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On Which Length Scales Can Temperature Exist in Quantum Systems?

Michael Hartmann·Guenter Mahler·Ortwin Hess
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Abstract

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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Michael Hartmann, Guenter Mahler, Ortwin Hess. 2005-02-02. On Which Length Scales Can Temperature Exist in Quantum Systems?. https://doi.org/10.1143/jpsjs.74s.26

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