Non-markovian irreversible behavior in a simple model.

Abstract

The soluble model of an oscillator coupled to a scalar field is used as an example of irreversible behavior. By studying the reduced density operator for the oscillator, a generalized Fokker-Planek-Kramers-Chandrasekhar equation for the Wigner distribution function is derived. The diagonal matrix elements of the reduced density operator satisfy a generalized non-Markovian master equation. By application of a time-averaged method, the ordinary Pauli master equation is derived. The time evolution of the occupation probabilities of the oscillator levels has been numerically computed, and compared with the solutions of the Pauli equation.