Theory and application of the quantum phase-space distribution functions

Abstract

A review is given of the quantum phase-space distribution functions with emphasis on both the fundamental characteristics and practical applications of the distribution functions. The distribution functions, such as the Wigner distribution function, the Glauber-Sudarshan P and Q functions, the Kirkwood distribution function and the Husimi distribution function, are treated in a unified fashion based on the classification scheme of Cohen. The fundamental relations of the distribution functions are discussed both in ( q, p) phase space and in (α, α ∗ ) complex space, the properties of the distribution functions are compared and relations between them derived. Also discussed is the dynamical equations that govern the time development of the distribution functions. Applications of the distribution functions are illustrated, with particular attention to the Wigner distribution function in studies of collision systems and to the Husimi distribution function in studies of classically chaotic nonlinear systems.