Phase Space Methods for Quantum Dynamics

F. H. Molzahn, T. A. Osborn

Vladimir S. Filinov

Jérôme Daligault

A Lagrangian, moving-with-the-fluid, picture in the quantum Wigner phase space is rigorously defined, introducing a state-dependent current in phase space. Contrary to its classical counterpart, the Lagrangian dynamics in quantum phase space is non-Hamiltonian and elementary phase-space volumes are not conserved. The consequences for the numerical implementation of a fluid trajectory method in quantum phase space are discussed.

Dmytro Babyuk

A combined method for analyzing quantum dynamical equations which uses the Bohmian mechanics and the quantum phase space representation is proposed. It is based on a presentation of the wave function in phase space in a polar form. The combined method is very effective for comparison of classical and quantum dynamics for polynomial potentials of order no higher than second. Application for the harmonic oscillator and quartic double well potential is performed. Quantum fluxes and particle energy are derived by means of the proposed method.

Anatoli Polkovnikov

Walter J. Deal