On Which Length Scales Can Temperature Exist in Quantum Systems?

Details On Which Length Scales Can Temperature Exist in Quantum Systems? On Which Length Scales Can Temperature Exist in Quantum Systems?

2005-02-02

arxiv.org/abs/cond-mat/0502045v1

J. Phys. Soc. Jpn. 74 (Suppl.), p. 26-29 (2005)

Physics

Condensed Matter

Statistical Mechanics

To appear in: Proceedings of the SPQS conference, J. Phys. Soc. Jpn. 74 (2005) Suppl

Scientific paper

We consider a regular chain of elementary quantum systems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of $n$ subsystems each, and when these groups have the same temperature $T$. While in classical mechanics the validity of this procedure only depends on the size of the groups $n$, in quantum mechanics the minimum group size $n_{\text{min}}$ also depends on the temperature $T $! As examples, we apply our analysis to different types of Heisenberg spin chains.

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