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arXiv:quant-ph/0307222 · Birkhäuser Boston eBooks

On a Rigorous Proof of the Joos–Zeh Formula for Decoherence in a Two-body Problem

Alessandro Teta

Published Jan 1, 2004• 3 citations
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Abstract

We consider a simple one-dimensional system consisting of two particles interacting with a δ-potential and we discuss a rigorous derivation of the asymptotic wave function of the system in the limit of small mass ratio. We apply the result for the explicit computation of the decoherence effect induced on the heavy particle in a concrete example of quantum evolution.

DOI
10.1007/978-0-8176-8202-6_16

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We consider a simple one-dimensional system consisting of two particles interacting with a δ-potential and we discuss a rigorous derivation of the asymptotic wave function of the system in the limit of small mass ratio. We apply the result for the explicit computation of the decoherence effect induced on the heavy particle in a concrete example of quantum evolution.
We recall the classical picture about the decoherence effects induced on a quantum sub-system by the interaction with a macroscopic environment. We discuss the need of a rigorous treatment, in mathematically reasonable models, of the dynamical process bringing the system in an entangled state with the environment. We consider a simple system consisting of two particles interacting via a two-body potential and we discuss a rigorous derivation of the asymptotic wave function of the system in the limit of small mass ratio. We apply the result to the explicit computation of the decoherence effect induced on the heavy particle, in concrete examples of quantum evolution.
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The dynamical process of generation of entanglement between subsystems of an evolving quantum system is analysed in this paper. We consider one of the simplest possible continuous systems in which such a process can be rigorously studied: a quantum ‘heavy’ particle (the system) interacting via zero range forces with a lighter particle (the environment). In a three-dimensional model we study the asymptotic dynamics when the ratio between the masses of the light and the heavy particle is very small. The effect of decoherence on the heavy particle induced by the interaction is explicitly computed.