Non-Hamiltonian dynamics and trajectory methods in quantum phase spaces

Abstract

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.