange (HREX) methods. Unlike constant pH methods based on variable and continuous charge models, our method is based on discrete protonation states. EDS generates a hybrid Hamiltonian of different protonation states. A smoothness parameter s is used to control the heights of energy barriers of the hybrid-state energy landscape. A small s value facilitates state transitions by lowering energy barriers. Replica exchange between EDS potentials with different s values allows us to readily obtain a thermodynamically accurate ensemble of multiple protonation states with frequent state transitions. The analysis is performed with an ensemble obtained from an EDS Hamiltonian without smoothing, s = ∞, which strictly follows the minimum energy surface of the end states. The accuracy and efficiency of this method is tested on aspartic acid, lysine, and glutamic acid, which have two protonation states, a histidine with three states, a four-residue peptide with four states, and snake cardiotoxin with eight states. The pKa values estimated with the EDS-HREX method agree well with the experimental pKa values. The mean absolute errors of small benchmark systems range from 0.03 to 0.17 pKa units, and those of three titratable groups of snake cardiotoxin range from 0.2 to 1.6 pKa units. This study demonstrates that EDS-HREX is a potent theoretical framework, which gives the correct description of multiple protonation states and good calculated pKa values. PMID:25061443

Hamiltonian structure of three-dimensional gravity in Vielbein formalism

NASA Astrophysics Data System (ADS)

Hajihashemi, Mahdi; Shirzad, Ahmad

2018-01-01

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

Perspective: Quantum Hamiltonians for optical interactions

NASA Astrophysics Data System (ADS)

Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy

2018-01-01

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Is the addition of an assisted driving Hamiltonian always useful for adiabatic evolution?

NASA Astrophysics Data System (ADS)

Sun, Jie; Lu, Songfeng; Li, Li

2017-04-01

It has been known that when an assisted driving item is added to the main system Hamiltonian, the efficiency of the resultant adiabatic evolution can be significantly improved. In some special cases, it can be seen that only through adding an assisted driving Hamiltonian can the resulting adiabatic evolution be made not to fail. Thus the additional driving Hamiltonian plays an important role in adiabatic computing. In this paper, we show that if the driving Hamiltonian is chosen inappropriately, the adiabatic computation may still fail. More importantly, we find that the adiabatic computation can only succeed if the assisted driving Hamiltonian has a relatively fixed form. This may help us understand why in the related literature all of the driving Hamiltonians used share the same form.

Hamiltonian BVMs (HBVMs): Implementation Details and Applications

NASA Astrophysics Data System (ADS)

Brugnano, Luigi; Iavernaro, Felice; Susca, Tiziana

2009-09-01

Hamiltonian Boundary Value Methods are one step schemes of high order where the internal stages are partly exploited to impose the order conditions (fundamental stages) and partly to confer the formula the property of conserving the Hamiltonian function when this is a polynomial with a given degree v. The term "silent stages" has been coined for these latter set of extra-stages to mean that their presence does not cause an increase of the dimension of the associated nonlinear system to be solved at each step. By considering a specific method in this class, we give some details about how the solution of the nonlinear system may be conveniently carried out and how to compensate the effect of roundoff errors.

On the domain of the Nelson Hamiltonian

NASA Astrophysics Data System (ADS)

Griesemer, M.; Wünsch, A.

2018-04-01

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

Multi-Hamiltonian structure of Plebanski's second heavenly equation

NASA Astrophysics Data System (ADS)

Neyzi, F.; Nutku, Y.; Sheftel, M. B.

2005-09-01

We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions.

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

NASA Astrophysics Data System (ADS)

Mengxia, Zhang; Xiaomin, Yang

2018-05-01

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

On the complete and partial integrability of non-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.

1984-11-01

The methods of singularity analysis are applied to several third order non-Hamiltonian systems of physical significance including the Lotka-Volterra equations, the three-wave interaction and the Rikitake dynamo model. Complete integrability is defined and new completely integrable systems are discovered by means of the Painlevé property. In all these cases we obtain integrals, which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation (ODE) solved by Painlevé transcendents. Relaxing the Painlevé property we find many partially integrable cases whose movable singularities are poles at leading order, with In( t- t0) terms entering at higher orders. In an Nth order, generalized Rössler model a precise relation is established between the partial fulfillment of the Painlevé conditions and the existence of N - 2 integrals of the motion.

Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach

NASA Astrophysics Data System (ADS)

Camassa, R.; Falqui, G.; Ortenzi, G.

2017-02-01

The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite two-dimensional channel. The Hamiltonian structure of the averaged equations is obtained directly from that of the Euler equations through the process of Hamiltonian reduction. Long-wave asymptotics together with the Boussinesq approximation of neglecting the fluids’ inertia is then applied to reduce the leading order vertically averaged equations to the shallow-water Airy system, albeit in a non-trivial way. The full non-Boussinesq system for the dispersionless limit can then be viewed as a deformation of this well known equation. In a perturbative study of this deformation, a family of approximate constants of the motion are explicitly constructed and used to find local solutions of the evolution equations by means of hodograph-like formulae.

Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems

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

Oshemkov, Andrey A

2010-10-06

A complete invariant is constructed that is a solution of the problem of semilocal classification of saddle singularities of integrable Hamiltonian systems. Namely, a certain combinatorial object (an f{sub n}-graph) is associated with every nondegenerate saddle singularity of rank zero; as a result, the problem of semilocal classification of saddle singularities of rank zero is reduced to the problem of enumeration of the f{sub n}-graphs. This enables us to describe a simple algorithm for obtaining the lists of saddle singularities of rank zero for a given number of degrees of freedom and a given complexity. Bibliography: 24 titles.

Time-dependent theoretical treatments of the dynamics of electrons and nuclei in molecular systems

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

Deumens, E.; Diz, A.; Longo, R.

1994-07-01

An overview is presented of methods for time-dependent treatments of molecules as systems of electrons and nuclei. The theoretical details of these methods are reviewed and contrasted in the light of a recently developed time-dependent method called electron-nuclear dynamics. Electron-nuclear dynamics (END) is a formulation of the complete dynamics of electrons and nuclei of a molecular system that eliminates the necessity of constructing potential-energy surfaces. Because of its general formulation, it encompasses many aspects found in other formulations and can serve as a didactic device for clarifying many of the principles and approximations relevant in time-dependent treatments of molecular systems.more » The END equations are derived from the time-dependent variational principle applied to a chosen family of efficiently parametrized approximate state vectors. A detailed analysis of the END equations is given for the case of a single-determinantal state for the electrons and a classical treatment of the nuclei. The approach leads to a simple formulation of the fully nonlinear time-dependent Hartree-Fock theory including nuclear dynamics. The nonlinear END equations with the [ital ab] [ital initio] Coulomb Hamiltonian have been implemented at this level of theory in a computer program, ENDyne, and have been shown feasible for the study of small molecular systems. Implementation of the Austin Model 1 semiempirical Hamiltonian is discussed as a route to large molecular systems. The linearized END equations at this level of theory are shown to lead to the random-phase approximation for the coupled system of electrons and nuclei. The qualitative features of the general nonlinear solution are analyzed using the results of the linearized equations as a first approximation. Some specific applications of END are presented, and the comparison with experiment and other theoretical approaches is discussed.« less

Cluster expansion for ground states of local Hamiltonians

NASA Astrophysics Data System (ADS)

Bastianello, Alvise; Sotiriadis, Spyros

2016-08-01

A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.

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

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

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

2014-04-28

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

Divide and conquer approach to quantum Hamiltonian simulation

NASA Astrophysics Data System (ADS)

Hadfield, Stuart; Papageorgiou, Anargyros

2018-04-01

We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.

Fermion bag approach to Hamiltonian lattice field theories in continuous time

NASA Astrophysics Data System (ADS)

Huffman, Emilie; Chandrasekharan, Shailesh

2017-12-01

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

Solving a Hamiltonian Path Problem with a bacterial computer

PubMed Central

Baumgardner, Jordan; Acker, Karen; Adefuye, Oyinade; Crowley, Samuel Thomas; DeLoache, Will; Dickson, James O; Heard, Lane; Martens, Andrew T; Morton, Nickolaus; Ritter, Michelle; Shoecraft, Amber; Treece, Jessica; Unzicker, Matthew; Valencia, Amanda; Waters, Mike; Campbell, A Malcolm; Heyer, Laurie J; Poet, Jeffrey L; Eckdahl, Todd T

2009-01-01

Background The Hamiltonian Path Problem asks whether there is a route in a directed graph from a beginning node to an ending node, visiting each node exactly once. The Hamiltonian Path Problem is NP complete, achieving surprising computational complexity with modest increases in size. This challenge has inspired researchers to broaden the definition of a computer. DNA computers have been developed that solve NP complete problems. Bacterial computers can be programmed by constructing genetic circuits to execute an algorithm that is responsive to the environment and whose result can be observed. Each bacterium can examine a solution to a mathematical problem and billions of them can explore billions of possible solutions. Bacterial computers can be automated, made responsive to selection, and reproduce themselves so that more processing capacity is applied to problems over time. Results We programmed bacteria with a genetic circuit that enables them to evaluate all possible paths in a directed graph in order to find a Hamiltonian path. We encoded a three node directed graph as DNA segments that were autonomously shuffled randomly inside bacteria by a Hin/hixC recombination system we previously adapted from Salmonella typhimurium for use in Escherichia coli. We represented nodes in the graph as linked halves of two different genes encoding red or green fluorescent proteins. Bacterial populations displayed phenotypes that reflected random ordering of edges in the graph. Individual bacterial clones that found a Hamiltonian path reported their success by fluorescing both red and green, resulting in yellow colonies. We used DNA sequencing to verify that the yellow phenotype resulted from genotypes that represented Hamiltonian path solutions, demonstrating that our bacterial computer functioned as expected. Conclusion We successfully designed, constructed, and tested a bacterial computer capable of finding a Hamiltonian path in a three node directed graph. This proof

Ergodicity and model quality in template-restrained canonical and temperature/Hamiltonian replica exchange coarse-grained molecular dynamics simulations of proteins.

PubMed

Karczyńska, Agnieszka S; Czaplewski, Cezary; Krupa, Paweł; Mozolewska, Magdalena A; Joo, Keehyoung; Lee, Jooyoung; Liwo, Adam

2017-12-05

Molecular simulations restrained to single or multiple templates are commonly used in protein-structure modeling. However, the restraints introduce additional barriers, thus impairing the ergodicity of simulations, which can affect the quality of the resulting models. In this work, the effect of restraint types and simulation schemes on ergodicity and model quality was investigated by performing template-restrained canonical molecular dynamics (MD), multiplexed replica-exchange molecular dynamics, and Hamiltonian replica exchange molecular dynamics (HREMD) simulations with the coarse-grained UNRES force field on nine selected proteins, with pseudo-harmonic log-Gaussian (unbounded) or Lorentzian (bounded) restraint functions. The best ergodicity was exhibited by HREMD. It has been found that non-ergodicity does not affect model quality if good templates are used to generate restraints. However, when poor-quality restraints not covering the entire protein are used, the improved ergodicity of HREMD can lead to significantly improved protein models. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

NASA Astrophysics Data System (ADS)

Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

1996-12-01

A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

Plasticity of 150-loop in influenza neuraminidase explored by Hamiltonian replica exchange molecular dynamics simulations.

PubMed

Han, Nanyu; Mu, Yuguang

2013-01-01

Neuraminidase (NA) of influenza is a key target for antiviral inhibitors, and the 150-cavity in group-1 NA provides new insight in treating this disease. However, NA of 2009 pandemic influenza (09N1) was found lacking this cavity in a crystal structure. To address the issue of flexibility of the 150-loop, Hamiltonian replica exchange molecular dynamics simulations were performed on different groups of NAs. Free energy landscape calculated based on the volume of 150-cavity indicates that 09N1 prefers open forms of 150-loop. The turn A (residues 147-150) of the 150-loop is discovered as the most dynamical motif which induces the inter-conversion of this loop among different conformations. In the turn A, the backbone dynamic of residue 149 is highly related with the shape of 150-loop, thus can function as a marker for the conformation of 150-loop. As a contrast, the closed conformation of 150-loop is more energetically favorable in N2, one of group-2 NAs. The D147-H150 salt bridge is found having no correlation with the conformation of 150-loop. Instead the intimate salt bridge interaction between the 150 and 430 loops in N2 variant contributes the stabilizing factor for the closed form of 150-loop. The clustering analysis elaborates the structural plasticity of the loop. This enhanced sampling simulation provides more information in further structural-based drug discovery on influenza virus.

Plasticity of 150-Loop in Influenza Neuraminidase Explored by Hamiltonian Replica Exchange Molecular Dynamics Simulations

PubMed Central

Han, Nanyu; Mu, Yuguang

2013-01-01

Neuraminidase (NA) of influenza is a key target for antiviral inhibitors, and the 150-cavity in group-1 NA provides new insight in treating this disease. However, NA of 2009 pandemic influenza (09N1) was found lacking this cavity in a crystal structure. To address the issue of flexibility of the 150-loop, Hamiltonian replica exchange molecular dynamics simulations were performed on different groups of NAs. Free energy landscape calculated based on the volume of 150-cavity indicates that 09N1 prefers open forms of 150-loop. The turn A (residues 147–150) of the 150-loop is discovered as the most dynamical motif which induces the inter-conversion of this loop among different conformations. In the turn A, the backbone dynamic of residue 149 is highly related with the shape of 150-loop, thus can function as a marker for the conformation of 150-loop. As a contrast, the closed conformation of 150-loop is more energetically favorable in N2, one of group-2 NAs. The D147-H150 salt bridge is found having no correlation with the conformation of 150-loop. Instead the intimate salt bridge interaction between the 150 and 430 loops in N2 variant contributes the stabilizing factor for the closed form of 150-loop. The clustering analysis elaborates the structural plasticity of the loop. This enhanced sampling simulation provides more information in further structural-based drug discovery on influenza virus. PMID:23593372

Stable schemes for dissipative particle dynamics with conserved energy

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

Stoltz, Gabriel, E-mail: stoltz@cermics.enpc.fr

2017-07-01

This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal conduction) to effective single-variable dynamics, and to approximate the solution of these dynamics with one step of a Metropolis–Hastings algorithm. This ensures by construction that no negative internal energies are encountered during the simulation, and hence allows to increase the admissible timesteps to integrate the dynamics, even for systems with small heat capacities. Stability is only limited by the Hamiltonian part of the dynamics, which suggests resorting to multiplemore » timestep strategies where the stochastic part is integrated less frequently than the Hamiltonian one.« less

Hamiltonian approaches to spatial and temporal discretization of fully compressible equations

NASA Astrophysics Data System (ADS)

Dubos, Thomas; Dubey, Sarvesh

2017-04-01

The fully compressible Euler (FCE) equations are the most accurate for representing atmospheric motion, compared to approximate systems like the hydrostatic, anelastic or pseudo-incompressible systems. The price to pay for this accuracy is the presence of additional degrees of freedom and high-frequency acoustic waves that must be treated implicitly. In this work we explore a Hamiltonian approach to the issue of stable spatial and temporal discretization of the FCE using a non-Eulerian vertical coordinate. For scalability, a horizontally-explicit, vertically-implicit (HEVI) time discretization is adopted. The Hamiltonian structure of the equations is used to obtain the spatial finite-difference discretization and also in order to identify those terms of the equations of motion that need to be treated implicitly. A novel treatment of the lower boundary condition in the presence of orography is introduced: rather than enforcing a no-normal-flow boundary condition, which couples the horizontal and vertical velocity components and interferes with the HEVI structure, the ground is treated as a flexible surface with arbitrarily large stiffness, resulting in a decoupling of the horizontal and vertical dynamics and yielding a simple implicit problem which can be solved efficiently. Standard test cases performed in a vertical slice configuration suggest that an effective horizontal acoustic Courant number close to 1 can be achieved.

Constructing Dense Graphs with Unique Hamiltonian Cycles

ERIC Educational Resources Information Center

Lynch, Mark A. M.

2012-01-01

It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems

NASA Astrophysics Data System (ADS)

Kuwahara, Tomotaka; Mori, Takashi; Saito, Keiji

2016-04-01

This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems.

Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

NASA Astrophysics Data System (ADS)

Xin-Lei, Kong; Hui-Bin, Wu; Feng-Xiang, Mei

2016-01-01

In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities. Project supported by the National Natural Science Foundation of China (Grant No. 11272050), the Excellent Young Teachers Program of North China University of Technology (Grant No. XN132), and the Construction Plan for Innovative Research Team of North China University of Technology (Grant No. XN129).

Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians.

PubMed

Vidmar, Lev; Hackl, Lucas; Bianchi, Eugenio; Rigol, Marcos

2017-07-14

In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291], Page proved that the average entanglement entropy of subsystems of random pure states is S_{ave}≃lnD_{A}-(1/2)D_{A}^{2}/D for 1≪D_{A}≤sqrt[D], where D_{A} and D are the Hilbert space dimensions of the subsystem and the system, respectively. Hence, typical pure states are (nearly) maximally entangled. We develop tools to compute the average entanglement entropy ⟨S⟩ of all eigenstates of quadratic fermionic Hamiltonians. In particular, we derive exact bounds for the most general translationally invariant models lnD_{A}-(lnD_{A})^{2}/lnD≤⟨S⟩≤lnD_{A}-[1/(2ln2)](lnD_{A})^{2}/lnD. Consequently, we prove that (i) if the subsystem size is a finite fraction of the system size, then ⟨S⟩Hamiltonian departs from the result for typical pure states, and (ii) in the limit in which the subsystem size is a vanishing fraction of the system size, the average entanglement entropy is maximal; i.e., typical eigenstates of such Hamiltonians exhibit eigenstate thermalization.

Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

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

Tronko, Natalia; Brizard, Alain J.

A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint onmore » the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.« less

Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model

NASA Astrophysics Data System (ADS)

Cugliandolo, Leticia F.; Lozano, Gustavo S.; Nessi, Nicolás; Picco, Marco; Tartaglia, Alessandro

2018-06-01

We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body random interactions. In the statistical physics framework, the potential energy is of the so-called p  =  2 kind, closely linked to the scalar field theory. Most importantly for our setting, the energy conserving dynamics are equivalent to the ones of the Neumann integrable model. We take initial conditions from the Boltzmann equilibrium measure at a temperature that can be above or below the static phase transition, typical of a disordered (paramagnetic) or of an ordered (disguised ferromagnetic) equilibrium phase. We subsequently evolve the configurations with Newton dynamics dictated by a different Hamiltonian, obtained from an instantaneous global rescaling of the elements in the interaction random matrix. In the limit of infinitely many degrees of freedom, , we identify three dynamical phases depending on the parameters that characterise the initial state and the final Hamiltonian. We next set the analysis of the system with finite number of degrees of freedom in terms of N non-linearly coupled modes. We argue that in the limit the modes decouple at long times. We evaluate the mode temperatures and we relate them to the frequency-dependent effective temperature measured with the fluctuation-dissipation relation in the frequency domain, similarly to what was recently proposed for quantum integrable cases. Finally, we analyse the N  ‑  1 integrals of motion, notably, their scaling with N, and we use them to show that the system is out of equilibrium in all phases, even for parameters that show an apparent Gibbs–Boltzmann behaviour of the global observables. We elaborate on the role played by these constants of motion after the quench and we briefly discuss the possible description of the asymptotic dynamics in terms of a generalised Gibbs ensemble.

Chern-Simons improved Hamiltonians for strings in three space dimensions

NASA Astrophysics Data System (ADS)

Gordeli, Ivan; Melnikov, Dmitry; Niemi, Antti J.; Sedrakyan, Ara

2016-07-01

In the case of a structureless string the extrinsic curvature and torsion determine uniquely its shape in three-dimensional ambient space, by way of solution of the Frenet equation. In many physical scenarios there are in addition symmetries that constrain the functional form of the ensuing energy function. For example, the energy of a structureless string should be independent of the way the string is framed in the Frenet equation. Thus the energy should only involve the curvature and torsion as dynamical variables, in a manner that resembles the Hamiltonian of the Abelian Higgs model. Here we investigate the effect of symmetry principles in the construction of Hamiltonians for structureless strings. We deduce from the concept of frame independence that in addition to extrinsic curvature and torsion, the string can also engage a three-dimensional Abelian bulk gauge field as a dynamical variable. We find that the presence of a bulk gauge field gives rise to a long-range interaction between different strings. Moreover, when this gauge field is subject to Chern-Simons self-interaction, it becomes plausible that interacting strings are subject to fractional statistics in three space dimensions.

Low eigenvalues of the entanglement Hamiltonian, localization length, and rare regions in one-dimensional disordered interacting systems

NASA Astrophysics Data System (ADS)

Berkovits, Richard

2018-03-01

The properties of the low-lying eigenvalues of the entanglement Hamiltonian and their relation to the localization length of a disordered interacting one-dimensional many-particle system are studied. The average of the first entanglement Hamiltonian level spacing is proportional to the ground-state localization length and shows the same dependence on the disorder and interaction strength as the localization length. This is the result of the fact that entanglement is limited to distances of order of the localization length. The distribution of the first entanglement level spacing shows a Gaussian-type behavior as expected for level spacings much larger than the disorder broadening. For weakly disordered systems (localization length larger than sample length), the distribution shows an additional peak at low-level spacings. This stems from rare regions in some samples which exhibit metalliclike behavior of large entanglement and large particle-number fluctuations. These intermediate microemulsion metallic regions embedded in the insulating phase are discussed.

Hamiltonian structure of Dubrovin's equation of associativity in 2-d topological field theory

NASA Astrophysics Data System (ADS)

Galvão, C. A. P.; Nutku, Y.

1996-12-01

A third order Monge-Ampère type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac's theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra.

Maximum Renyi entropy principle for systems with power-law Hamiltonians.

PubMed

Bashkirov, A G

2004-09-24

The Renyi distribution ensuring the maximum of Renyi entropy is investigated for a particular case of a power-law Hamiltonian. Both Lagrange parameters alpha and beta can be eliminated. It is found that beta does not depend on a Renyi parameter q and can be expressed in terms of an exponent kappa of the power-law Hamiltonian and an average energy U. The Renyi entropy for the resulting Renyi distribution reaches its maximal value at q=1/(1+kappa) that can be considered as the most probable value of q when we have no additional information on the behavior of the stochastic process. The Renyi distribution for such q becomes a power-law distribution with the exponent -(kappa+1). When q=1/(1+kappa)+epsilon (0

Unified formalism for higher order non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

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

2012-03-01

This work is devoted to giving a geometric framework for describing higher order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.

The limits of hamiltonian structures in three-dimensional elasticity, shells, and rods

NASA Astrophysics Data System (ADS)

Ge, Z.; Kruse, H. P.; Marsden, J. E.

1996-01-01

This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material and derive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to

Extended space expectation values in quantum dynamical system evolutions

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

Demiralp, Metin

2014-10-06

The time variant power series expansion for the expectation value of a given quantum dynamical operator is well-known and well-investigated issue in quantum dynamics. However, depending on the operator and Hamiltonian singularities this expansion either may not exist or may not converge for all time instances except the beginning of the evolution. This work focuses on this issue and seeks certain cures for the negativities. We work in the extended space obtained by adding all images of the initial wave function under the system Hamiltonian’s positive integer powers. This requires the introduction of certain appropriately defined weight operators. The resultingmore » better convergence in the temporal power series urges us to call the new defined entities “extended space expectation values” even though they are constructed over certain weight operators and are somehow pseudo expectation values.« less

The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.

PubMed

Dridi, G; Julien, R; Hliwa, M; Joachim, C

2015-08-28

The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

NASA Astrophysics Data System (ADS)

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; Wang, Huajia

2016-09-01

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on {{R}}^{1,d-1} . We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. These methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. We also discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.

Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time

NASA Astrophysics Data System (ADS)

Noble, J. H.; Jentschura, U. D.

2016-03-01

We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Isospectral Hamiltonian for position-dependent mass for an arbitrary quantum system and coherent states

NASA Astrophysics Data System (ADS)

Yahiaoui, Sid-Ahmed; Bentaiba, Mustapha

2017-06-01

By means of the unitary transformation, a new way for discussing the ordering prescription of the Schrödinger equation with a position-dependent mass (PDM) for isospectral Hamiltonian operators is presented. We show that the ambiguity parameter choices in the kinetic part of the Hamiltonian can be explained through an exact SUSY QM symmetry as well as a consequence of an accidental symmetry under the Z2 action. By making use of the unitary transformation, we construct coherent states for a family of PDM isospectral Hamiltonians from a suitable choice of ladder operators. We show that these states preserve the usual structure of Klauder-Perelomov's states and thus saturate and minimize the position-momentum uncertainty relation (PMUR) under some special restrictions. We show that PMUR properties can be used to determine the sign of the superpotential.

Reductions of topologically massive gravity I: Hamiltonian analysis of second order degenerate Lagrangians

NASA Astrophysics Data System (ADS)

Ćaǧatay Uçgun, Filiz; Esen, Oǧul; Gümral, Hasan

2018-01-01

We present Skinner-Rusk and Hamiltonian formalisms of second order degenerate Clément and Sarıoğlu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed to obtain Hamiltonian realizations of Lagrangian theories. The Gotay-Nester-Hinds algorithm is used to investigate Skinner-Rusk formalisms of these systems.

Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

NASA Astrophysics Data System (ADS)

Bagarello, F.

2011-12-01

We have recently proposed a strategy to produce, starting from a given Hamiltonian h and a certain operator x for which [h,xx]=0 and xx is invertible, a second Hamiltonian h with the same eigenvalues as h and whose eigenvectors are related to those of h by x. Here we extend this procedure to build up a second Hamiltonian, whose eigenvalues are different from those of h, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian Hamiltonians.

sdg Interacting boson hamiltonian in the seniority scheme

NASA Astrophysics Data System (ADS)

Yoshinaga, N.

1989-03-01

The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian

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

Wahlen-Strothman, J. M.; Henderson, T. H.; Hermes, M. R.

Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems, but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories.more » We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.« less

Limit Cycle Bifurcations by Perturbing a Piecewise Hamiltonian System with a Double Homoclinic Loop

NASA Astrophysics Data System (ADS)

Xiong, Yanqin

2016-06-01

This paper is concerned with the bifurcation problem of limit cycles by perturbing a piecewise Hamiltonian system with a double homoclinic loop. First, the derivative of the first Melnikov function is provided. Then, we use it, together with the analytic method, to derive the asymptotic expansion of the first Melnikov function near the loop. Meanwhile, we present the first coefficients in the expansion, which can be applied to study the limit cycle bifurcation near the loop. We give sufficient conditions for this system to have 14 limit cycles in the neighborhood of the loop. As an application, a piecewise polynomial Liénard system is investigated, finding six limit cycles with the help of the obtained method.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Phase equilibria in polymer blend thin films: A Hamiltonian approach

NASA Astrophysics Data System (ADS)

Souche, M.; Clarke, N.

2009-12-01

We propose a Hamiltonian formulation of the Flory-Huggins-de Gennes theory describing a polymer blend thin film. We then focus on the case of 50:50 polymer blends confined between antisymmetric walls. The different phases of the system and the transitions between them, including finite-size effects, are systematically studied through their relation with the geometry of the Hamiltonian flow in phase space. This method provides an easy and efficient way, with strong graphical insight, to infer the qualitative physical behavior of polymer blend thin films.

Designing non-Hermitian dynamics for conservative state evolution on the Bloch sphere

NASA Astrophysics Data System (ADS)

Yu, Sunkyu; Piao, Xianji; Park, Namkyoo

2018-03-01

An evolution on the Bloch sphere is the fundamental state transition, including optical polarization controls and qubit operations. Conventional evolution of a polarization state or qubit is implemented within a closed system that automatically satisfies energy conservation from the Hermitian formalism. Although particular forms of static non-Hermitian Hamiltonians, such as parity-time-symmetric Hamiltonians, allow conservative states in an open system, the criteria for the energy conservation in a dynamical open system have not been fully explored. Here, we derive the condition of conservative state evolution in open-system dynamics and its inverse design method, by developing the non-Hermitian modification of the Larmor precession equation. We show that the geometrically designed locus on the Bloch sphere can be realized by different forms of dynamics, leading to the isolocus family of non-Hermitian dynamics. This increased degree of freedom allows the complementary phenomena of error-robust and highly sensitive evolutions on the Bloch sphere, which could be applicable to stable polarizers, quantum gates, and optimized sensors in dynamical open systems.

Moyal dynamics and trajectories

NASA Astrophysics Data System (ADS)

Braunss, G.

2010-01-01

We give first an approximation of the operator δh: f → δhf := h*planckf - f*planckh in terms of planck2n, n >= 0, where h\\equiv h(p,q), (p,q)\\in {\\mathbb R}^{2 n} , is a Hamilton function and *planck denotes the star product. The operator, which is the generator of time translations in a *planck-algebra, can be considered as a canonical extension of the Liouville operator Lh: f → Lhf := {h, f}Poisson. Using this operator we investigate the dynamics and trajectories of some examples with a scheme that extends the Hamilton-Jacobi method for classical dynamics to Moyal dynamics. The examples we have chosen are Hamiltonians with a one-dimensional quartic potential and two-dimensional radially symmetric nonrelativistic and relativistic Coulomb potentials, and the Hamiltonian for a Schwarzschild metric. We further state a conjecture concerning an extension of the Bohr-Sommerfeld formula for the calculation of the exact eigenvalues for systems with classically periodic trajectories.

Canonical formalism for modelling and control of rigid body dynamics.

PubMed

Gurfil, P

2005-12-01

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

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

PubMed

Marvian, Iman; Lidar, Daniel A

2014-12-31

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

Political Dynamics Affected by Turncoats

NASA Astrophysics Data System (ADS)

Di Salvo, Rosa; Gorgone, Matteo; Oliveri, Francesco

2017-11-01

An operatorial theoretical model based on raising and lowering fermionic operators for the description of the dynamics of a political system consisting of macro-groups affected by turncoat-like behaviors is presented. The analysis of the party system dynamics is carried on by combining the action of a suitable quadratic Hamiltonian operator with specific rules (depending on the variations of the mean values of the observables) able to adjust periodically the conservative model to the political environment.

Nonlinear Dynamics and Chaos in Astrophysics: A Festschrift in Honor of George Contopoulos

NASA Astrophysics Data System (ADS)

Buchler, J. Robert; Gottesman, Stephen T.; Kandrup, Henry E.

1998-12-01

The annals of the New York Academy of Sciences is a compilation of work in the area of nonlinear dynamics and chaos in Astrophysics. Sections included are: From Quasars to Extraordinary N-body Problems; Dynamical Spectra and the Onset of Chaos; Orbital Complexity, Short-Time Lyapunov Exponents, and Phase Space Transport in Time-Independent Hamiltonian Systems; Bifurcations of Periodic Orbits in Axisymmetric Scalefree Potentials; Irregular Period-Tripling Bifurcations in Axisymmetric Scalefree Potentials; Negative Energy Modes and Gravitational Instability of Interpenetrating Fluids; Invariants and Labels in Lie-Poisson Systems; From Jupiter's Great Red Spot to the Structure of Galaxies: Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems; N-Body Simulations of Galaxies and Groups of Galaxies with the Marseille GRAPE Systems; On Nonlinear Dynamics of Three-Dimensional Astrophysical Disks; Satellites as Probes of the Masses of Spiral Galaxies; Chaos in the Centers of Galaxies; Counterrotating Galaxies and Accretion Disks; Global Spiral Patterns in Galaxies: Complexity and Simplicity; Candidates for Abundance Gradients at Intermediate Red-Shift Clusters; Scaling Regimes in the Distribution of Galaxies; Recent Progress in the Study of One-Dimensional Gravitating Systems; Modeling the Time Variability of Black Hole Candidates; Stellar Oscillons; Chaos in Cosmological Hamiltonians; and Phase Space Transport in Noisy Hamiltonian Systems.

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

NASA Astrophysics Data System (ADS)

Crampé, N.; Frappat, L.; Ragoucy, E.

2013-10-01

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

Modeling the dynamics of multipartite quantum systems created departing from two-level systems using general local and non-local interactions

NASA Astrophysics Data System (ADS)

Delgado, Francisco

2017-12-01

Quantum information is an emergent area merging physics, mathematics, computer science and engineering. To reach its technological goals, it is requiring adequate approaches to understand how to combine physical restrictions, computational approaches and technological requirements to get functional universal quantum information processing. This work presents the modeling and the analysis of certain general type of Hamiltonian representing several physical systems used in quantum information and establishing a dynamics reduction in a natural grammar for bipartite processing based on entangled states.

Entanglement Hamiltonians for Chiral Fermions with Zero Modes.

PubMed

Klich, Israel; Vaman, Diana; Wong, Gabriel

2017-09-22

In this Letter, we study the effect of topological zero modes on entanglement Hamiltonians and the entropy of free chiral fermions in (1+1)D. We show how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain exact expressions for entanglement Hamiltonians. In the absence of the zero mode, the resulting entanglement Hamiltonians consist of local and bilocal terms. In the periodic sector, the presence of a zero mode leads to an additional nonlocal contribution to the entanglement Hamiltonian. We derive an exact expression for this term and for the resulting change in the entanglement entropy.

Studies of perturbed three vortex dynamics

NASA Astrophysics Data System (ADS)

Blackmore, Denis; Ting, Lu; Knio, Omar

2007-06-01

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated with completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half plane, three coaxial slender vortex rings in three space, and "restricted" four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser- and Poincaré-Birkhoff-type arguments and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.

Non-commuting two-local Hamiltonians for quantum error suppression

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Rieffel, Eleanor G.

