Quantum corrections to the equilibrium rate constants of inelastic processes

Eletskii, Aleksandr V.; Starostin, A. N.; Taran, M. D.

doi:10.1070/pu2005v048n03abeh002039

Cited by 32 publications

(35 citation statements)

References 30 publications

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“…without using empiric suggestions or different kind of perturbation theories, which require small physical parameters. Moreover numerical simulations are able to predict properties of matter under extreme conditions, when experiment is difficult [5,6] or even impossible nowadays. Based on the 3D quasiparticle model of the quark-gluon plasma (QGP), a color quantum path-integral Monte-Carlo (PIMC) method for the calculation of thermodynamic properties and -closely related to the latter -a Wigner dynamics method for calculation of transport properties of the QGP have been developed in [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…The equilibrium and nonequilibrium Green's function methods are ones of the most powerful and versatile formalisms in physics and in many research fields, ranging from molecules and nanostructures to metals, plasma and insulators [1][2][3][4][5][6]. We are going to develop the numerical Wigner version of this approach for treatment the strongly interacting systems of particles under extreme conditions, when there are no small physical parameters and analytical approximations usually used in different kind of perturbation theories can not be applied.…”

Section: Introductionmentioning

confidence: 99%

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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%

Section: Introductionmentioning

confidence: 99%

Path Integral Representation of the Wigner Function in Canonical Ensemble

Larkin

Филинов

Fortov

2016

Contrib. Plasma Phys.

View full text Add to dashboard Cite

show abstract

“…Quantum effects may strongly disturb the momentum Maxwellian distribution function [13] and are important in studies of kinetic properties of matter at low temperatures and under extreme conditions, when particles are strongly coupled and perturbative methods cannot be applied. The mentioned before PIMC methods or even recently developed "Configuration Path Integral Monte Carlo" approach [4] [5] [14] up to now cannot also solve kinetic problem.…”

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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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“…Interesting is the non monotonic behavior of discrepancy between PIMC momentum distributions and FD or MD in asymptotic regions with increasing classical coupling parameter Γ = βe 2 /(3/4πn a ) 1/3 from top (Γ = 1) to bottom (Γ = 4) panels. Namely for electrons and holes at low , while results for holes are presented by lines (4,5,6,8,9). Detailed description of the meaning of these lines is given in text.…”

Section: Results Of Numerical Calculationsmentioning

confidence: 99%

Peculiarities of the momentum distribution functions of strongly correlated charged fermions

Larkin¹,

Филинов²,

Fortov³

2017

J. Phys. A: Math. Theor.

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The new numerical version of Wigner approach to quantum thermodynamics of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations obtained in different kind of perturbation theories can not be applied. Explicit analytical expression of Wigner function has been obtained in linear and harmonic approximations. Fermi statistical effects are accounted by effective pair pseudopotential depending on coordinates, momenta and degeneracy parameter of particles and taking into account Pauli blocking of fermions. The new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been proposed. Calculations of the momentum distribution functions and pair correlation functions of the degenerate ideal Fermi gas have been carried out for testing the developed approach. Comparison of obtained momentum distribution functions of strongly correlated Coulomb systems with MaxwellBoltzmann and Fermi distributions shows the significant influence of interparticle interaction both at small momenta and in high energy quantum 'tails'.

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Quantum corrections to the equilibrium rate constants of inelastic processes

Cited by 32 publications

References 30 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

Peculiarities of the momentum distribution functions of strongly correlated charged fermions

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