Classical analog to the Airy wave packet

The solution of the Liouville equation for the ensemble of free particles is presented and the classical analog to the quantum accelerating Airy wave packet is constructed and discussed. Considering the motion of various classical packets – with an infinite and restricted distribution of velocities of particles – and also the motion of their fronts, we demonstrate in the simplest and most definite way why the packet can display a more sophisticated behaviour (even acceleration) as compared with a free individual particle that moves at a fixed velocity. A comparison of this classical solution with the quantum one in the Wigner representation of quantum mechanics, which provides the closest analogy, is also presented.

Quantum Dynamics of Charged Fermions in the Wigner Formulation of Quantum Mechanics

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.