2017-04-01

Physical constraints make it challenging to implement and control many-body interactions. For this reason, designing quantum information processes with Hamiltonians consisting of only one- and two-local terms is a worthwhile challenge. Enabling error suppression with two-local Hamiltonians is particularly challenging. A no-go theorem of Marvian and Lidar (Phys Rev Lett 113(26):260504, 2014) demonstrates that, even allowing particles with high Hilbert space dimension, it is impossible to protect quantum information from single-site errors by encoding in the ground subspace of any Hamiltonian containing only commuting two-local terms. Here, we get around this no-go result by encoding in the ground subspace of a Hamiltonian consisting of non-commuting two-local terms arising from the gauge operators of a subsystem code. Specifically, we show how to protect stored quantum information against single-qubit errors using a Hamiltonian consisting of sums of the gauge generators from Bacon-Shor codes (Bacon in Phys Rev A 73(1):012340, 2006) and generalized-Bacon-Shor code (Bravyi in Phys Rev A 83(1):012320, 2011). Our results imply that non-commuting two-local Hamiltonians have more error-suppressing power than commuting two-local Hamiltonians. While far from providing full fault tolerance, this approach improves the robustness achievable in near-term implementable quantum storage and adiabatic quantum computations, reducing the number of higher-order terms required to encode commonly used adiabatic Hamiltonians such as the Ising Hamiltonians common in adiabatic quantum optimization and quantum annealing.

Hamiltonian theory of guiding-center motion

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

Littlejohn, R.G.

1980-05-01

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

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

DOE PAGES

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; ...

2016-09-08

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R 1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Ourmore » main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.« less

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

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

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R 1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Ourmore » main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.« less

Global Melnikov Theory in Hamiltonian Systems with General Time-Dependent Perturbations

NASA Astrophysics Data System (ADS)

Gidea, Marian; de la Llave, Rafael

2018-04-01

We consider a mechanical system consisting of n-penduli and a d-degree-of-freedom rotator. The phase space of the rotator defines a normally hyperbolic invariant manifold Λ _0 . We apply a time-dependent perturbation, which is not assumed to be either Hamiltonian, or periodic, or quasi-periodic, as we allow for rather general time dependence. The strength of the perturbation is given by a parameter ɛ \\in R . For all |ɛ | sufficiently small, the augmented flow—obtained by making the time into a new variable—has a normally hyperbolic locally invariant manifold \\tilde{Λ }_ɛ . For ɛ =0 , \\tilde{Λ }_0=Λ _0× R . We define a Melnikov-type vector, which gives the first-order expansion of the displacement of the stable and unstable manifolds of \\tilde{Λ }_0 under the perturbation. We provide an explicit formula for the Melnikov vector in terms of convergent improper integrals of the perturbation along homoclinic orbits of the unperturbed system. We show that if the perturbation satisfies some explicit non-degeneracy conditions, then the stable and unstable manifolds of \\tilde{Λ }_ɛ , W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) , respectively, intersect along a transverse homoclinic manifold, and, moreover, the splitting of W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) can be explicitly computed, up to the first order, in terms of the Melnikov-type vector. This implies that the excursions along some homoclinic trajectories yield a non-trivial increase of order O(ɛ ) in the action variables of the rotator, for all sufficiently small perturbations. The formulas that we obtain are independent of the unperturbed motions in Λ _0 , and give, at the same time, the effects on periodic, quasi-periodic, or general-type orbits. When the perturbation is Hamiltonian, we express the effects of the perturbation, up to the first order, in terms of a Melnikov potential. In addition, if the perturbation is periodic, we obtain that the non-degeneracy conditions on

Thermalization Time Bounds for Pauli Stabilizer Hamiltonians

NASA Astrophysics Data System (ADS)

Temme, Kristan

2017-03-01

We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))}, where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.

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

NASA Astrophysics Data System (ADS)

Harikumar, E.; Sivakumar, M.

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

The gravity duals of modular Hamiltonians

DOE PAGES

Jafferis, Daniel L.; Suh, S. Josephine

2016-09-12

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-likemore » to the causal completion of the region.« less

The gravity duals of modular Hamiltonians

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

Jafferis, Daniel L.; Suh, S. Josephine

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-likemore » to the causal completion of the region.« less

Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories

NASA Astrophysics Data System (ADS)

Román-Roy, Narciso

2009-11-01

This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.

Optimal control of open quantum systems: A combined surrogate Hamiltonian optimal control theory approach applied to photochemistry on surfaces

NASA Astrophysics Data System (ADS)

Asplund, Erik; Klüner, Thorsten

2012-03-01

In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)], 10.1063/1.473950. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998), 10.1063/1.475576; Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)], 10.1063/1.1650297. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ℏ = me = e = a0 = 1, have been used unless otherwise stated.

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

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

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

2016-06-15

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

Reverse engineering of a Hamiltonian by designing the evolution operators

NASA Astrophysics Data System (ADS)

Kang, Yi-Hao; Chen, Ye-Hong; Wu, Qi-Cheng; Huang, Bi-Hua; Xia, Yan; Song, Jie

2016-07-01

We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD), the present scheme is focus on only one or parts of moving states in a D-dimension (D ≥ 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfer for a Rydberg atom. The influences of various decoherence processes are discussed by numerical simulation and the result shows that the scheme is fast and robust against the decoherence and operational imperfection. Therefore, this scheme may be used to construct a Hamiltonian which can be realized in experiments.

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

PubMed

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

2008-10-01

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

Geometric construction of quantum hall clustering Hamiltonians

DOE PAGES

Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny

2015-10-08

In this study, many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z 3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicatedmore » many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.« less

Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2013-10-01

The Euclidean action with acceleration has been analyzed in Ref. 1, and referred to henceforth as Paper I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation and destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.

Hamiltonian replica exchange combined with elastic network analysis to enhance global domain motions in atomistic molecular dynamics simulations.

PubMed

Ostermeir, Katja; Zacharias, Martin

2014-12-01

Coarse-grained elastic network models (ENM) of proteins offer a low-resolution representation of protein dynamics and directions of global mobility. A Hamiltonian-replica exchange molecular dynamics (H-REMD) approach has been developed that combines information extracted from an ENM analysis with atomistic explicit solvent MD simulations. Based on a set of centers representing rigid segments (centroids) of a protein, a distance-dependent biasing potential is constructed by means of an ENM analysis to promote and guide centroid/domain rearrangements. The biasing potentials are added with different magnitude to the force field description of the MD simulation along the replicas with one reference replica under the control of the original force field. The magnitude and the form of the biasing potentials are adapted during the simulation based on the average sampled conformation to reach a near constant biasing in each replica after equilibration. This allows for canonical sampling of conformational states in each replica. The application of the methodology to a two-domain segment of the glycoprotein 130 and to the protein cyanovirin-N indicates significantly enhanced global domain motions and improved conformational sampling compared with conventional MD simulations. © 2014 Wiley Periodicals, Inc.

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

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

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

2015-09-14

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

Quadratic time dependent Hamiltonians and separation of variables

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2017-06-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

A New Scheme of Integrability for (bi)Hamiltonian PDE

NASA Astrophysics Data System (ADS)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2016-10-01

We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.

Gravitational surface Hamiltonian and entropy quantization

NASA Astrophysics Data System (ADS)

Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav

2017-02-01

The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.

First principles of Hamiltonian medicine.

PubMed

Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

2014-05-19

We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.

Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains

NASA Technical Reports Server (NTRS)

Schaffer, L.; Burns, J. A.

1994-01-01

We use a combination of analytical and numerical methods to investigate the dynamics of charged dust grains in planetary magnetospheres. Our emphasis is on obtaining results valid for particles that are not necessarily dominated either by gravitational or electromagnetic forces. A Hamiltonian formulation of the problem yields exact results, for all values of charge-to-mass ratio, when we introduce two constraints: particles remain in the equatorial plane and the magnetic field is taken as axially symmetric. In particular, we obtain locations of equilibrium points, the frequencies of stable periodic orbits, the topology of separatrices in phase space, and the rate of longitudinal drift. These results are significant for specific applications: motion in the nearly aligned dipolar field of Saturn, and the trajectories of arbitrarily charged particles in complex magnetic fields for limited periods of time after ejection from parent bodies. Since the model is restrictive, we also use numerical integrations of the full three-dimensional equations of motion and illustrate under what conditions the constrained problem yields reasonable results. We show that a large fraction of the intermediately charged and highly charged (gyrating) particles will always be lost to a planet's atmosphere within a few hundred hours, for motion through tilted-dipole magnetic fields. We find that grains must have a very high charge-to-mass ratio in order to be mirrored back to the ring plane. Thus, except perhaps at Saturn where the dipole tilt is very small, the likely inhabitants of the dusty ring systems are those particles that are either nearly Keplerian (weakly charged) grains or grains whose charges place them in the lower end of the intermediate charge zone. Fianlly, we demonstrate the effect of plasma drag on the orbits of gyrating particles to be a rapid decrease in gyroradius followed by a slow radial evolution of the guiding center.

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state.

PubMed

Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H

2015-10-01

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

Kondo effect in systems with dynamical symmetries

NASA Astrophysics Data System (ADS)

Kuzmenko, T.; Kikoin, K.; Avishai, Y.

2004-05-01

This paper is devoted to a systematic exposure of the Kondo physics in quantum dots for which the low-energy spin excitations consist of a few different spin multiplets |SiMi>. Under certain conditions (to be explained below), some of the lowest energy levels ESi are nearly degenerate. The dot in its ground state cannot then be regarded as a simple quantum top, in the sense that beside its spin operator other dot (vector) operators Rn are needed (in order to fully determine its quantum states), which have nonzero matrix elements between states of different spin multiplets ≠0. These Runge-Lenz operators do not appear in the isolated dot Hamiltonian (so in some sense they are “hidden”). Yet, they are exposed when tunneling between dot and leads is switched on. The effective spin Hamiltonian which couples the metallic electron spin s with the operators of the dot then contains exchange terms JnsṡRn besides the ubiquitous ones JisṡSi. The operators Si and Rn generate a dynamical group [usually SO(n)]. Remarkably, the value of n can be controlled by gate voltages, indicating that abstract concepts such as dynamical symmetry groups are experimentally realizable. Moreover, when an external magnetic field is applied, under favorable circumstances the exchange interaction involves solely the Runge-Lenz operators Rn and the corresponding dynamical symmetry group is SU(n). For example, the celebrated group SU(3) is realized in a triple quantum dot with four electrons.

Integrable Time-Dependent Quantum Hamiltonians

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

A Hamiltonian replica exchange method for building protein-protein interfaces applied to a leucine zipper

NASA Astrophysics Data System (ADS)

Cukier, Robert I.

2011-01-01

Leucine zippers consist of alpha helical monomers dimerized (or oligomerized) into alpha superhelical structures known as coiled coils. Forming the correct interface of a dimer from its monomers requires an exploration of configuration space focused on the side chains of one monomer that must interdigitate with sites on the other monomer. The aim of this work is to generate good interfaces in short simulations starting from separated monomers. Methods are developed to accomplish this goal based on an extension of a previously introduced [Su and Cukier, J. Phys. Chem. B 113, 9595, (2009)] Hamiltonian temperature replica exchange method (HTREM), which scales the Hamiltonian in both potential and kinetic energies that was used for the simulation of dimer melting curves. The new method, HTREM_MS (MS designates mean square), focused on interface formation, adds restraints to the Hamiltonians for all but the physical system, which is characterized by the normal molecular dynamics force field at the desired temperature. The restraints in the nonphysical systems serve to prevent the monomers from separating too far, and have the dual aims of enhancing the sampling of close in configurations and breaking unwanted correlations in the restrained systems. The method is applied to a 31-residue truncation of the 33-residue leucine zipper (GCN4-p1) of the yeast transcriptional activator GCN4. The monomers are initially separated by a distance that is beyond their capture length. HTREM simulations show that the monomers oscillate between dimerlike and monomerlike configurations, but do not form a stable interface. HTREM_MS simulations result in the dimer interface being faithfully reconstructed on a 2 ns time scale. A small number of systems (one physical and two restrained with modified potentials and higher effective temperatures) are sufficient. An in silico mutant that should not dimerize because it lacks charged residues that provide electrostatic stabilization of the dimer

Hamiltonian of Mean Force and Dissipative Scalar Field Theory

NASA Astrophysics Data System (ADS)

Jafari, Marjan; Kheirandish, Fardin

2018-04-01

Quantum dynamics of a dissipative scalar field is investigated. Using the Hamiltonian of mean force, internal energy, free energy and entropy of a dissipative scalar field are obtained. It is shown that a dissipative massive scalar field can be considered as a free massive scalar field described by an effective mass and dispersion relation. Internal energy of the scalar field, as the subsystem, is found in the limit of low temperature and weak and strong couplings to an Ohimc heat bath. Correlation functions for thermal and coherent states are derived.

Quantum spin chains with multiple dynamics

NASA Astrophysics Data System (ADS)

Chen, Xiao; Fradkin, Eduardo; Witczak-Krempa, William

2017-11-01

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultracold atoms. We investigate such nontrivial quantum dynamics in a different setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled ground state, but a gapless excitation spectrum that is poorly understood. By using large-scale density matrix renormalization group simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2 ≤z <2.7 , which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wave function for the ground state, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the nonequilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in two dimensions.

Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

NASA Astrophysics Data System (ADS)

Risser, Steven Michael

This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb

Alternative bi-Hamiltonian structures for WDVV equations of associativity

NASA Astrophysics Data System (ADS)

Kalayci, J.; Nutku, Y.

1998-01-01

The WDVV equations of associativity in two-dimensional topological field theory are completely integrable third-order Monge-Ampère equations which admit bi-Hamiltonian structure. The time variable plays a distinguished role in the discussion of Hamiltonian structure, whereas in the theory of WDVV equations none of the independent variables merits such a distinction. WDVV equations admit very different alternative Hamiltonian structures under different possible choices of the time variable, but all these various Hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure. They can be identified as different components of the covariant Witten-Zuckerman symplectic 2-form current density where a variational formulation of the WDVV equation that leads to the Hamiltonian operator through the Dirac bracket is available.

Evolution of multiple quantum coherences with scaled dipolar Hamiltonian

NASA Astrophysics Data System (ADS)

Sánchez, Claudia M.; Buljubasich, Lisandro; Pastawski, Horacio M.; Chattah, Ana K.

2017-08-01

In this article, we introduce a pulse sequence which allows the monitoring of multiple quantum coherences distribution of correlated spin states developed with scaled dipolar Hamiltonian. The pulse sequence is a modification of our previous Proportionally Refocused Loschmidt echo (PRL echo) with phase increment, in order to verify the accuracy of the weighted coherent quantum dynamics. The experiments were carried out with different scaling factors to analyze the evolution of the total magnetization, the time dependence of the multiple quantum coherence orders, and the development of correlated spins clusters. In all cases, a strong dependence between the evolution rate and the weighting factor is observed. Remarkably, all the curves appeared overlapped in a single trend when plotted against the self-time, a new time scale that includes the scaling factor into the evolution time. In other words, the spin system displayed always the same quantum evolution, slowed down as the scaling factor decreases, confirming the high performance of the new pulse sequence.

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

NASA Astrophysics Data System (ADS)

Garg, Rajat; Ramachandran, Ramesh

2017-05-01

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

Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians

NASA Astrophysics Data System (ADS)

Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V.

2011-12-01

The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

Greenberger-Horne-Zeilinger states and few-body Hamiltonians.

PubMed

Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V

2011-12-23

The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

Approximate symmetries of Hamiltonians

NASA Astrophysics Data System (ADS)

Chubb, Christopher T.; Flammia, Steven T.

2017-08-01

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

Enhanced conformational sampling of carbohydrates by Hamiltonian replica-exchange simulation.

PubMed

Mishra, Sushil Kumar; Kara, Mahmut; Zacharias, Martin; Koca, Jaroslav

2014-01-01

Knowledge of the structure and conformational flexibility of carbohydrates in an aqueous solvent is important to improving our understanding of how carbohydrates function in biological systems. In this study, we extend a variant of the Hamiltonian replica-exchange molecular dynamics (MD) simulation to improve the conformational sampling of saccharides in an explicit solvent. During the simulations, a biasing potential along the glycosidic-dihedral linkage between the saccharide monomer units in an oligomer is applied at various levels along the replica runs to enable effective transitions between various conformations. One reference replica runs under the control of the original force field. The method was tested on disaccharide structures and further validated on biologically relevant blood group B, Lewis X and Lewis A trisaccharides. The biasing potential-based replica-exchange molecular dynamics (BP-REMD) method provided a significantly improved sampling of relevant conformational states compared with standard continuous MD simulations, with modest computational costs. Thus, the proposed BP-REMD approach adds a new dimension to existing carbohydrate conformational sampling approaches by enhancing conformational sampling in the presence of solvent molecules explicitly at relatively low computational cost.

