Abstract
To study the kinetic properties of dense quantum plasma, a new quantum dynamics method in the Wigner representation of quantum mechanics has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. This method combines the Feynman and Wigner formulation of quantum mechanics and uses for calculation the path integral Monte-Carlo (WPIMC) in phase space and quantum generalization of the classical molecular dynamics methods (WMD) allowing to solve the quantum Wigner–Liouville-like equation. The Fermi–Dirac statistical effects are accounted for by the effective pair pseudopotential depending on coordinates and momenta and allowing to avoid the famous “sign problem” due to realization of the Pauli blocking of fermions. Significant influence of the interparticle interaction on the high energy asymptotics of the momentum distribution functions have been observed. According to the quantum Kubo formula, we also study the electron conductivity of dense plasma media.
Highlights
The main advantage of the Wigner formulation of the quantum mechanics in the phase space is that it allows obtaining more information on the quantum system than can be done by any other quantum description
We use the generalization of the classical molecular dynamics methods allowing to take into account quantum effects
We use the Feynman and Wigner formulations of quantum mechanics combining with Monte Carlo methods for numerical treatment of the kinetic properties of dense quantum plasma media
Summary
The main advantage of the Wigner formulation of the quantum mechanics in the phase space is that it allows obtaining more information on the quantum system than can be done by any other quantum description. The main results of this work can be formulated as follows: to overcome disadvantages of the standard PIMC methods in configuration space, we use a new numerical approach (WPIMC) based on combining the path integral and the Wigner formulation of quantum mechanics [9,10]; to account for the Fermi–Dirac statistical effects in explicit formm the effective pair pseudopotential depending on coordinates and momenta has been used, avoiding the famous “sign problem” due to realization of the Pauli blocking of fermions in phase space at the finite temperature; the high energy asymptotics of the momentum distribution functions has been studied under strong interparticle Coulomb interaction; and, according to the quantum Kubo formula, the electron conductivity of strongly-coupled hydrogen plasma has been calculated using the Wigner generalization of the standard classical molecular dynamics method
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