A benchmark study of the Wigner Monte Carlo method

Sellier, Jean Michel; Nedjalkov, Mihail; Dimov, Ivan; Selberherr, S.

doi:10.1515/mcma-2013-0018

Cited by 39 publications

(53 citation statements)

References 7 publications

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“…Thereby average values of arbitrary physical quantities can be calculated by formulas, similar to classical statistics. Methods for treatment the single-particle quantum dynamics in Wigner approach in microcanonical ensemble were proposed in [20][21][22][23][24]. Recently a generalization of these virtual particle one-body Wigner Monte Carlo methods to the many-body Wigner equation for distinguishable particles has been done in [25].…”

Section: Introductionmentioning

confidence: 99%

Path Integral Representation of the Wigner Function in Canonical Ensemble

Larkin

Филинов

Fortov

2016

Contrib. Plasma Phys.

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Quantum effects can affect the shape of the particle kinetic energy distribution function, as the interaction of a particle with its surroundings restricts the volume of configuration space, which, due to the uncertainty relation, results in an increase in the volume of the momentum space, i.e., in a rise in the fraction of particles with higher momenta. Allowing for quantum effects at calculations of the equilibrium rate constants of inelastic processes is important in consideration of such phenomena as the transition of combustion into detonation, flame propagation, vibrational relaxation, and even thermonuclear fusion at high pressure and low temperatures. Quantum effects are also important in treatment of transport properties of the strongly interacting systems of many particles. In this work the new path integral representation of the quantum Wigner function in the phase space has been developed for canonical ensemble. Explicit analytical expression of the Wigner function has been obtained in harmonic approximation. New quantum Monte-Carlo method for ab initio calculations of the average values of quantum operators, Wigner function, momentum and position distributions and wave functions of the ground state has been developed and tested. Obtained results are in a very good agreement with available analytical results and results of usual path-integral Monte-Carlo method. The developed approach allows simulation of thermodynamic and kinetic properties of quantum systems and calculation average values of quantum operators, when the usual path integral Monte Carlo methods in configurational space failed.

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Section: Introductionmentioning

confidence: 99%

Path Integral Representation of the Wigner Function in Canonical Ensemble

Larkin

Филинов

Fortov

2016

Contrib. Plasma Phys.

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“…Methods for phase space treatment of single-particle quantum dynamics in Wigner approach in microcanonical ensemble were proposed in [15] [16] [17] [18] [19]. Recently a generalization of these one-body Wigner Monte Carlo methods to the many-body distinguishable particles has been done in [20].…”

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confidence: 99%

Phase Space Path Integral Representation for Wigner Function

Larkin¹,

Филинов²

2017

JAMP

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Quantum interference and exchange statistical effects can affect the momentum distribution functions making them non-Maxwellian. Such effects may be important in studies of kinetic properties of matter at low temperatures and under extreme conditions. In this work we have generalized the path integral representation for Wigner function to strongly coupled three-dimensional quantum system of particles with Boltzmann and Fermi statistics. In suggested approach the explicit expression for Wigner function was obtained in harmonic approximation and Monte Carlo method allowing numerical calculation of Wigner function, distribution functions and average quantum values has been developed. As alternative more accurate single-momentum approach and related Monte Carlo method have been developed to calculation of the distribution functions of degenerate system of interacting fermions. It allows partially overcoming the well-known sign problem for degenerate Fermi systems.

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“…In this case, quantum systems differs from classical systems only by their initial conditions [12]. (6) [5]. For the sake of clarity, we restrict the exposition to a single-body in a one-dimensional spatial domain.…”

Section: Transient Regimementioning

confidence: 99%

“…For the sake of clarity, we restrict the exposition to a single-body in a one-dimensional spatial domain. More mathematical details can be found in [5,6] for the single-and many-body Wigner equations respectively. For practical details on the implementation, the interested reader is also invited to download the source code [13].…”

Section: Transient Regimementioning

confidence: 99%

“…Only recently, Monte Carlo techniques have been implemented which overcome the many problems involved in the resolution of such model. It has open the way towards quantitative, time-dependent, multi-dimensional, single-and many-body quantum problems even for the case of indistinguishable particles, a particularly difficult computational problem [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

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Wigner functions, signed particles, and the harmonic oscillator

Sellier

Dimov

2015

J Comput Electron

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In this paper, we introduce the simple harmonic oscillator and we address it in the Wigner formulation of quantum mechanics, therefore describing the whole problem in terms of quasi-distribution functions defined over the phase-space. The harmonic oscillator represents a very important problem as it provides exact solutions in both stationary and transient regimes. Subsequently, we outline the time-dependent signed particle Wigner Monte Carlo method and simulate the oscillator problem starting from stationary initial conditions, i.e. rotationally invariant functions in the phase-space, showing no evolution in time of the distribution function as expected. This work is, thus, twofold. On the one hand, one may see it as a short review effort to demonstrate the convenience of utilizing a phase-space approach in this particular context, suggesting that it could be the case again for different interesting problems. On the other hand, it represents a further opportunity to validate the signed particle Monte Carlo method, showing that a new reliable and powerful tool is available for the time-dependent simulation of quantum systems.

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A benchmark study of the Wigner Monte Carlo method

Cited by 39 publications

References 7 publications

Path Integral Representation of the Wigner Function in Canonical Ensemble

Path Integral Representation of the Wigner Function in Canonical Ensemble

Phase Space Path Integral Representation for Wigner Function

Wigner functions, signed particles, and the harmonic oscillator

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