Construction of Hamiltonians by supervised learning of energy and entanglement spectra

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Stability of Inhomogeneous Equilibria of Hamiltonian Continuous Media Field Theories

NASA Astrophysics Data System (ADS)

Hagstrom, George

2013-10-01

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

Low-energy effective Hamiltonians for correlated electron systems beyond density functional theory

NASA Astrophysics Data System (ADS)

Hirayama, Motoaki; Miyake, Takashi; Imada, Masatoshi; Biermann, Silke

2017-08-01

We propose a refined scheme of deriving an effective low-energy Hamiltonian for materials with strong electronic Coulomb correlations beyond density functional theory (DFT). By tracing out the electronic states away from the target degrees of freedom in a controlled way by a perturbative scheme, we construct an effective Hamiltonian for a restricted low-energy target space incorporating the effects of high-energy degrees of freedom in an effective manner. The resulting effective Hamiltonian can afterwards be solved by accurate many-body solvers. We improve this "multiscale ab initio scheme for correlated electrons" (MACE) primarily in two directions by elaborating and combining two frameworks developed by Hirayama et al. [M. Hirayama, T. Miyake, and M. Imada, Phys. Rev. B 87, 195144 (2013), 10.1103/PhysRevB.87.195144] and Casula et al. [M. Casula, P. Werner, L. Vaugier, F. Aryasetiawan, T. Miyake, A. J. Millis, and S. Biermann, Phys. Rev. Lett. 109, 126408 (2012), 10.1103/PhysRevLett.109.126408]: (1) Double counting of electronic correlations between the DFT and the low-energy solver is avoided by using the constrained G W scheme; and (2) the frequency dependent interactions emerging from the partial trace summation are successfully separated into a nonlocal part that is treated following ideas by Hirayama et al. and a local part treated nonperturbatively in the spirit of Casula et al. and are incorporated into the renormalization of the low-energy dispersion. The scheme is favorably tested on the example of SrVO3.

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

PubMed

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

2015-04-10

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

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

Effective time-independent analysis for quantum kicked systems.

PubMed

Bandyopadhyay, Jayendra N; Guha Sarkar, Tapomoy

2015-03-01

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

Effective time-independent analysis for quantum kicked systems

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Jayendra N.; Guha Sarkar, Tapomoy

2015-03-01

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

Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems

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

Kuwahara, Tomotaka, E-mail: tomotaka.phys@gmail.com; WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577; Mori, Takashi

2016-04-15

This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet–Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian onmore » the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems. -- Highlights: •A general framework to describe transient dynamics for periodically driven systems. •The theory is applicable to generic quantum many-body systems including long-range interacting systems. •Physical meaning of the truncation of the Floquet–Magnus expansion is rigorously established. •New mechanism of the prethermalization is proposed. •Revealing an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed.« less

Weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1991-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

The use of an analytic Hamiltonian matrix for solving the hydrogenic atom

NASA Astrophysics Data System (ADS)

Bhatti, Mohammad

2001-10-01

The non-relativistic Hamiltonian corresponding to the Shrodinger equation is converted into analytic Hamiltonian matrix using the kth order B-splines functions. The Galerkin method is applied to the solution of the Shrodinger equation for bound states of hydrogen-like systems. The program Mathematica is used to create analytic matrix elements and exact integration is performed over the knot-sequence of B-splines and the resulting generalized eigenvalue problem is solved on a specified numerical grid. The complete basis set and the energy spectrum is obtained for the coulomb potential for hydrogenic systems with Z less than 100 with B-splines of order eight. Another application is given to test the Thomas-Reiche-Kuhn sum rule for the hydrogenic systems.

A Few Discrete Lattice Systems and Their Hamiltonian Structures, Conservation Laws

NASA Astrophysics Data System (ADS)

Guo, Xiu-Rong; Zhang, Yu-Feng; Zhang, Xiang-Zhi; Yue, Rong

2017-04-01

With the help of three shift operators and r-matrix theory, a few discrete lattice systems are obtained which can be reduced to the well-known Toda lattice equation with a constraint whose Hamiltonian structures are generated by Poisson tensors of some induced Lie-Poisson bracket. The recursion operators of these lattice systems are constructed starting from Lax representations. Finally, reducing the given shift operators to get a simpler one and its expanding shift operators, we produce a lattice system with three vector fields whose recursion operator is given. Furthermore, we reduce the lattice system with three vector fields to get a lattice system whose Lax pair and conservation laws are obtained, respectively. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province Hosted by China University of Mining and Technology (2014), the the Key Discipline Construction by China University of Mining and Technology under Grant No. XZD201602, the Shandong Provincial Natural Science Foundation, China under Grant Nos. ZR2016AM31, ZR2016AQ19, ZR2015EM042, the Development of Science and Technology Plan Projects of TaiAn City under Grant No. 2015NS1048, National Social Science Foundation of China under Grant No. 13BJY026, and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58

Does finite-temperature decoding deliver better optima for noisy Hamiltonians?

NASA Astrophysics Data System (ADS)

Ochoa, Andrew J.; Nishimura, Kohji; Nishimori, Hidetoshi; Katzgraber, Helmut G.

The minimization of an Ising spin-glass Hamiltonian is an NP-hard problem. Because many problems across disciplines can be mapped onto this class of Hamiltonian, novel efficient computing techniques are highly sought after. The recent development of quantum annealing machines promises to minimize these difficult problems more efficiently. However, the inherent noise found in these analog devices makes the minimization procedure difficult. While the machine might be working correctly, it might be minimizing a different Hamiltonian due to the inherent noise. This means that, in general, the ground-state configuration that correctly minimizes a noisy Hamiltonian might not minimize the noise-less Hamiltonian. Inspired by rigorous results that the energy of the noise-less ground-state configuration is equal to the expectation value of the energy of the noisy Hamiltonian at the (nonzero) Nishimori temperature [J. Phys. Soc. Jpn., 62, 40132930 (1993)], we numerically study the decoding probability of the original noise-less ground state with noisy Hamiltonians in two space dimensions, as well as the D-Wave Inc. Chimera topology. Our results suggest that thermal fluctuations might be beneficial during the optimization process in analog quantum annealing machines.

Nonlinear Slewing Spacecraft Control Based on Exergy, Power Flow, and Static and Dynamic Stability

NASA Astrophysics Data System (ADS)

Robinett, Rush D.; Wilson, David G.

2009-10-01

This paper presents a new nonlinear control methodology for slewing spacecraft, which provides both necessary and sufficient conditions for stability by identifying the stability boundaries, rigid body modes, and limit cycles. Conservative Hamiltonian system concepts, which are equivalent to static stability of airplanes, are used to find and deal with the static stability boundaries: rigid body modes. The application of exergy and entropy thermodynamic concepts to the work-rate principle provides a natural partitioning through the second law of thermodynamics of power flows into exergy generator, dissipator, and storage for Hamiltonian systems that is employed to find the dynamic stability boundaries: limit cycles. This partitioning process enables the control system designer to directly evaluate and enhance the stability and performance of the system by balancing the power flowing into versus the power dissipated within the system subject to the Hamiltonian surface (power storage). Relationships are developed between exergy, power flow, static and dynamic stability, and Lyapunov analysis. The methodology is demonstrated with two illustrative examples: (1) a nonlinear oscillator with sinusoidal damping and (2) a multi-input-multi-output three-axis slewing spacecraft that employs proportional-integral-derivative tracking control with numerical simulation results.

Experimental Observation of Classical Dynamical Monodromy

NASA Astrophysics Data System (ADS)

Nerem, M. P.; Salmon, D.; Aubin, S.; Delos, J. B.

2018-03-01

A Hamiltonian system is said to have nontrivial monodromy if its fundamental action-angle loops do not return to their initial topological state at the end of a closed circuit in angular momentum-energy space. This process has been predicted to have consequences which can be seen in dynamical systems, called dynamical monodromy. Using an apparatus consisting of a spherical pendulum subject to magnetic potentials and torques, we observe nontrivial monodromy by the associated topological change in the evolution of a loop of trajectories.

The dynamics of the de Sitter resonance

NASA Astrophysics Data System (ADS)

Celletti, Alessandra; Paita, Fabrizio; Pucacco, Giuseppe

2018-02-01

We study the dynamics of the de Sitter resonance, namely the stable equilibrium configuration of the first three Galilean satellites. We clarify the relation between this family of configurations and the more general Laplace resonant states. In order to describe the dynamics around the de Sitter stable equilibrium, a one-degree-of-freedom Hamiltonian normal form is constructed and exploited to identify initial conditions leading to the two families. The normal form Hamiltonian is used to check the accuracy in the location of the equilibrium positions. Besides, it gives a measure of how sensitive it is with respect to the different perturbations acting on the system. By looking at the phase plane of the normal form, we can identify a Laplace-like configuration, which highlights many substantial aspects of the observed one.

A Hamilton-Jacobi theory for implicit differential systems

NASA Astrophysics Data System (ADS)

Esen, Oǧul; de León, Manuel; Sardón, Cristina

2018-02-01

In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of TT*Q generated by Morse families. The implicit character implies the nonexistence of a Hamiltonian function describing the dynamics. This fact is here amended by a generating family of Morse functions which plays the role of a Hamiltonian. A Hamilton-Jacobi equation is obtained with the aid of this generating family of functions. To conclude, we apply our results to singular Lagrangians by employing the construction of special symplectic structures.

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

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

Baskan, O.; Clercx, H. J. H; Speetjens, M. F. M.

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progressionmore » by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.« less

Local modular Hamiltonians from the quantum null energy condition

NASA Astrophysics Data System (ADS)

Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin

2018-03-01

The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .

Hamiltonian surface charges using external sources

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

Troessaert, Cédric, E-mail: troessaert@cecs.cl

2016-05-15

In this work, we interpret part of the boundary conditions as external sources in order to partially solve the integrability problem present in the computation of surface charges associated to gauge symmetries in the hamiltonian formalism. We start by describing the hamiltonian structure of external symmetries preserving the action up to a transformation of the external sources of the theory. We then extend these results to the computation of surface charges for field theories with non-trivial boundary conditions.

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

NASA Astrophysics Data System (ADS)

Fring, Andreas; Jones, Hugh; Znojil, Miloslav

2008-06-01

Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong interactions at high energies via Regge models, in condensed matter physics in the context of the XXZ-spin chain, in interacting boson models in nuclear physics, in integrable quantum field theories as Toda field theories with complex coupling constants, and also very recently in a field theoretical scenario in the quantization procedure of strings on an AdS5 x S5 background. Concrete experimental realizations of these types of systems in the form of optical lattices have been proposed in 2007. In the area of mathematical physics similar non-systematic results appeared sporadically over the years. However, intensive and more systematic investigation of these types of non- Hermitian Hamiltonians with real eigenvalue spectra only began about ten years ago, when the surprising discovery was made that a large class of one-particle systems perturbed by a simple non-Hermitian potential term possesses a real energy spectrum. Since then regular international workshops devoted to this theme have taken place. This special issue is centred around the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics held in July 2007 at City University London. All the contributions contain significant new results or alternatively provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants were also invited. Meanwhile many interesting results have been obtained and consensus has been reached on various central conceptual issues in the

Scattering matrix of arbitrary tight-binding Hamiltonians

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

Ramírez, C., E-mail: carlos@ciencias.unam.mx; Medina-Amayo, L.A.

2017-03-15

A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.

Hamiltonian structure of Dubrovin{close_quote}s equation of associativity in 2-d topological field theory

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

Galvao, C.A.; Nutku, Y.

1996-12-01

mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}

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

NASA Astrophysics Data System (ADS)

Falaize, Antoine; Hélie, Thomas

2017-03-01

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

Quantum Hamiltonian identification from measurement time traces.

PubMed

Zhang, Jun; Sarovar, Mohan

2014-08-22

Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.

Quasi-hamiltonian quotients as disjoint unions of symplectic manifolds

NASA Astrophysics Data System (ADS)

Schaffhauser, Florent

2007-08-01

The main result of this paper is Theorem 2.12 which says that the quotient μ-1({1})/U associated to a quasi-hamiltonian space (M, ω, μ: M → U) has a symplectic structure even when 1 is not a regular value of the momentum map μ. Namely, it is a disjoint union of symplectic manifolds of possibly different dimensions, which generalizes the result of Alekseev, Malkin and Meinrenken in [AMM98]. We illustrate this theorem with the example of representation spaces of surface groups. As an intermediary step, we give a new class of examples of quasi-hamiltonian spaces: the isotropy submanifold MK whose points are the points of M with isotropy group K ⊂ U. The notion of quasi-hamiltonian space was introduced by Alekseev, Malkin and Meinrenken in their paper [AMM98]. The main motivation for it was the existence, under some regularity assumptions, of a symplectic structure on the associated quasi-hamiltonian quotient. Throughout their paper, the analogy with usual hamiltonian spaces is often used as a guiding principle, replacing Lie-algebra-valued momentum maps with Lie-group-valued momentum maps. In the hamiltonian setting, when the usual regularity assumptions on the group action or the momentum map are dropped, Lerman and Sjamaar showed in [LS91] that the quotient associated to a hamiltonian space carries a stratified symplectic structure. In particular, this quotient space is a disjoint union of symplectic manifolds. In this paper, we prove an analogous result for quasi-hamiltonian quotients. More precisely, we show that for any quasi-hamiltonian space (M, ω, μ: M → U), the associated quotient M//U := μ-1({1})/U is a disjoint union of symplectic manifolds (Theorem 2.12): [ mu^{-1}(\\{1\\})/U = bigsqcup_{jin J} (mu^{-1}(\\{1\\})\\cap M_{K_j})/L_{K_j} . ] Here Kj denotes a closed subgroup of U and MKj denotes the isotropy submanifold of type Kj: MKj = {x ∈ M | Ux = Kj}. Finally, LKj is the quotient group LKj = { N

A quantum-classical theory with nonlinear and stochastic dynamics

NASA Astrophysics Data System (ADS)

Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

2014-12-01

The method of constrained dynamical systems on the quantum-classical phase space is utilized to develop a theory of quantum-classical hybrid systems. Effects of the classical degrees of freedom on the quantum part are modeled using an appropriate constraint, and the interaction also includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement.

Five-dimensional collective Hamiltonian with the Gogny force: An ongoing saga

NASA Astrophysics Data System (ADS)

Libert, J.; Delaroche, J.-P.; Girod, M.

2016-07-01

We provide a sample of analyses for nuclear spectroscopic properties based on the five-dimensional collective Hamiltonian (5DCH) implemented with the Gogny force. The very first illustration is dating back to the late 70's. It is next followed by others, focusing on shape coexistence, shape isomerism, superdeformation, and systematics over the periodic table. Finally, the inclusion of Thouless-Valatin dynamical contributions to vibrational mass parameters is briefly discussed as a mean of strengthening the basis of the 5DCH theory.

Intertwined Hamiltonians in two-dimensional curved spaces

NASA Astrophysics Data System (ADS)

Aghababaei Samani, Keivan; Zarei, Mina

2005-04-01

The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincaré half plane (AdS2), de Sitter plane (dS2), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle.

Poincaré-Treshchev Mechanism in Multi-scale, Nearly Integrable Hamiltonian Systems

NASA Astrophysics Data System (ADS)

Xu, Lu; Li, Yong; Yi, Yingfei

2018-02-01

This paper is a continuation to our work (Xu et al. in Ann Henri Poincaré 18(1):53-83, 2017) concerning the persistence of lower-dimensional tori on resonant surfaces of a multi-scale, nearly integrable Hamiltonian system. This type of systems, being properly degenerate, arise naturally in planar and spatial lunar problems of celestial mechanics for which the persistence problem ties closely to the stability of the systems. For such a system, under certain non-degenerate conditions of Rüssmann type, the majority persistence of non-resonant tori and the existence of a nearly full measure set of Poincaré non-degenerate, lower-dimensional, quasi-periodic invariant tori on a resonant surface corresponding to the highest order of scale is proved in Han et al. (Ann Henri Poincaré 10(8):1419-1436, 2010) and Xu et al. (2017), respectively. In this work, we consider a resonant surface corresponding to any intermediate order of scale and show the existence of a nearly full measure set of Poincaré non-degenerate, lower-dimensional, quasi-periodic invariant tori on the resonant surface. The proof is based on a normal form reduction which consists of a finite step of KAM iterations in pushing the non-integrable perturbation to a sufficiently high order and the splitting of resonant tori on the resonant surface according to the Poincaré-Treshchev mechanism.

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

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

Ghosh, Soumen; Andersen, Amity; Gagliardi, Laura

2017-08-16

We present an implementation of a time-dependent semiempirical method (INDO/S) in NWChem using real-time (RT) propagation to address, in principle, the entire spectrum of valence electronic excitations. Adopting this model, we study the UV-visible spectra of medium-sized systems like P3B2, f-coronene, and in addition much larger systems like ubiquitin in the gas phase and the betanin chromophore in the presence of two explicit solvents (water and methanol). RT-INDO/S provides qualitatively and indeed often quantitatively accurate results when compared with RT- TDDFT or experimental spectra. While demonstrated here for INDO/S in particular, our implementation provides a framework for performing electron dynamicsmore » in large systems using semiempirical Hartree-Fock (HF) Hamiltonians in general.« less

Quantum dynamics intervened by repeated nonselective measurements

NASA Astrophysics Data System (ADS)

Filippov, Sergey N.

We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time-independent and time-dependent Hamiltonian dynamics between the measurements and find the approximate master equation in the stroboscopic limit. We also consider a situation, in which the measurement basis changes in time, and illustrate it by nonselective measurements in the basis of diabatic states of the Landau-Zener model.

NLO renormalization in the Hamiltonian truncation

NASA Astrophysics Data System (ADS)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-09-01

Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

Quantum dynamical simulation of photoinduced electron transfer processes in dye-semiconductor systems: theory and application to coumarin 343 at TiO₂.

