On Which Length Scales Can Temperature Exist in Quantum Systems?

Abstract

We consider a regular chain of elementary quantum systems 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 different types of Heisenberg spin chains.

To appear in: Proceedings of the SPQS conference, J. Phys. Soc. Jpn. 74 (2005) Suppl

References in corpus (7)

• Entanglement in quantum critical phenomena
• Existence of temperature on the nanoscale
• Fourier's Law confirmed for a class of small quantum systems
• Entanglement Energetics at Zero Temperature
• Gaussian quantum fluctuations in interacting many particle systems
• Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures
• Scaling behavior of interactions in a modular quantum system and the existence of local temperature