Physics – Quantum Physics
Scientific paper
2004-04-29
Phys. Rev. E 70, 066148 (2004)
Physics
Quantum Physics
12 pages, 5 figures, discussion of results extended, accepted for publication in Phys. Rev. E
Scientific paper
10.1103/PhysRevE.70.066148
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 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.
Hartmann Markus
Hess Ortwin
Mahler Günter
No associations
LandOfFree
Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-567884