PubMed

Li, Jingrui; Kondov, Ivan; Wang, Haobin; Thoss, Michael

2015-04-10

A recently developed methodology to simulate photoinduced electron transfer processes at dye-semiconductor interfaces is outlined. The methodology employs a first-principles-based model Hamiltonian and accurate quantum dynamics simulations using the multilayer multiconfiguration time-dependent Hartree approach. This method is applied to study electron injection in the dye-semiconductor system coumarin 343-TiO2. Specifically, the influence of electronic-vibrational coupling is analyzed. Extending previous work, we consider the influence of Dushinsky rotation of the normal modes as well as anharmonicities of the potential energy surfaces on the electron transfer dynamics.

An algorithm for finding a similar subgraph of all Hamiltonian cycles

NASA Astrophysics Data System (ADS)

Wafdan, R.; Ihsan, M.; Suhaimi, D.

2018-01-01

This paper discusses an algorithm to find a similar subgraph called findSimSubG algorithm. A similar subgraph is a subgraph with a maximum number of edges, contains no isolated vertex and is contained in every Hamiltonian cycle of a Hamiltonian Graph. The algorithm runs only on Hamiltonian graphs with at least two Hamiltonian cycles. The algorithm works by examining whether the initial subgraph of the first Hamiltonian cycle is a subgraph of comparison graphs. If the initial subgraph is not in comparison graphs, the algorithm will remove edges and vertices of the initial subgraph that are not in comparison graphs. There are two main processes in the algorithm, changing Hamiltonian cycle into a cycle graph and removing edges and vertices of the initial subgraph that are not in comparison graphs. The findSimSubG algorithm can find the similar subgraph without using backtracking method. The similar subgraph cannot be found on certain graphs, such as an n-antiprism graph, complete bipartite graph, complete graph, 2n-crossed prism graph, n-crown graph, n-möbius ladder, prism graph, and wheel graph. The complexity of this algorithm is O(m|V|), where m is the number of Hamiltonian cycles and |V| is the number of vertices of a Hamiltonian graph.

Spatial Dynamics Methods for Solitary Waves on a Ferrofluid Jet

NASA Astrophysics Data System (ADS)

Groves, M. D.; Nilsson, D. V.

2018-04-01

This paper presents existence theories for several families of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet surrounding a stationary metal rod. The ferrofluid, which is governed by a general (nonlinear) magnetisation law, is subject to an azimuthal magnetic field generated by an electric current flowing along the rod. The ferrohydrodynamic problem for axisymmetric travelling waves is formulated as an infinite-dimensional Hamiltonian system in which the axial direction is the time-like variable. A centre-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite number of degrees of freedom, and homoclinic solutions to the reduced system, which correspond to solitary waves, are detected by dynamical-systems methods.

Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method.

PubMed

Yao, Yao; Sun, Ke-Wei; Luo, Zhen; Ma, Haibo

2018-01-18

The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.

A weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1989-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

A weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1990-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Dynamical generation of noiseless quantum subsystems

PubMed

Viola; Knill; Lloyd

2000-10-16

We combine dynamical decoupling and universal control methods for open quantum systems with coding procedures. By exploiting a general algebraic approach, we show how appropriate encodings of quantum states result in obtaining universal control over dynamically generated noise-protected subsystems with limited control resources. In particular, we provide a constructive scheme based on two-body Hamiltonians for performing universal quantum computation over large noiseless spaces which can be engineered in the presence of arbitrary linear quantum noise.

Boson Hamiltonians and stochasticity for the vorticity equation

NASA Technical Reports Server (NTRS)

Shen, Hubert H.

1990-01-01

The evolution of the vorticity in time for two-dimensional inviscid flow and in Lagrangian time for three-dimensional viscous flow is written in Hamiltonian form by introducing Bose operators. The addition of the viscous and convective terms, respectively, leads to an interpretation of the Hamiltonian contribution to the evolution as Langevin noise.

Scaling with System Size of the Lyapunov Exponents for the Hamiltonian Mean Field Model

NASA Astrophysics Data System (ADS)

Manos, Thanos; Ruffo, Stefano

2011-12-01

The Hamiltonian Mean Field model is a prototype for systems with long-range interactions. It describes the motion of N particles moving on a ring, coupled with an infinite-range potential. The model has a second-order phase transition at the energy density Uc =3/4 and its dynamics is exactly described by the Vlasov equation in the N→∞ limit. Its chaotic properties have been investigated in the past, but the determination of the scaling with N of the Lyapunov Spectrum (LS) of the model remains a challenging open problem. Here we show that the N -1/3 scaling of the Maximal Lyapunov Exponent (MLE), found in previous numerical and analytical studies, extends to the full LS; scaling is "precocious" for the LS, meaning that it becomes manifest for a much smaller number of particles than the one needed to check the scaling for the MLE. Besides that, the N -1/3 scaling appears to be valid not only for U>Uc , as suggested by theoretical approaches based on a random matrix approximation, but also below a threshold energy Ut ≈0.2. Using a recently proposed method (GALI) devised to rapidly check the chaotic or regular nature of an orbit, we find that Ut is also the energy at which a sharp transition from weak to strong chaos is present in the phase-space of the model. Around this energy the phase of the vector order parameter of the model becomes strongly time dependent, inducing a significant untrapping of particles from a nonlinear resonance.

Nonunitary quantum computation in the ground space of local Hamiltonians

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Non-Hermitian Operator Modelling of Basic Cancer Cell Dynamics

NASA Astrophysics Data System (ADS)

Bagarello, Fabio; Gargano, Francesco

2018-04-01

We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth.

Gravitational Field as a Pressure Force from Logarithmic Lagrangians and Non-Standard Hamiltonians: The Case of Stellar Halo of Milky Way

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2018-03-01

Recently, the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations. Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties. One interesting form related to the inverse variational problem is the logarithmic Lagrangian, which has a number of motivating features related to the Liénard-type and Emden nonlinear differential equations. Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians. In this communication, we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians. One interesting consequence concerns the emergence of an extra pressure term, which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field. The case of the stellar halo of the Milky Way is considered.

Hamiltonian thermodynamics of three-dimensional dilatonic black holes

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

Dias, Goncalo A. S.; Lemos, Jose P. S.

2008-08-15

The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free {omega} parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcationmore » 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates (M,P{sub M}), M being the mass parameter and P{sub M} its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.« less

Formalism for the solution of quadratic Hamiltonians with large cosine terms

NASA Astrophysics Data System (ADS)

Ganeshan, Sriram; Levin, Michael

2016-02-01

We consider quantum Hamiltonians of the form H =H0-U ∑jcos(Cj) , where H0 is a quadratic function of position and momentum variables {x1,p1,x2,p2,⋯} and the Cj's are linear in these variables. We allow H0 and Cj to be completely general with only two restrictions: we require that (1) the Cj's are linearly independent and (2) [Cj,Ck] is an integer multiple of 2 π i for all j ,k so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low-energy spectrum in the limit U →∞ . This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite U limit, we also discuss how to analyze these systems when U is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

Non-equilibrium many-body dynamics following a quantum quench

NASA Astrophysics Data System (ADS)

Vyas, Manan

2017-12-01

We study analytically and numerically the non-equilibrium dynamics of an isolated interacting many-body quantum system following a random quench. We model the system Hamiltonian by Embedded Gaussian Orthogonal Ensemble (EGOE) of random matrices with one plus few-body interactions for fermions. EGOE are paradigmatic models to study the crossover from integrability to chaos in interacting many-body quantum systems. We obtain a generic formulation, based on spectral variances, for describing relaxation dynamics of survival probabilities as a function of rank of interactions. Our analytical results are in good agreement with numerics.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Bounds on Energy Absorption and Prethermalization in Quantum Systems with Long-Range Interactions

NASA Astrophysics Data System (ADS)

Ho, Wen Wei; Protopopov, Ivan; Abanin, Dmitry A.

2018-05-01

Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general rigorous bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as 1 /rα with α >d /2 . We show that the disorder averaged energy absorption rate at high temperatures decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of heating and new dynamical regimes described by effective Hamiltonians in such long-range systems.

Dynamics and control of three-body tethered system in large elliptic orbits

NASA Astrophysics Data System (ADS)

Shi, Gefei; Zhu, Zhanxia; Zhu, Zheng H.

2018-03-01

This paper investigates the dynamic characteristics a three-body tethered satellite system in large elliptic orbits and the control strategy to suppress the libration of the system in orbital transfer process. The system is modeled by a two-piece dumbbell model in the domain of true anomaly. The model consists of one main satellite and two subsatellites connected with two straight, massless and inextensible tethers. Two control strategies based on the sliding mode control are developed to control the libration to the zero state and the steady state respectively. The results of numerical simulations show that the proposed control scheme has good performance in controlling the libration motion of a three-body tethered satellite system in an elliptic orbit with large eccentricity by limited control inputs. Furthermore, Hamiltonians in both states are examined and it shows that less control input is required to control the libration motion to the steady state than that of zero state.

Exact solution for the quench dynamics of a nested integrable system

NASA Astrophysics Data System (ADS)

Mestyán, Márton; Bertini, Bruno; Piroli, Lorenzo; Calabrese, Pasquale

2017-08-01

Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has focussed on models with an elementary (i.e. not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the quench action approach. Specifically, we consider the spin-1 Lai-Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.

Accurate and general treatment of electrostatic interaction in Hamiltonian adaptive resolution simulations

NASA Astrophysics Data System (ADS)

Heidari, M.; Cortes-Huerto, R.; Donadio, D.; Potestio, R.

2016-10-01

In adaptive resolution simulations the same system is concurrently modeled with different resolution in different subdomains of the simulation box, thereby enabling an accurate description in a small but relevant region, while the rest is treated with a computationally parsimonious model. In this framework, electrostatic interaction, whose accurate treatment is a crucial aspect in the realistic modeling of soft matter and biological systems, represents a particularly acute problem due to the intrinsic long-range nature of Coulomb potential. In the present work we propose and validate the usage of a short-range modification of Coulomb potential, the Damped shifted force (DSF) model, in the context of the Hamiltonian adaptive resolution simulation (H-AdResS) scheme. This approach, which is here validated on bulk water, ensures a reliable reproduction of the structural and dynamical properties of the liquid, and enables a seamless embedding in the H-AdResS framework. The resulting dual-resolution setup is implemented in the LAMMPS simulation package, and its customized version employed in the present work is made publicly available.

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Mapping repulsive to attractive interaction in driven-dissipative quantum systems

NASA Astrophysics Data System (ADS)

Li, Andy C. Y.; Koch, Jens

2017-11-01

Repulsive and attractive interactions usually lead to very different physics. Striking exceptions exist in the dynamics of driven-dissipative quantum systems. For the example of a photonic Bose-Hubbard dimer, we establish a one-to-one mapping relating cases of onsite repulsion and attraction. We prove that the mapping is valid for an entire class of Markovian open quantum systems with a time-reversal-invariant Hamiltonian and physically meaningful inverse-sign Hamiltonian. To underline the broad applicability of the mapping, we illustrate the one-to-one correspondence between the nonequilibrium dynamics in a geometrically frustrated spin lattice and those in a non-frustrated partner lattice.

What is a completely integrable nonholonomic dynamical system?

NASA Astrophysics Data System (ADS)

Bates, Larry; Cushman, Richard

1999-10-01

We compare the geometry of a toral fibration defined by the common level sets of the integrals of a Liouville integrable Hamiltonian system with a toral fibration coming from a completely integrable nonholonomic system. We illustrate their differences using the following examples: the nonholonomic oscillator, Chaplygin's skate, Routh's sphere and the rolling oblate ellipsoid of revolution.

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

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

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

2003-08-01

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

New quantum number for the many-electron Dirac-Coulomb Hamiltonian

NASA Astrophysics Data System (ADS)

Komorovsky, Stanislav; Repisky, Michal; Bučinský, Lukáš

2016-11-01

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator K+, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator K , the K+2 has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that K+ is connected to K through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call K+ the generator of the many-electron TR symmetry. By diagonalizing the operator K+2 in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with K+2 has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree-Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.

Hydrodynamically induced oscillations and traffic dynamics in 1D microfludic networks

NASA Astrophysics Data System (ADS)

Bartolo, Denis; Jeanneret, Raphael

2011-03-01

We report on the traffic dynamics of particles driven through a minimal microfluidic network. Even in the minimal network consisting in a single loop, the traffic dynamics has proven to yield complex temporal patterns, including periodic, multi-periodic or chaotic sequences. This complex dynamics arises from the strongly nonlinear hydrodynamic interactions between the particles, that takes place at a junction. To better understand the consequences of this nontrivial coupling, we combined theoretical, numerical and experimental efforts and solved the 3-body problem in a 1D loop network. This apparently simple dynamical system revealed a rich and unexpected dynamics, including coherent spontaneous oscillations along closed orbits. Striking similarities between Hamiltonian systems and this driven dissipative system will be explained.

Lie-algebraic Approach to Dynamics of Closed Quantum Systems and Quantum-to-Classical Correspondence

NASA Astrophysics Data System (ADS)

Galitski, Victor

2012-02-01

I will briefly review our recent work on a Lie-algebraic approach to various non-equilibrium quantum-mechanical problems, which has been motivated by continuous experimental advances in the field of cold atoms. First, I will discuss non-equilibrium driven dynamics of a generic closed quantum system. It will be emphasized that mathematically a non-equilibrium Hamiltonian represents a trajectory in a Lie algebra, while the evolution operator is a trajectory in a Lie group generated by the underlying algebra via exponentiation. This turns out to be a constructive statement that establishes, in particular, the fact that classical and quantum unitary evolutions are two sides of the same coin determined uniquely by the same dynamic generators in the group. An equation for these generators - dubbed dual Schr"odinger-Bloch equation - will be derived and analyzed for a few of specific examples. This non-linear equation allows one to construct new exact non-linear solutions to quantum-dynamical systems. An experimentally-relevant example of a family of exact solutions to the many-body Landau-Zener problem will be presented. One practical application of the latter result includes dynamical means to optimize molecular production rate following a quench across the Feshbach resonance.

Spin Hamiltonian Analysis of the SMM V15 Using High Field ESR

NASA Astrophysics Data System (ADS)

Martens, Mathew; van Tol, Hans; Bertaina, Sylvain; Barbara, Bernard; Muller, Achim; Chiorescu, Irinel

2014-03-01

We have studied molecular magnets using high field / high frequency Electron Spin Resonance. Such molecular structures contain many quantum spins linked by exchange interactions and consequently their energy structure is often complex and require a good understanding of the molecular spin Hamiltonian. In particular, we studied the V15 molecule, comprised of 15 spins 1/2 and a total spin 1/2, which is a system that recently showed quantum Rabi oscillations of its total quantum spin. This type of molecule is an essential system for advancing molecular structures into quantum computing. We used high frequency characterization techniques (of hundreds of GHz) to gain insight into the exchange anisotropy interactions, crystal field, and anti-symmetric interactions present in this system. We analyzed the data using a detailed numerical analysis of spin interactions and our findings regarding the V15 spin Hamiltonian will be discussed. Supported by the NSF Cooperative Agreement Grant No. DMR-0654118 and No. NHMFL UCGP 5059, NSF grant No. DMR-0645408.

Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties

NASA Astrophysics Data System (ADS)

Karp, Jonathan; Torres-Herrera, Jonathan; TáVora, Marco; Santos, Lea

We study the static and dynamical properties of isolated spin 1/2 systems as prototypes of many-body quantum systems and compare the results to those of full random matrices from a Gaussian orthogonal ensemble. Full random matrices do not represent realistic systems, because they imply that all particles interact at the same time, as opposed to realistic Hamiltonians, which are sparse and have only few-body interactions. Nevertheless, with full random matrices we can derive analytical results that can be used as references and bounds for the corresponding properties of realistic systems. In particular, we show that the results for the Shannon information entropy are very similar to those for the von Neumann entanglement entropy, with the former being computationally less expensive. We also discuss the behavior of the survival probability of the initial state at different time scales and show that it contains more information about the system than the entropies. Support from the NSF Grant No. DMR-1147430.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

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

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

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

Sequential Feedback Scheme Outperforms the Parallel Scheme for Hamiltonian Parameter Estimation.

PubMed

Yuan, Haidong

2016-10-14

Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find the highest achievable precision with the given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in the quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter, we show that the sequential feedback scheme has a threefold improvement over the parallel scheme for Hamiltonian parameter estimations on two-dimensional systems, and an order of O(d+1) improvement for Hamiltonian parameter estimation on d-dimensional systems. We also show that, contrary to the conventional belief, it is possible to simultaneously achieve the highest precision for estimating all three components of a magnetic field, which sets a benchmark on the local precision limit for the estimation of a magnetic field.

Relational time in anyonic systems

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation.

PubMed

Ilias, Miroslav; Saue, Trond

2007-02-14

The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.

Applications of the trilinear Hamiltonian with three trapped ions

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Isochronous extension of the Hamiltonian describing free motion in the Poincaré half-plane: Classical and quantum treatments

NASA Astrophysics Data System (ADS)

Calogero, F. A.; Leyvraz, F.

2007-09-01

We modify (in two different manners) the Hamiltonian describing motions in the Poincaré half-plane so that the modified Hamiltonians thereby obtained are entirely isochronous: indeed, in the classical context, all the motions they entail are periodic with the same period. We then investigate suitably quantized versions of these systems and show that their spectra are equispaced.

