Quantum Equilibration under Constraints and Transport Balance

Abstract

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.

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

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• Counting statistics of collective photon transmissions
• Adaptive machine and its thermodynamic costs
• Dynamics of interacting transport qubits
• Entangling color centers via magnon-antimagnon pair creation
• Equation of motion method for Full Counting Statistics: Steady state superradiance
• Quantum thermochemical engines
• Open quantum systems and the grand canonical ensemble
• Breaking conservation law enables steady-state entanglement out of equilibrium
• Finite speed heat transport in a quantum spin chain after quenched local cooling