Existence of temperature on the nanoscale

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.

Version that appeared in PRL

References in corpus (6)

• Threshold temperature for pairwise and many-particle thermal entanglement in the isotropic Heisenberg model
• Fourier's Law confirmed for a class of small quantum systems
• On testing the violation of the Clausius inequality in nanoscale electric circuits
• Entanglement Energetics at Zero Temperature
• Proximity effect thermometer for local temperature measurements on mesoscopic samples
• Scaling behavior of interactions in a modular quantum system and the existence of local temperature

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