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Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures

Hartmann, M, Mahler, G and Hess, O (2004) Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures Physical Review E, 70 (6).


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We consider a quantum system consisting of a regular chain of elementary subsystems 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(min) also depends on the temperature T! As examples, we apply our analysis to a harmonic chain and different types of Ising spin chains. We discuss various features that show up due to the characteristics of the models considered. For the harmonic chain, which successfully describes thermal properties of insulating solids, our approach gives a quantitative estimate of the minimal length scale on which temperature can exist: This length scale is found to be constant for temperatures above the Debye temperature and proportional to T-3 below.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Physics
Authors :
Hartmann, M
Mahler, G
Date : 1 January 2004
DOI : 10.1103/PhysRevE.70.066148
Additional Information : Published in <i>Physical Review E,</i> Vol. 70, Iss. 6, Pt. 2. Copyright 2004 American Physical Society. Click <a href=>here</a> to access the journal's website.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:08
Last Modified : 31 Oct 2017 13:57

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