Quantum Equilibration under Constraints and Transport Balance

Details Quantum Equilibration under Constraints and Transport Balance Quantum Equilibration under Constraints and Transport Balance

2010-10-15

arxiv.org/abs/1010.3094v3

Physical Review E 83, 31111 (2011)

Physics

Quantum Physics

8 pages, 1 figure, leaner presentation, to appear in PRE

Scientific paper

10.1103/PhysRevE.83.031111

For open quantum systems coupled to a thermal bath at inverse temperature $\beta$, it is well known that under the Born-, Markov-, and secular approximations the system density matrix will approach the thermal Gibbs state with the bath inverse temperature $\beta$. We generalize this to systems where there exists a conserved quantity (e.g., the total particle number), where for a bath characterized by inverse temperature $\beta$ and chemical potential $\mu$ we find equilibration of both temperature and chemical potential. For couplings to multiple baths held at different temperatures and different chemical potentials, we identify a class of systems that equilibrates according to a single hypothetical average but in general non-thermal bath, which may be exploited to generate desired non-thermal states. Under special circumstances the stationary state may be again be described by a unique Boltzmann factor. These results are illustrated by several examples.

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