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Michael Hartmann

Publications and source records attributed to Michael Hartmann.

21 records · Page 2Linked to original sources
arXiv2005

On Which Length Scales Can Temperature Exist in Quantum Systems?

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.

cond-mat.stat-mech↗
arXiv2004

Existence of temperature on the nanoscale

We consider a regular chain of quantum particles with nearest neighbour interactions in a canonical state with temperature $T$. We analyse the conditions under which the state factors into a product of canonical density matrices with respect to groups of $n$ particles each and under which these groups have the same temperature $T$. In quantum mechanics the minimum group size $n_{min}$ depends on the temperature $T$, contrary to the classical case. We apply our analysis to a harmonic chain and find that $n_{min} = const.$ for temperatures above the Debye temperature and $n_{min} \propto T^{-3}$ below.

quant-ph↗