Random repeated interaction quantum systems

Abstract

We consider a quantum system S interacting sequentially with independent systems E_m, m=1,2,... Before interacting, each E_m is in a possibly random state, and each interaction is characterized by an interaction time and an interaction operator, both possibly random. We prove that any initial state converges to an asymptotic state almost surely in the ergodic mean, provided the couplings satisfy a mild effectiveness condition. We analyze the macroscopic properties of the asymptotic state and show that it satisfies a second law of thermodynamics. We solve exactly a model in which S and all the E_m are spins: we find the exact asymptotic state, in case the interaction time, the temperature, and the excitation energies of the E_m vary randomly. We analyze a model in which S is a spin and the E_m are thermal fermion baths and obtain the asymptotic state by rigorous perturbation theory, for random interaction times varying slightly around a fixed mean, and for small values of a coupling constant.

Statements of Theorem 1.5 and 3.2, and proof of Theorem 3.3 modified. To appear in Comm. Math. Phys

References in corpus (2)

• Decoherence and Thermalization
• Theory of Non-Equilibrium Sationary States as a Theory of Resonances

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• Non-equilibrium states of a photon cavity pumped by an atomic beam
• Mixing properties of the one-atom maser
• Purification in Rapid Repeated Interaction Systems
• Linear response theory and entropic fluctuations in repeated interaction quantum systems
• Repeated Interaction Quantum Systems: van Hove Limits and Asymptotic States
• Markovian Repeated Interaction Quantum Systems
• A resonance theory for open quantum systems with time-dependent dynamics
• Quantum Measurements of Scattered Particles
• Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir