Existence of temperature on the nanoscale

Details Existence of temperature on the nanoscale Existence of temperature on the nanoscale

2003-12-30

arxiv.org/abs/quant-ph/0312214v4

Phys. Rev. Lett. 93, 080402 (2004)

Physics

Quantum Physics

Version that appeared in PRL

Scientific paper

10.1103/PhysRevLett.93.080402

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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