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Existence of temperature on the nanoscale

Michael Hartmann·Guenter Mahler·Ortwin Hess
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Abstract

We consider a regular chain of quantum particles with nearest neighbour interactions in a canonical state with temperature $T$. We analyse the conditions under which the state factors into a product of canonical density matrices with respect to groups of $n$ particles each and under which these groups have the same temperature $T$. In quantum mechanics the minimum group size $n_{min}$ depends on the temperature $T$, contrary to the classical case. We apply our analysis to a harmonic chain and find that $n_{min} = const.$ for temperatures above the Debye temperature and $n_{min} \propto T^{-3}$ below.

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Michael Hartmann, Guenter Mahler, Ortwin Hess. 2004-09-08. Existence of temperature on the nanoscale. https://doi.org/10.1103/physrevlett.93.080402

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