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arXiv:gr-qc/9402007

Decoherence in Quantum Brownian Motion

Juan Pablo Paz

Published Feb 2, 1994• 12 citations
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Abstract

We examine the dependence of decoherence on the spectral density of the environment as well as on the initial state of the system. We use two simple examples to illustrate some important effects. The simplest derivation of the general form of the master equation for a general quantum Brownian motion is outlined in an Appendix.
DOI
10.48550/arxiv.gr-qc/9402007

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We analyze the evolution of a quantum Brownian particle starting from an initial state that contains correlations between this system and its environment. Using a path-integral approach, we obtain a master equation for the reduced density matrix of the system finding relatively simple expressions for its time-dependent coefficients. We examine the evolution of delocalized initial states (Schr\"odinger cats) investigating the effectiveness of the decoherence process. Analytic results are obtained for an Ohmic environment (Drude's model) at zero temperature.
Decoherence and dissipation in quantum systems has been studied extensively in the context of Quantum Brownian Motion. Effective decoherence in coarse grained quantum systems has been a central issue in recent efforts by Zurek and by Hartle and Gell-Mann to address the Quantum Measurement Problem. Although these models can yield very general classical phenomenology, they are incapable of reproducing relevant characteristics expected of a local environment on a quantum system, such as the characteristic dependence of decoherence on environment spatial correlations. I discuss the characteristics of Quantum Brownian Motion in a local environment by examining aspects of first principle calculations and by the construction of phenomenological models. Effective quantum Langevin equations and master equations are presented in a variety of representations. Comparisons are made with standard results such as the Caldeira-Leggett master equation.