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

NASA Astrophysics Data System (ADS)

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

2015-01-01

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

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

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

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

2015-03-28

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

Dynamics of Large Systems of Nonlinearly Evolving Units

NASA Astrophysics Data System (ADS)

Lu, Zhixin

The dynamics of large systems of many nonlinearly evolving units is a general research area that has great importance for many areas in science and technology, including biology, computation by artificial neural networks, statistical mechanics, flocking in animal groups, the dynamics of coupled neurons in the brain, and many others. While universal principles and techniques are largely lacking in this broad area of research, there is still one particular phenomenon that seems to be broadly applicable. In particular, this is the idea of emergence, by which is meant macroscopic behaviors that "emerge" from a large system of many "smaller or simpler entities such that...large entities" [i.e., macroscopic behaviors] arise which "exhibit properties the smaller/simpler entities do not exhibit." In this thesis we investigate mechanisms and manifestations of emergence in four dynamical systems consisting many nonlinearly evolving units. These four systems are as follows. (a) We first study the motion of a large ensemble of many noninteracting particles in a slowly changing Hamiltonian system that undergoes a separatrix crossing. In such systems, we find that separatrix-crossing induces a counterintuitive effect. Specifically, numerical simulation of two sets of densely sprinkled initial conditions on two energy curves appears to suggest that the two energy curves, one originally enclosing the other, seemingly interchange their positions. This, however, is topologically forbidden. We resolve this paradox by introducing a numerical simulation method we call "robust" and study its consequences. (b) We next study the collective dynamics of oscillatory pacemaker neurons in Suprachiasmatic Nucleus (SCN), which, through synchrony, govern the circadian rhythm of mammals. We start from a high-dimensional description of the many coupled oscillatory neuronal units within the SCN. This description is based on a forced Kuramoto model. We then reduce the system dimensionality by using

Interacting quantum dot coupled to a kondo spin: a universal Hamiltonian study.

PubMed

Rotter, Stefan; Türeci, Hakan E; Alhassid, Y; Stone, A Douglas

2008-04-25

We study a Kondo spin coupled to a mesoscopic interacting quantum dot that is described by the "universal Hamiltonian." The problem is solved numerically by diagonalizing the system Hamiltonian in a good-spin basis and analytically in the weak and strong Kondo coupling limits. The ferromagnetic exchange interaction within the dot leads to a stepwise increase of the ground-state spin (Stoner staircase), which is modified nontrivially by the Kondo interaction. We find that the spin-transition steps move to lower values of the exchange coupling for weak Kondo interaction, but shift back up for sufficiently strong Kondo coupling. The interplay between Kondo and ferromagnetic exchange correlations can be probed with experimentally tunable parameters.

Bifurcation of Limit Cycles in a Near-Hamiltonian System with a Cusp of Order Two and a Saddle

NASA Astrophysics Data System (ADS)

Bakhshalizadeh, Ali; Zangeneh, Hamid R. Z.; Kazemi, Rasool

In this paper, the asymptotic expansion of first-order Melnikov function of a heteroclinic loop connecting a cusp of order two and a hyperbolic saddle for a planar near-Hamiltonian system is given. Next, we consider the limit cycle bifurcations of a hyper-elliptic Liénard system with this kind of heteroclinic loop and study the least upper bound of limit cycles bifurcated from the period annulus inside the heteroclinic loop, from the heteroclinic loop itself and the center. We find that at most three limit cycles can be bifurcated from the period annulus, also we present different distributions of bifurcated limit cycles.

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

NASA Astrophysics Data System (ADS)

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

2010-06-01

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

Hamiltonian indices and rational spectral densities

NASA Technical Reports Server (NTRS)

Byrnes, C. I.; Duncan, T. E.

1980-01-01

Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.

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

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

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

2015-09-15

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

Unifying perspective: Solitary traveling waves as discrete breathers in Hamiltonian lattices and energy criteria for their stability

NASA Astrophysics Data System (ADS)

Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna; Xu, Haitao

2017-09-01

In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H''(c0) evaluated at the critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.

Quantum Hamiltonian daemons: Unitary analogs of combustion engines

NASA Astrophysics Data System (ADS)

Thesing, Eike P.; Gilz, Lukas; Anglin, James R.

2017-07-01

Hamiltonian daemons have recently been defined classically as small, closed Hamiltonian systems which can exhibit secular energy transfer from high-frequency to low-frequency degrees of freedom (steady downconversion), analogous to the steady transfer of energy in a combustion engine from the high terahertz frequencies of molecular excitations to the low kilohertz frequencies of piston motion [L. Gilz, E. P. Thesing, and J. R. Anglin, Phys. Rev. E 94, 042127 (2016), 10.1103/PhysRevE.94.042127]. Classical daemons achieve downconversion within a small, closed system by exploiting nonlinear resonances; the adiabatic theorem permits their operation but imposes nontrivial limitations on their efficiency. Here we investigate a simple example of a quantum mechanical daemon. In the correspondence regime it obeys similar efficiency limits to its classical counterparts, but in the strongly quantum mechanical regime the daemon operates in an entirely different manner. It maintains an engine-like behavior in a distinctly quantum mechanical form: a weight is lifted at a steady average speed through a long sequence of quantum jumps in momentum, at each of which a quantum of fuel is consumed. The quantum daemon can cease downconversion at any time through nonadiabatic Landau-Zener transitions, and continuing operation of the quantum daemon is associated with steadily growing entanglement between fast and slow degrees of freedom.

Does a Single Eigenstate Encode the Full Hamiltonian?

NASA Astrophysics Data System (ADS)

Garrison, James R.; Grover, Tarun

2018-04-01

The eigenstate thermalization hypothesis (ETH) posits that the reduced density matrix for a subsystem corresponding to an excited eigenstate is "thermal." Here we expound on this hypothesis by asking: For which class of operators, local or nonlocal, is ETH satisfied? We show that this question is directly related to a seemingly unrelated question: Is the Hamiltonian of a system encoded within a single eigenstate? We formulate a strong form of ETH where, in the thermodynamic limit, the reduced density matrix of a subsystem corresponding to a pure, finite energy density eigenstate asymptotically becomes equal to the thermal reduced density matrix, as long as the subsystem size is much less than the total system size, irrespective of how large the subsystem is compared to any intrinsic length scale of the system. This allows one to access the properties of the underlying Hamiltonian at arbitrary energy densities (or temperatures) using just a single eigenstate. We provide support for our conjecture by performing an exact diagonalization study of a nonintegrable 1D quantum lattice model with only energy conservation. In addition, we examine the case in which the subsystem size is a finite fraction of the total system size, and we find that, even in this case, many operators continue to match their canonical expectation values, at least approximately. In particular, the von Neumann entanglement entropy equals the thermal entropy as long as the subsystem is less than half the total system. Our results are consistent with the possibility that a single eigenstate correctly predicts the expectation values of all operators with support on less than half the total system, as long as one uses a microcanonical ensemble with vanishing energy width for comparison. We also study, both analytically and numerically, a particle-number conserving model at infinite temperature that substantiates our conjectures.

A general formula for Rayleigh-Schroedinger perturbation energy utilizing a power series expansion of the quantum mechanical Hamiltonian

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

Herbert, J.M.

1997-02-01

Perturbation theory has long been utilized by quantum chemists as a method for approximating solutions to the Schroedinger equation. Perturbation treatments represent a system`s energy as a power series in which each additional term further corrects the total energy; it is therefore convenient to have an explicit formula for the nth-order energy correction term. If all perturbations are collected into a single Hamiltonian operator, such a closed-form expression for the nth-order energy correction is well known; however, use of a single perturbed Hamiltonian often leads to divergent energy series, while superior convergence behavior is obtained by expanding the perturbed Hamiltonianmore » in a power series. This report presents a closed-form expression for the nth-order energy correction obtained using Rayleigh-Schroedinger perturbation theory and a power series expansion of the Hamiltonian.« less

S-Lagrangian dynamics of many-body systems and behavior of social groups: Dominance and hierarchy formation

NASA Astrophysics Data System (ADS)

Sandler, U.

2017-11-01

In this paper, we extend our generalized Lagrangian dynamics (i.e., S-Lagrangian dynamics, which can be applied equally to physical and non-physical systems as per Sandler (2014)) to many-body systems. Unlike common Lagrangian dynamics, this is not a trivial task. For many-body systems with S-dependent Lagrangians, the Lagrangian and the corresponding Hamiltonian or energy become vector functions, conjugated momenta become second-order tensors, and the system inevitably develops a hierarchical structure, even if all bodies initially have similar status and Lagrangians. As an application of our theory, we consider dominance and hierarchy formation, which is present in almost all communities of living species. As a biological basis for this application, we assume that the primary motivation of a groups activity is to attempt to cope with stress arising as pressure from the environment and from intrinsic unmet needs of individuals. It has been shown that the S-Lagrangian approach to a group's evolution naturally leads to formation of linear or despotic dominance hierarchies, depending on differences between individuals in coping with stress. That is, individuals that cope more readily with stress take leadership roles during the evolution. Experimental results in animal groups which support our assumption and findings are considered.

Nonequilibrium quantum dynamics and transport: from integrability to many-body localization

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Moore, Joel E.

2016-06-01

We review the non-equilibrium dynamics of many-body quantum systems after a quantum quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We focus on integrable and many-body localized systems that fail to self-thermalize in isolation and for which the standard hydrodynamical picture breaks down. The emphasis is on universal dynamics, non-equilibrium steady states and new dynamical phases of matter, and on phase transitions far from thermal equilibrium. We describe how the infinite number of conservation laws of integrable and many-body localized systems lead to complex non-equilibrium states beyond the traditional dogma of statistical mechanics.

A Keplerian-based Hamiltonian splitting for gravitational N-body simulations

NASA Astrophysics Data System (ADS)

Gonçalves Ferrari, G.; Boekholt, T.; Portegies Zwart, S. F.

2014-05-01

We developed a Keplerian-based Hamiltonian splitting for solving the gravitational N-body problem. This splitting allows us to approximate the solution of a general N-body problem by a composition of multiple, independently evolved two-body problems. While the Hamiltonian splitting is exact, we show that the composition of independent two-body problems results in a non-symplectic non-time-symmetric first-order map. A time-symmetric second-order map is then constructed by composing this basic first-order map with its self-adjoint. The resulting method is precise for each individual two-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with primordial binaries. The superposition of Kepler solutions for each pair of particles makes the method excellently suited for parallel computing; we achieve ≳64 per cent efficiency for only eight particles per core, but close to perfect scaling for 16 384 particles on a 128 core distributed-memory computer. We present several implementations in SAKURA, one of which is publicly available via the AMUSE framework.

Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

NASA Astrophysics Data System (ADS)

Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan

2018-02-01

Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

Lie algebraic similarity transformed Hamiltonians for lattice model systems

NASA Astrophysics Data System (ADS)

Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.

2015-01-01

We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.

Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity

NASA Astrophysics Data System (ADS)

Ruz, Soumendranath; Mandal, Ranajit; Debnath, Subhra; Sanyal, Abhik Kumar

2016-07-01

The Hamiltonian constraint H_c = N{H} = 0, defines a diffeomorphic structure on spatial manifolds by the lapse function N in general theory of relativity. However, it is not manifest in Lanczos-Lovelock gravity, since the expression for velocity in terms of the momentum is multivalued. Thus the Hamiltonian is a branch function of momentum. Here we propose an extended theory of Lanczos-Lovelock gravity to construct a unique Hamiltonian in its minisuperspace version, which results in manifest diffeomorphic invariance and canonical quantization.

Ab Initio Effective Rovibrational Hamiltonians for Non-Rigid Molecules via Curvilinear VMP2

NASA Astrophysics Data System (ADS)

Changala, Bryan; Baraban, Joshua H.

2017-06-01

Accurate predictions of spectroscopic constants for non-rigid molecules are particularly challenging for ab initio theory. For all but the smallest systems, ``brute force'' diagonalization of the full rovibrational Hamiltonian is computationally prohibitive, leaving us at the mercy of perturbative approaches. However, standard perturbative techniques, such as second order vibrational perturbation theory (VPT2), are based on the approximation that a molecule makes small amplitude vibrations about a well defined equilibrium structure. Such assumptions are physically inappropriate for non-rigid systems. In this talk, we will describe extensions to curvilinear vibrational Møller-Plesset perturbation theory (VMP2) that account for rotational and rovibrational effects in the molecular Hamiltonian. Through several examples, we will show that this approach provides predictions to nearly microwave accuracy of molecular constants including rotational and centrifugal distortion parameters, Coriolis coupling constants, and anharmonic vibrational and tunneling frequencies.

A Hamiltonian Model of Dissipative Wave-particle Interactions and the Negative-mass Effect

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

A. Zhmoginov

2011-02-07

The effect of radiation friction is included in the Hamiltonian treatment of wave-particle interactions with autoresonant phase-locking, yielding a generalized canonical approach to the problem of dissipative dynamics near a nonlinear resonance. As an example, the negativemass eff ect exhibited by a charged particle in a pump wave and a static magnetic field is studied in the presence of the friction force due to cyclotron radiation. Particles with negative parallel masses m! are shown to transfer their kinetic energy to the pump wave, thus amplifying it. Counterintuitively, such particles also undergo stable dynamics, decreasing their transverse energy monotonically due tomore » cyclotron cooling, whereas some of those with positive m! undergo cyclotron heating instead, extracting energy from the pump wave.« less

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1975-01-01

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

On the Hamiltonian formalism of the tetrad-gravity with fermions

NASA Astrophysics Data System (ADS)

Lagraa, M. H.; Lagraa, M.

2018-06-01

We extend the analysis of the Hamiltonian formalism of the d-dimensional tetrad-connection gravity to the fermionic field by fixing the non-dynamic part of the spatial connection to zero (Lagraa et al. in Class Quantum Gravity 34:115010, 2017). Although the reduced phase space is equipped with complicated Dirac brackets, the first-class constraints which generate the diffeomorphisms and the Lorentz transformations satisfy a closed algebra with structural constants analogous to that of the pure gravity. We also show the existence of a canonical transformation leading to a new reduced phase space equipped with Dirac brackets having a canonical form leading to the same algebra of the first-class constraints.

Flexible and experimentally feasible shortcut to quantum Zeno dynamic passage

NASA Astrophysics Data System (ADS)

Li, Wenlin; Zhang, Fengyang; Jiang, Yunfeng; Li, Chong; Song, Heshan

2016-10-01

We propose and discuss a theoretical scheme to speed up Zeno dynamic passage by an external acceleration Hamiltonian. This scheme is a flexible and experimentally feasible acceleration because the acceleration Hamiltonian does not adhere rigidly to an invariant relationship, whereas it can be a more general form ∑uj (t)Hcj. Here Hcj can be arbitrarily selected without any limitation, and therefore one can always construct an acceleration Hamiltonian by only using realizable Hcj. Applying our scheme, we finally design an experimentally feasible Hamiltonian as an example to speed up an entanglement preparation passage.

Multi-Lagrangians for integrable systems

NASA Astrophysics Data System (ADS)

Nutku, Y.; Pavlov, M. V.

2002-03-01

We propose a general scheme to construct multiple Lagrangians for completely integrable nonlinear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit N-fold first order local Hamiltonian structure can be cast into variational form with 2N-1 Lagrangians which will be local functionals of Clebsch potentials. This number increases to 3N-2 when the Miura transformation is invertible. Furthermore we construct a new Lagrangian for polytropic gas dynamics in 1+1 dimensions which is a free, local functional of the physical field variables, namely density and velocity, thus dispensing with the necessity of introducing Clebsch potentials entirely. This is a consequence of bi-Hamiltonian structure with a compatible pair of first and third order Hamiltonian operators derived from Sheftel's recursion operator.

Time and a physical Hamiltonian for quantum gravity.

PubMed

Husain, Viqar; Pawłowski, Tomasz

2012-04-06

We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society

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.

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

Relaxation dynamics of ultracold bosons in a double-well potential: Thermalization and prethermalization in a nearly integrable model

NASA Astrophysics Data System (ADS)

Cosme, Jayson G.

2015-09-01

We numerically investigate the relaxation dynamics in an isolated quantum system of interacting bosons trapped in a double-well potential after an integrability breaking quench. Using the statistics of the spectrum, we identify the postquench Hamiltonian as nonchaotic and close to integrability over a wide range of interaction parameters. We demonstrate that the system exhibits thermalization in the context of the eigenstate thermalization hypothesis (ETH). We also explore the possibility of an initial state to delocalize with respect to the eigenstates of the postquench Hamiltonian even for energies away from the middle of the spectrum. We observe distinct regimes of equilibration process depending on the initial energy. For low energies, the system rapidly relaxes in a single step to a thermal state. As the energy increases towards the middle of the spectrum, the relaxation dynamics exhibits prethermalization and the lifetime of the metastable states grows. Time evolution of the occupation numbers and the von Neumann entropy in the mode-partitioned system underpins the analyses of the relaxation dynamics.

The Lagrangian-Hamiltonian formalism for higher order field theories

NASA Astrophysics Data System (ADS)

Vitagliano, Luca

2010-06-01

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.

Effective Hamiltonian for protected edge states in graphene

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

Winkler, R.; Deshpande, H.

