Hannover 2010 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 10: Quantum Gases: Bosons II
Q 10.9: Talk
Monday, March 8, 2010, 18:30–18:45, E 001
Cold and hot finite quantum systems in contact: energy flow and temperature equilibration — •Alexey V. Ponomarev, Sergey Denisov, and Peter Hanggi — Institute of Physics, University of Augsburg, Germany
Relaxation toward the canonical state is commonly attributed to a situation where a small system of interest is coupled to a huge one (the Universe, a heat bath, etc). Here we focus on the case of two identical quantum systems composed of a finite number of bosons. Both the systems are initially prepared in Gibbs states at different temperatures, ρA(TA) and ρB(TB), and isolated from the external environment. Then the systems are brought into a thermal contact.
We demonstrate that the energy starts to flow from a “hot” system to a “cold” one until the system energies equilibrate. There are two possible distinguishable relaxation regimes. In the first regime, each of the systems evolves toward the state characterized by the arithmetic average of their initial density matrices, ρA(TA)/2+ρB(TB)/2. The second regime substantiates what we would expect from the equilibration of two big, classical bodies: (i) both the quantum systems relax to the thermal (Boltzmann) states with equal temperatures; and (ii) the relaxation process has a quasistatic character, i. e. each system passes through a chain of intermediate thermal (Boltzmann) states. With that, we show for the first time that a non-equilibrium thermodynamic process can be reproduced within an isolated finite bipartite quantum system.