Canonical Typicality

Details Canonical Typicality Canonical Typicality

2005-11-03

arxiv.org/abs/cond-mat/0511091v2

Phys. Rev. Lett. 96, 050403 (2006)

Physics

Condensed Matter

Statistical Mechanics

6 pages LaTeX, no figures; v2 minor improvements and additions

Scientific paper

10.1103/PhysRevLett.96.050403

It is well known that a system, S, weakly coupled to a heat bath, B, is described by the canonical ensemble when the composite, S+B, is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true both for classical distributions on the phase space and for quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subspace corresponding to the energy interval encompassed by the microcanonical ensemble. This clarifies, expands and justifies remarks made by Schr\"odinger in 1952.

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