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

Effective Hamiltonian for protected edge states in graphene

DOE PAGES

Winkler, R.; Deshpande, H.

2017-06-15

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

Connections between the dynamical symmetries in the microscopic shell model

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

Georgieva, A. I., E-mail: anageorg@issp.bas.bg; Drumev, K. P.

2016-03-25

The dynamical symmetries of the microscopic shell model appear as the limiting cases of a symmetry adapted Pairing-Plus-Quadrupole Model /PQM/, with a Hamiltonian containing isoscalar and isovector pairing and quadrupole interactions. We establish a correspondence between each of the three types of pairing bases and Elliott’s SU(3) basis, that describes collective rotation of nuclear systems with quadrupole deformation. It is derived from their complementarity to the same LS coupling chain of the shell model number conserving algebra. The probability distribution of the S U(3) basis states within the pairing eigenstates is also obtained through a numerical diagonalization of the PQMmore » Hamiltonian in each limit. We introduce control parameters, which define the phase diagram of the model and determine the role of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.« less

Extended estimator approach for 2×2 games and its mapping to the Ising Hamiltonian

NASA Astrophysics Data System (ADS)

Ariosa, D.; Fort, H.

2005-01-01

We consider a system of adaptive self-interested agents interacting by playing an iterated pairwise prisoner’s dilemma (PD) game. Each player has two options: either cooperate (C) or defect (D). Agents have no (long term) memory to reciprocate nor identifying tags to distinguish C from D. We show how their 16 possible elementary Markovian (one-step memory) strategies can be cast in a simple general formalism in terms of an estimator of expected utilities Δ* . This formalism is helpful to map a subset of these strategies into an Ising Hamiltonian in a straightforward way. This connection in turn serves to shed light on the evolution of the iterated games played by agents, which can represent a broad variety of individuals from firms of a market to species coexisting in an ecosystem. Additionally, this magnetic description may be useful to introduce noise in a natural and simple way. The equilibrium states reached by the system depend strongly on whether the dynamics are synchronous or asynchronous and also on the system connectivity.

Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes

NASA Astrophysics Data System (ADS)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).

Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow

NASA Astrophysics Data System (ADS)

Kajigaya, Toru; Kunikawa, Keita

2018-06-01

In this paper, we generalize several results for the Hamiltonian stability and the mean curvature flow of Lagrangian submanifolds in a Kähler-Einstein manifold to more general Kähler manifolds including a Fano manifold equipped with a Kähler form ω ∈ 2 πc1(M) by using the method proposed by Behrndt (2011). Namely, we first consider a weighted measure on a Lagrangian submanifold L in a Kähler manifold M and investigate the variational problem of L for the weighted volume functional. We call a stationary point of the weighted volume functional f-minimal, and define the notion of Hamiltonian f-stability as a local minimizer under Hamiltonian deformations. We show such examples naturally appear in a toric Fano manifold. Moreover, we consider the generalized Lagrangian mean curvature flow in a Fano manifold which is introduced by Behrndt and Smoczyk-Wang. We generalize the result of H. Li, and show that if the initial Lagrangian submanifold is a small Hamiltonian deformation of an f-minimal and Hamiltonian f-stable Lagrangian submanifold, then the generalized MCF converges exponentially fast to an f-minimal Lagrangian submanifold.

Regime of validity of the pairing Hamiltonian in the study of Fermi gases

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

Chang, S. Y.; Pandharipande, V. R.

2006-06-01

The ground state energy and pairing gap of the interacting Fermi gases calculated by the ab initio stochastic method are compared with those estimated from the Bardeen-Cooper-Schrieffer pairing Hamiltonian. We discuss the ingredients of this Hamiltonian in various regimes of interaction strength. In the weakly interacting (1/ak{sub F}<<0) regime the BCS Hamiltonian should describe Landau quasiparticle energies and interactions, on the other hand, in the strongly pairing regime, that is, 1/ak{sub F} > or approx. 0, it becomes part of the bare Hamiltonian. However, the bare BCS Hamiltonian is not adequate for describing atomic gases in the regime of weakmore » to moderate interaction strength -{infinity}<1/ak{sub F}<0 such as ak{sub F}{approx}-1.« less

Hamiltonian methods: BRST, BFV

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

Garcia, J. Antonio

2006-09-25

The range of applicability of Hamiltonian methods to gauge theories is very diverse and cover areas of research from phenomenology to mathematical physics. We review some of the areas developed in Mexico in the last decades. They cover the study of symplectic methods, BRST-BFV and BV approaches, Klauder projector program, and non perturbative technics used in the study of bound states in relativistic field theories.

Hamiltonian methods: BRST, BFV

NASA Astrophysics Data System (ADS)

García, J. Antonio

2006-09-01

The range of applicability of Hamiltonian methods to gauge theories is very diverse and cover areas of research from phenomenology to mathematical physics. We review some of the areas developed in México in the last decades. They cover the study of symplectic methods, BRST-BFV and BV approaches, Klauder projector program, and non perturbative technics used in the study of bound states in relativistic field theories.

Decoherence dynamics of interacting qubits coupled to a bath of local optical phonons

NASA Astrophysics Data System (ADS)

Lone, Muzaffar Qadir; Yarlagadda, S.

2016-04-01

We study decoherence in an interacting qubit system described by infinite range Heisenberg model (IRHM) in a situation where the system is coupled to a bath of local optical phonons. Using perturbation theory in polaron frame of reference, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under nonadiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM upto leading orders of perturbation and thus has the same eigenstates as the IRHM. Using a quantum master equation with Markovian approximation of dynamical evolution, we show that the off-diagonal elements of the density matrix do not decay in the energy eigen basis of IRHM.

Connection between optimal control theory and adiabatic-passage techniques in quantum systems

NASA Astrophysics Data System (ADS)

Assémat, E.; Sugny, D.

2012-08-01

This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from Pontryagin's maximum principle. In a three-level quantum system, we show that the stimulated Raman adiabatic passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.

Wavepacket dynamics and the multi-configurational time-dependent Hartree approach

NASA Astrophysics Data System (ADS)

Manthe, Uwe

2017-06-01

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.

Parity-time symmetry breaking in magnetic systems

DOE PAGES

Galda, Alexey; Vinokur, Valerii M.

2016-07-14

The understanding of out-of-equilibrium physics, especially dynamic instabilities and dynamic phase transitions, is one of the major challenges of contemporary science, spanning the broadest wealth of research areas that range from quantum optics to living organisms. By focusing on nonequilibrium dynamics of an open dissipative spin system, we introduce a non-Hermitian Hamiltonian approach, in which non-Hermiticity reflects dissipation and deviation from equilibrium. The imaginary part of the proposed spin Hamiltonian describes the effects of Gilbert damping and applied Slonczewski spin-transfer torque. In the classical limit, our approach reproduces Landau-Lifshitz-Gilbert-Slonczewski dynamics of a large macrospin. Here, we reveal the spin-transfer torque-drivenmore » parity-time symmetry-breaking phase transition corresponding to a transition from precessional to exponentially damped spin dynamics. Micromagnetic simulations for nanoscale ferromagnetic disks demonstrate the predicted effect. These findings can pave the way to a general quantitative description of out-of-equilibrium phase transitions driven by spontaneous parity-time symmetry breaking.« less

Classical Affine W-Algebras and the Associated Integrable Hamiltonian Hierarchies for Classical Lie Algebras

NASA Astrophysics Data System (ADS)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2018-06-01

We prove that any classical affine W-algebra W (g, f), where g is a classical Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable Hamiltonian hierarchy of Lax type equations. This is based on the theories of generalized Adler type operators and of generalized quasideterminants, which we develop in the paper. Moreover, we show that under certain conditions, the product of two generalized Adler type operators is a Lax type operator. We use this fact to construct a large number of integrable Hamiltonian systems, recovering, as a special case, all KdV type hierarchies constructed by Drinfeld and Sokolov.

Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes

NASA Astrophysics Data System (ADS)

Marvian, Milad; Lidar, Daniel A.

2017-01-01

We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.

Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes.

PubMed

Marvian, Milad; Lidar, Daniel A

2017-01-20

We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.

Chaotic dynamics of Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions

NASA Astrophysics Data System (ADS)

Blessy, B. S. Gnana; Latha, M. M.

2017-10-01

We investigate the chaotic dynamics of one dimensional Heisenberg ferromagnetic spin chain by constructing the Hamiltonian equations of motion. We present the trajectory and phase plots of the system with bilinear and also biquadratic interactions. The stability of the system is analysed in both cases by constructing the Jacobian matrix and by measuring the Lyapunov exponents. The results are illustrated graphically.

Free Energy Perturbation Hamiltonian Replica-Exchange Molecular Dynamics (FEP/H-REMD) for Absolute Ligand Binding Free Energy Calculations.

PubMed

Jiang, Wei; Roux, Benoît

2010-07-01

Free Energy Perturbation with Replica Exchange Molecular Dynamics (FEP/REMD) offers a powerful strategy to improve the convergence of free energy computations. In particular, it has been shown previously that a FEP/REMD scheme allowing random moves within an extended replica ensemble of thermodynamic coupling parameters "lambda" can improve the statistical convergence in calculations of absolute binding free energy of ligands to proteins [J. Chem. Theory Comput. 2009, 5, 2583]. In the present study, FEP/REMD is extended and combined with an accelerated MD simulations method based on Hamiltonian replica-exchange MD (H-REMD) to overcome the additional problems arising from the existence of kinetically trapped conformations within the protein receptor. In the combined strategy, each system with a given thermodynamic coupling factor lambda in the extended ensemble is further coupled with a set of replicas evolving on a biased energy surface with boosting potentials used to accelerate the inter-conversion among different rotameric states of the side chains in the neighborhood of the binding site. Exchanges are allowed to occur alternatively along the axes corresponding to the thermodynamic coupling parameter lambda and the boosting potential, in an extended dual array of coupled lambda- and H-REMD simulations. The method is implemented on the basis of new extensions to the REPDSTR module of the biomolecular simulation program CHARMM. As an illustrative example, the absolute binding free energy of p-xylene to the nonpolar cavity of the L99A mutant of T4 lysozyme was calculated. The tests demonstrate that the dual lambda-REMD and H-REMD simulation scheme greatly accelerates the configurational sampling of the rotameric states of the side chains around the binding pocket, thereby improving the convergence of the FEP computations.

Enhanced conformational sampling using replica exchange with concurrent solute scaling and hamiltonian biasing realized in one dimension.

PubMed

Yang, Mingjun; Huang, Jing; MacKerell, Alexander D

2015-06-09

Replica exchange (REX) is a powerful computational tool for overcoming the quasi-ergodic sampling problem of complex molecular systems. Recently, several multidimensional extensions of this method have been developed to realize exchanges in both temperature and biasing potential space or the use of multiple biasing potentials to improve sampling efficiency. However, increased computational cost due to the multidimensionality of exchanges becomes challenging for use on complex systems under explicit solvent conditions. In this study, we develop a one-dimensional (1D) REX algorithm to concurrently combine the advantages of overall enhanced sampling from Hamiltonian solute scaling and the specific enhancement of collective variables using Hamiltonian biasing potentials. In the present Hamiltonian replica exchange method, termed HREST-BP, Hamiltonian solute scaling is applied to the solute subsystem, and its interactions with the environment to enhance overall conformational transitions and biasing potentials are added along selected collective variables associated with specific conformational transitions, thereby balancing the sampling of different hierarchical degrees of freedom. The two enhanced sampling approaches are implemented concurrently allowing for the use of a small number of replicas (e.g., 6 to 8) in 1D, thus greatly reducing the computational cost in complex system simulations. The present method is applied to conformational sampling of two nitrogen-linked glycans (N-glycans) found on the HIV gp120 envelope protein. Considering the general importance of the conformational sampling problem, HREST-BP represents an efficient procedure for the study of complex saccharides, and, more generally, the method is anticipated to be of general utility for the conformational sampling in a wide range of macromolecular systems.

Simple model for deriving sdg interacting boson model Hamiltonians: 150Nd example

NASA Astrophysics Data System (ADS)

Devi, Y. D.; Kota, V. K. B.

1993-07-01

A simple and yet useful model for deriving sdg interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle (pp and nn) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from pn interaction, with an IBM-2 to IBM-1 projection of the resulting p-n sdg IBM Hamiltonian. The applicability of this model in generating sdg IBM Hamiltonians is demonstrated, using a single-j-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, B(E2)'s, and E4 strength distribution in the example of 150Nd.

A Hamiltonian electromagnetic gyrofluid model

NASA Astrophysics Data System (ADS)

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

2009-03-01

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

Surface hopping trajectory simulations with spin-orbit and dynamical couplings

NASA Astrophysics Data System (ADS)

Granucci, Giovanni; Persico, Maurizio; Spighi, Gloria

2012-12-01

In this paper we consider the inclusion of the spin-orbit interaction in surface hopping molecular dynamics simulations to take into account spin forbidden transitions. Two alternative approaches are examined. The spin-diabatic one makes use of eigenstates of the spin-free electronic Hamiltonian and of hat{S}^2 and is commonly applied when the spin-orbit coupling is weak. We point out some inconsistencies of this approach, especially important when more than two spin multiplets are coupled. The spin-adiabatic approach is based on the eigenstates of the total electronic Hamiltonian including the spin-orbit coupling. Advantages and drawbacks of both strategies are discussed and illustrated with the help of two model systems.

A Note on Hamiltonian Graphs

ERIC Educational Resources Information Center

Skurnick, Ronald; Davi, Charles; Skurnick, Mia

2005-01-01

Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

Robust state preparation in quantum simulations of Dirac dynamics

NASA Astrophysics Data System (ADS)

Song, Xue-Ke; Deng, Fu-Guo; Lamata, Lucas; Muga, J. G.

2017-02-01

A nonrelativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between momentum and internal levels poses some difficulties to manipulate the internal states accurately in wave packets. We use invariants of motion to inverse engineer robust population inversion processes with a homogeneous, time-dependent simulated electric field. This exemplifies the usefulness of inverse-engineering techniques to improve the performance of quantum simulation protocols.

Noise-induced phase space transport in two-dimensional Hamiltonian systems.

PubMed

Pogorelov, I V; Kandrup, H E

1999-08-01

First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of periodic driving. The objective was to quantify and understand the manner in which "sticky" chaotic orbits that, in the absence of perturbations, are confined near regular islands for very long times, can become "unstuck" much more quickly when subjected to even very weak perturbations. For both noise and periodic driving, the typical escape time scales logarithmically with the amplitude of the perturbation. For white noise, the details seem unimportant: Additive and multiplicative noise typically have very similar effects, and the presence or absence of a friction related to the noise by a fluctuation-dissipation theorem is also largely irrelevant. Allowing for colored noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that there is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. Similarly, periodic driving is relatively inefficient when the driving frequency is not comparable to these natural frequencies. This suggests that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. The logarithmic dependence of the escape time on amplitude reflects the fact that the time required for perturbed and unperturbed orbits to diverge a given distance scales logarithmically in the amplitude of the perturbation.

Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems

NASA Astrophysics Data System (ADS)

Mei, Lijie; Wu, Xinyuan

2017-06-01

Symplecticity is also an important property for exponential Runge-Kutta (ERK) methods in the sense of structure preservation once the underlying problem is a Hamiltonian system, though ERK methods provide a good performance of higher accuracy and better efficiency than classical Runge-Kutta (RK) methods in dealing with stiff problems: y‧ (t) = My + f (y). On account of this observation, the main theme of this paper is to derive and analyze the symplectic conditions for ERK methods. Using the fundamental analysis of geometric integrators, we first establish one class of sufficient conditions for symplectic ERK methods. It is shown that these conditions will reduce to the conventional ones when M → 0, and this means that these conditions of symplecticity are extensions of the conventional ones in the literature. Furthermore, we also present a new class of structure-preserving ERK methods possessing the remarkable property of symplecticity. Meanwhile, the revised stiff order conditions are proposed and investigated in detail. Since the symplectic ERK methods are implicit and iterative solutions are required in practice, we also investigate the convergence of the corresponding fixed-point iterative procedure. Finally, the numerical experiments, including a nonlinear Schrödinger equation, a sine-Gordon equation, a nonlinear Klein-Gordon equation, and the well-known Fermi-Pasta-Ulam problem, are implemented in comparison with the corresponding symplectic RK methods and the prominent numerical results definitely coincide with the theories and conclusions made in this paper.

Quantum Entanglement Growth under Random Unitary Dynamics

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

Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement growsmore » linearly in time, while fluctuations grow like (time) 1/3 and are spatially correlated over a distance ∝(time) 2/3. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.« less

Quantum Entanglement Growth under Random Unitary Dynamics

NASA Astrophysics Data System (ADS)

Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; Haah, Jeongwan

2017-07-01

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the "entanglement tsunami" in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like (time )1/3 and are spatially correlated over a distance ∝(time )2/3. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a "minimal cut" picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the "velocity" of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.

Quantum Entanglement Growth under Random Unitary Dynamics

DOE PAGES

Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; ...

