Existence of Temperature on the Nanoscale

2003/12/31 by Michael Hartmann, Michael J. Hartmann, Guenter Mahler +2 · 5 citations
Materials Science · Physics and Astronomy · #Graphene research and applications #Thermal properties of materials #Topological Materials and Phenomena #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.1103/physrevlett.93.080402

published as Phys. Rev. Lett. 93, 080402 (2004) · Version that appeared in PRL

openalex publication_date 2004/08/19 · arxiv created 2004/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a regular chain of quantum particles with nearest neighbor interactions in a canonical state with temperature T. We analyze 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\ensuremath∝T^\ensuremath-3 below.

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