A Lindblad Model for Quantum Brownian Motion

Abstract

The theory of quantum Brownian motion describes the properties of a large class of open quantum systems. Nonetheless, its description in terms of a Born-Markov master equation, widely used in literature, is known to violate the positivity of the density operator at very low temperatures. We study an extension of existing models, leading to an equation in the Lindblad form, which is free of this problem. We study the dynamics of the model, including the detailed properties of its stationary solution, for both constant and position-dependent coupling of the Brownian particle to the bath, focusing in particular on the correlations and the squeezing of the probability distribution induced by the environment.

On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion

“…This function can be nonlinear in the system's position, in which case the particle is subject to inhomogeneous damping and diffusion [38,47,61]. The model can be viewed as a field version of the one studied in [47,61], a generalization of the Pauli-Fierz model [62][63][64], or a quantum analog of the one studied in Appendix A of [36]. It is a fundamental model which not only allows simple analytic treatments and provides physical insights, but also realistically models many open qantum systems -for instance, an atom in an electromagnetic field.…”