dorsal/arxiv
View SchemaNano-Thermodynamics: On the minimal length scale for the existence of temperature
| Authors | M. Hartmann, G. Mahler, O. Hess |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502023 |
| URL | https://arxiv.org/abs/quant-ph/0502023 |
| DOI | 10.1016/j.physe.2005.05.002 |
Abstract
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 $n_{\text{min}}$ also depends on the temperature $T $! As examples, we apply our analysis to a harmonic chain and an Ising spin chain. 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 first 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.
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"abstract": "We consider a quantum system consisting of a regular chain of elementary\nsubsystems with nearest neighbor interactions and assume that the total system\nis in a canonical state with temperature $T$. We analyze under what condition\nthe state factors into a product of canonical density matrices with respect to\ngroups of $n$ subsystems each, and when these groups have the same temperature\n$T$. While in classical mechanics the validity of this procedure only depends\non the size of the groups $n$, in quantum mechanics the minimum group size\n$n_{\\text{min}}$ also depends on the temperature $T $! As examples, we apply\nour analysis to a harmonic chain and an Ising spin chain. We discuss various\nfeatures that show up due to the characteristics of the models considered. For\nthe harmonic chain, which successfully describes thermal properties of\ninsulating solids, our approach gives a first quantitative estimate of the\nminimal length scale on which temperature can exist: This length scale is found\nto be constant for temperatures above the Debye temperature and proportional to\n$T^{-3}$ below.",
"arxiv_id": "quant-ph/0502023",
"authors": [
"M. Hartmann",
"G. Mahler",
"O. Hess"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.physe.2005.05.002",
"title": "Nano-Thermodynamics: On the minimal length scale for the existence of temperature",
"url": "https://arxiv.org/abs/quant-ph/0502023"
},
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