2017-07-24

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement growsmore » linearly in time, while fluctuations grow like (time) 1/3 and are spatially correlated over a distance ∝(time) 2/3. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.« less

Using Hamiltonian control to desynchronize Kuramoto oscillators

NASA Astrophysics Data System (ADS)

Gjata, Oltiana; Asllani, Malbor; Barletti, Luigi; Carletti, Timoteo

2017-02-01

Many coordination phenomena are based on a synchronization process, whose global behavior emerges from the interactions among the individual parts. Often in nature, such self-organized mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are, however, cases where synchronization acts against the stability of the system; for instance in some neurodegenerative diseases or epilepsy or the famous case of Millennium Bridge where the crowd synchronization of the pedestrians seriously endangered the stability of the structure. In this paper we propose an innovative control method to tackle the synchronization process based on the application of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronization. We present our results on a generalized class of the paradigmatic Kuramoto model.

Nonperturbative Dynamical Casimir Effect in Optomechanical Systems: Vacuum Casimir-Rabi Splittings

NASA Astrophysics Data System (ADS)

Macrı, Vincenzo; Ridolfo, Alessandro; Di Stefano, Omar; Kockum, Anton Frisk; Nori, Franco; Savasta, Salvatore

2018-01-01

We study the dynamical Casimir effect using a fully quantum-mechanical description of both the cavity field and the oscillating mirror. We do not linearize the dynamics, nor do we adopt any parametric or perturbative approximation. By numerically diagonalizing the full optomechanical Hamiltonian, we show that the resonant generation of photons from the vacuum is determined by a ladder of mirror-field vacuum Rabi splittings. We find that vacuum emission can originate from the free evolution of an initial pure mechanical excited state, in analogy with the spontaneous emission from excited atoms. By considering a coherent drive of the mirror, using a master-equation approach to take losses into account, we are able to study the dynamical Casimir effect for optomechanical coupling strengths ranging from weak to ultrastrong. We find that a resonant production of photons out of the vacuum can be observed even for mechanical frequencies lower than the cavity-mode frequency. Since high mechanical frequencies, which are hard to achieve experimentally, were thought to be imperative for realizing the dynamical Casimir effect, this result removes one of the major obstacles for the observation of this long-sought effect. We also find that the dynamical Casimir effect can create entanglement between the oscillating mirror and the radiation produced by its motion in the vacuum field, and that vacuum Casimir-Rabi oscillations can occur. Finally, we also show that all these findings apply not only to optomechanical systems, but also to parametric amplifiers operating in the fully quantum regime.

Quantum finance Hamiltonian for coupon bond European and barrier options.

PubMed

Baaquie, Belal E

2008-03-01

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

Conformational Dynamics Guides Coherent Exciton Migration in Conjugated Polymer Materials: First-Principles Quantum Dynamical Study

NASA Astrophysics Data System (ADS)

Binder, Robert; Lauvergnat, David; Burghardt, Irene

2018-06-01

We report on high-dimensional quantum dynamical simulations of photoinduced exciton migration in a single-chain oligothiophene segment, in view of elucidating the controversial nature of the elementary exciton transport steps in semiconducting polymers. A novel first-principles parametrized Frenkel J aggregate Hamiltonian is employed that goes significantly beyond the standard Frenkel-Holstein Hamiltonian. Departing from a nonequilibrium state created by photoexcitation, these simulations provide evidence of an ultrafast two-timescale process at low temperatures, involving exciton-polaron formation within tens of femtoseconds (fs), followed by torsional relaxation on an ˜400 fs timescale. The second step is the driving force for exciton migration, as initial conjugation breaks are removed by dynamical planarization. The quantum coherent nature of the elementary exciton migration step is consistent with experimental observations highlighting the correlated and vibrationally coherent nature of the dynamics on ultrafast timescales.

Conformational Dynamics Guides Coherent Exciton Migration in Conjugated Polymer Materials: First-Principles Quantum Dynamical Study.

PubMed

Binder, Robert; Lauvergnat, David; Burghardt, Irene

2018-06-01

We report on high-dimensional quantum dynamical simulations of photoinduced exciton migration in a single-chain oligothiophene segment, in view of elucidating the controversial nature of the elementary exciton transport steps in semiconducting polymers. A novel first-principles parametrized Frenkel J aggregate Hamiltonian is employed that goes significantly beyond the standard Frenkel-Holstein Hamiltonian. Departing from a nonequilibrium state created by photoexcitation, these simulations provide evidence of an ultrafast two-timescale process at low temperatures, involving exciton-polaron formation within tens of femtoseconds (fs), followed by torsional relaxation on an ∼400  fs timescale. The second step is the driving force for exciton migration, as initial conjugation breaks are removed by dynamical planarization. The quantum coherent nature of the elementary exciton migration step is consistent with experimental observations highlighting the correlated and vibrationally coherent nature of the dynamics on ultrafast timescales.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

PubMed

Compelli, A; Ivanov, R; Todorov, M

2018-01-28

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

Null lifts and projective dynamics

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

Cariglia, Marco, E-mail: marco@iceb.ufop.br

2015-11-15

We describe natural Hamiltonian systems using projective geometry. The null lift procedure endows the tangent bundle with a projective structure where the null Hamiltonian is identified with a projective conic and induces a Weyl geometry. Projective transformations generate a set of known and new dualities between Hamiltonian systems, as for example the phenomenon of coupling-constant metamorphosis. We conclude outlining how this construction can be extended to the quantum case for Eisenhart–Duval lifts.

The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications

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

Mei, Lijie, E-mail: bxhanm@126.com; Wu, Xinyuan, E-mail: xywu@nju.edu.cn

In general, extended Runge–Kutta–Nyström (ERKN) methods are more effective than traditional Runge–Kutta–Nyström (RKN) methods in dealing with oscillatory Hamiltonian systems. However, the theoretical analysis for ERKN methods, such as the order conditions, the symplectic conditions and the symmetric conditions, becomes much more complicated than that for RKN methods. Therefore, it is a bottleneck to construct high-order ERKN methods efficiently. In this paper, we first establish the ERKN group Ω for ERKN methods and the RKN group G for RKN methods, respectively. We then rigorously show that ERKN methods are a natural extension of RKN methods, that is, there exists anmore » epimorphism η of the ERKN group Ω onto the RKN group G. This epimorphism gives a global insight into the structure of the ERKN group by the analysis of its kernel and the corresponding RKN group G. Meanwhile, we establish a particular mapping φ of G into Ω so that each image element is an ideal representative element of the congruence class in Ω. Furthermore, an elementary theoretical analysis shows that this map φ can preserve many structure-preserving properties, such as the order, the symmetry and the symplecticity. From the epimorphism η together with its section φ, we may gain knowledge about the structure of the ERKN group Ω via the RKN group G. In light of the theoretical analysis of this paper, we obtain high-order structure-preserving ERKN methods in an effective way for solving oscillatory Hamiltonian systems. Numerical experiments are carried out and the results are very promising, which strongly support our theoretical analysis presented in this paper.« less

The chaotic dynamical aperture

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

Lee, S.Y.; Tepikian, S.

1985-10-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipolesmore » should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles.« less

Dynamical Localization in Molecular Systems.

NASA Astrophysics Data System (ADS)

Wang, Xidi

In the first four chapters of this thesis we concentrate on the Davydov model which describes the vibrational energy quanta of Amide I bonds (C=O bonds on the alpha -helix) coupled to the acoustic phonon modes of the alpha-helix backbone in the form of a Frohlich Hamiltonian. Following a brief introduction in chapter one, in chapter two we formulate the dynamics of vibrational quanta at finite temperature by using coherent state products. The fluctuation-dissipation relation is derived. At zero temperature, in the continuum limit, we recover the original results of Davydov. We also achieve good agreement with numerical simulations. In chapter three, the net contraction of the lattice is calculated exactly at any temperature, and its relation to the so -call "topological stability" of the Davydov soliton is discussed. In the second section of the chapter three we calculate the overtone spectra of crystalline acetanilide (according to some opinions ACN provides experimental evidence for the existence of Davydov solitons). Good agreement with experimental data has been obtained. In chapter four we study the self-trapped vibrational excitations by the Quantum Monte Carlo technique. For a single excitation, the temperature dependence of different physical observables is calculated. The quasi-particle which resembles the Davydov soliton has been found to be fairly narrow using the most commonly used data for the alpha -helix; at temperatures above a few Kelvin, the quasi-particle reaches its smallest limit (extends over three sites), which implies diffusive motion of the small polaron-like quasi-particle at high temperatures. For the multi-excitation case, bound pairs and clusters of excitations are found at low temperatures; they gradually dissociate when the temperature of the system is increased as calculated from the density-density correlation function. In the last chapter of this thesis, we study a more general model of dynamical local modes in molecular systems

Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity.

PubMed

Samsonov, Boris F

2013-04-28

One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.

BMS3 invariant fluid dynamics at null infinity

NASA Astrophysics Data System (ADS)

Penna, Robert F.

2018-02-01

We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary’s equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie–Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden–Ratiu–Weinstein formulation of the compressible Euler equations on a manifold, M, as Hamiltonian flow on the dual of the Lie algebra of \

On the Hamilton approach of the dissipative systems

NASA Astrophysics Data System (ADS)

Zimin, B. A.; Zorin, I. S.; Sventitskaya, V. E.

2018-05-01

In this paper we consider the problem of constructing equations describing the states of dissipative dynamical systems (media with absorption or damping). The approaches of Lagrange and Hamilton are discussed. A non-symplectic extension of the Poisson brackets is formulated. The application of the Hamiltonian formalism here makes it possible to obtain explicit equations for the dynamics of a nonlinear elastic system with damping and a one-dimensional continuous medium with internal friction.

Effective Hamiltonians for phosphorene and silicene

DOE PAGES

Lew Yan Voon, L. C.; Lopez-Bezanilla, A.; Wang, J.; ...

2015-02-04

Here, we derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work on silicene, and on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene.We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of themore » wave vector.We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k · p parameters.« less

Hamiltonian Cycle Enumeration via Fermion-Zeon Convolution

NASA Astrophysics Data System (ADS)

Staples, G. Stacey

2017-12-01

Beginning with a simple graph having finite vertex set V, operators are induced on fermion and zeon algebras by the action of the graph's adjacency matrix and combinatorial Laplacian on the vector space spanned by the graph's vertices. When the graph is simple (undirected with no loops or multiple edges), the matrices are symmetric and the induced operators are self-adjoint. The goal of the current paper is to recover a number of known graph-theoretic results from quantum observables constructed as linear operators on fermion and zeon Fock spaces. By considering an "indeterminate" fermion/zeon Fock space, a fermion-zeon convolution operator is defined whose trace recovers the number of Hamiltonian cycles in the graph. This convolution operator is a quantum observable whose expectation reveals the number of Hamiltonian cycles in the graph.

Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians.

PubMed

Vidmar, Lev; Rigol, Marcos

2017-12-01

In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the average entanglement entropy is known to be nearly maximal, with a deviation that is, at most, a constant. Here we prove that, in a system that is away from half filling and divided in two equal halves, an upper bound for the average entanglement entropy of random pure states with a fixed particle number and normally distributed real coefficients exhibits a deviation from the maximal value that grows with the square root of the volume of the system. Exact numerical results for highly excited eigenstates of a particle number conserving quantum chaotic model indicate that the bound is saturated with increasing system size.

Quantum phase transition and quench dynamics in the anisotropic Rabi model

NASA Astrophysics Data System (ADS)

Shen, Li-Tuo; Yang, Zhen-Biao; Wu, Huai-Zhi; Zheng, Shi-Biao

2017-01-01

We investigate the quantum phase transition (QPT) and quench dynamics in the anisotropic Rabi model when the ratio of the qubit transition frequency to the oscillator frequency approaches infinity. Based on the Schrieffer-Wolff transformation, we find an anti-Hermitian operator that maps the original Hamiltonian into a one-dimensional oscillator Hamiltonian within the spin-down subspace. We analytically derive the eigenenergy and eigenstate of the normal and superradiant phases and demonstrate that the system undergoes a second-order quantum phase transition at a critical border. The critical border is a straight line in a two-dimensional parameter space which essentially extends the dimensionality of QPT in the Rabi model. By combining the Kibble-Zurek mechanism and the adiabatic dynamics method, we find that the residual energy vanishes as the quench time tends to zero, which is a sharp contrast to the universal scaling where the residual energy diverges in the same limit.

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

NASA Astrophysics Data System (ADS)

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

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

The Hamiltonian structure of the (2+1)-dimensional Ablowitz--Kaup--Newell--Segur hierarchy

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

Athorne, C.; Dorfman, I.Y.

1993-08-01

By considering Hamiltonian theory over a suitable (noncommutative) ring the nonlinear evolution equations of the Ablowitz--Kaup--Newell--Segur (2+1) hierarchy are incorporated into a Hamiltonian framework and a modified Lenard scheme.

Investigating multiphoton phenomena using nonlinear dynamics

NASA Astrophysics Data System (ADS)

Huang, Shu

Many seemingly simple systems can display extraordinarily complex dynamics which has been studied and uncovered through nonlinear dynamical theory. The leitmotif of this thesis is changing phase-space structures and their (linear or non-linear) stabilities by adding control functions (which act on the system as external perturbations) to the relevant Hamiltonians. These phase-space structures may be periodic orbits, invariant tori or their stable and unstable manifolds. One-electron systems and diatomic molecules are fundamental and important staging ground for new discoveries in nonlinear dynamics. In past years, increasing emphasis and effort has been put on the control or manipulation of these systems. Recent developments of nonlinear dynamical tools can provide efficient ways of doing so. In the first subtopic of the thesis, we are adding a control function to restore tori at prescribed locations in phase space. In the remainder of the thesis, a control function with parameters is used to change the linear stability of the periodic orbits which govern the processes in question. In this thesis, we report our theoretical analyses on multiphoton ionization of Rydberg atoms exposed to strong microwave fields and the dissociation of diatomic molecules exposed to bichromatic lasers using nonlinear dynamical tools. This thesis is composed of three subtopics. In the first subtopic, we employ local control theory to reduce the stochastic ionization of hydrogen atom in a strong microwave field by adding a relatively small control term to the original Hamiltonian. In the second subtopic, we perform periodic orbit analysis to investigate multiphoton ionization driven by a bichromatic microwave field. Our results show quantitative and qualitative agreement with previous studies, and hence identify the mechanism through which short periodic orbits organize the dynamics in multiphoton ionization. In addition, we achieve substantial time savings with this approach. In the

Time-dependent nonlinear Jaynes-Cummings dynamics of a trapped ion

NASA Astrophysics Data System (ADS)

Krumm, F.; Vogel, W.

2018-04-01

In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact solutions of the dynamics are rarely available. Here we study the nonlinear vibronic dynamics of a trapped ion, driven in the resolved sideband regime with some small frequency mismatch. By describing the pump field in a quantized manner, we are able to derive exact solutions for the dynamics of the system. This eventually allows us to provide analytical solutions for various types of time-dependent quantities. In particular, we study in some detail the electronic and the motional quantum dynamics of the ion, as well as the time evolution of the nonclassicality of the motional quantum state.

Chaotic dynamics and thermodynamics of periodic systems with long-range forces

NASA Astrophysics Data System (ADS)

Kumar, Pankaj

Gravitational and electromagnetic interactions form the backbone of our theoretical understanding of the universe. While, in general, such interactions are analytically inexpressible for three-dimensional infinite systems, one-dimensional modeling allows one to treat the long-range forces exactly. Not only are one-dimensional systems of profound intrinsic interest, physicists often rely on one-dimensional models as a starting point in the analysis of their more complicated higher-dimensional counterparts. In the analysis of large systems considered in cosmology and plasma physics, periodic boundary conditions are a natural choice and have been utilized in the study of one dimensional Coulombic and gravitational systems. Such studies often employ numerical simulations to validate the theoretical predictions, and in cases where theoretical relations have not been mathematically formulated, numerical simulations serve as a powerful method in characterizing the system's physical properties. In this dissertation, analytic techniques are formulated to express the exact phase-space dynamics of spatially-periodic one-dimensional Coulombic and gravitational systems. Closed-form versions of the Hamiltonian and the electric field are derived for single-component and two-component Coulombic systems, placing the two on the same footing as the gravitational counterpart. Furthermore, it is demonstrated that a three-body variant of the spatially-periodic Coulombic or gravitational system may be reduced isomorphically to a periodic system of a single particle in a two-dimensional rhombic potential. The analytic results are utilized for developing and implementing efficient computational tools to study the dynamical and the thermodynamic properties of the systems without resorting to numerical approximations. Event-driven algorithms are devised to obtain Lyapunov spectra, radial distribution function, pressure, caloric curve, and Poincare surface of section through an N

Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes

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

Dias, Goncalo A. S.; Lemos, Jose P. S.; Centro Multidisciplinar de Astrofisica-CENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Avenida Rovisco Pais 1, 1049-001 Lisboa

2008-10-15

The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free {omega} parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{+-}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3), all with a Maxwell term. The Hamiltonian formalismmore » is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P{sub M};Q,P{sub Q}), where M is the mass parameter, which for {omega}<-(3/2) and for {omega}={+-}{infinity} needs a careful renormalization, P{sub M} is the conjugate momenta of M, Q is the charge parameter, and P{sub Q} is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field {phi}. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of