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Quantum Brownian Motion in a Simple Model System
- Publication Year :
- 2008
-
Abstract
- We consider a quantum particle coupled (with strength $\la$) to a spatial array of independent non-interacting reservoirs in thermal states (heat baths). Under the assumption that the reservoir correlations decay exponentially in time, we prove that the long-time behavior of the particle is diffusive for small, but finite $\la$. Our proof relies on an expansion around the kinetic scaling limit ($\la \searrow 0$, while time and space scale as $\la^{-2}$) in which the particle satisfies a Boltzmann equation. We also show an equipartition theorem: the distribution of the kinetic energy of the particle tends to a Maxwell-Boltzmann distribution, up to a correction of $O(\la^2)$.<br />Comment: v1--> v2, mistake corrected in Lemma 6.2, to appear in CMP
- Subjects :
- Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.0810.4537
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00220-009-0924-z