Scaling behavior of interactions in a modular quantum system and the existence of local temperature

Details Scaling behavior of interactions in a modular quantum system and the existence of local temperature Scaling behavior of interactions in a modular quantum system and the existence of local temperature

2003-12-18

arxiv.org/abs/quant-ph/0312158v1

Europhys. Lett. 65, 613-619 (2004)

Physics

Quantum Physics

7 pages, accepted for publication in Europhysics Letters

Scientific paper

10.1209/epl/i2003-10166-3

We consider a quantum system of fixed size consisting of a regular chain of $n$-level subsystems, where $n$ is finite. Forming groups of $N$ subsystems each, we show that the strength of interaction between the groups scales with $N^{- 1/2}$. As a consequence, if the total system is in a thermal state with inverse temperature $\beta$, a sufficient condition for subgroups of size $N$ to be approximately in a thermal state with the same temperature is $\sqrt{N} \gg \beta \bar{\delta E}$, where $\bar{\delta E}$ is the width of the occupied level spectrum of the total system. These scaling properties indicate on what scale local temperatures may be meaningfully defined as intensive variables. This question is particularly relevant for non-equilibrium scenarios such as heat conduction etc.

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