Open quantum systems and the damping of collective modes in deep inelastic collisions

Abstract

In the framework of the Lindblad theory for open quantum systems the following results are obtained: A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the corresponding master equations, a generalization of the Hasse pure-state condition, and a generalized Schrödinger-type nonlinear equation for an open system. Also, the Schrödinger, Heisenberg, and Weyl-Wigner-Moyal representations of the Lindblad equation are given explicitly. On the basis of these representations it is shown that various master equations for the damped quantum oscillator used in the literature for the description of the damped collective modes in deep inelastic collisions (DIC) are particular cases of the Lindblad equaton and that the majority of these equations are not satisfying the constraints on quantum mechanical diffusion coefficients. The solutions of the differential equations for the variances are put in a new synthetic form, suggested by a direct computation of the variances from the time dependent Weyl operators. The solution of the Lindblad equation in the Weyl-Wigner-Moyal representation is of Gaussian type if the initial form of the Wigner function is taken to be a Gaussian corresponding to a coherent wavefunction.