Semiclassical limits in quantum-transport theory

Abstract

Semiclassical limits for the dynamics of the Wigner function, and for the dynamics of the low-order moments of physical interest, are discussed in fluid-dynamical terms. The harmonic-oscillator solution yields local Maxwellian (ideal) fluid-dynamical behavior, and this is extended to locally quadratic problems in a straightforward manner. Coherent states are shown to have a particularly simple fluid-dynamical interpretation, and coherence may be easily demonstrated for mixed states having an arbitrary degree of uncertainty in the field variables. The semiclassical behavior of pure and mixed states is conveniently discussed in terms of coherent and incoherent limits, and the origin of quantum-mechanical behavior in the simple low-order approximations proposed is simply explained. The relation to the pure-state theory of Madelung is made explicit. A recently proposed method for the solution of a certain hierarchy of quantum-fluid-dynamical equations is analyzed in detail, and is demonstrated to be inconsistent with these semiclassical limits.