Dynamics of a Simple Quantum System in a Complex Environment

Abstract

We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective stochastic models which emerge from random matrix theory. Using the Feynman-Vernon path integral formalism, we derive the influence functional and obtain either analytical or numerical solutions for the time evolution of the entire quantum system. We discuss thoroughly the structure of the solutions for some representative cases and make connections to well known limiting results, particularly to Brownian motion, Kramers classical limit and the Caldeira-Leggett approach.

41 pages and 12 figures in revtex

References in corpus (3)

• Quantum Dissipation versus Classical Dissipation for Generalized Brownian Motion
• Turbulent-like Diffusion in Complex Quantum Systems
• Quantum Diffusion and Tunneling with Parametric Banded Random Matrix Hamiltonians

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