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We consider quantum systems consisting of a " small " system coupled to two reservoirs (called open systems). We show that such a system has no equilibrium states normal with respect to any state of the decoupled system in which the reservoirs are at different temperatures, provided that either the temperatures or the temperature difference divided by the… (More)

- M. Merkli, I. M. Sigal, G. P. Berman
- 2007

We present a rigorous analysis of the phenomenon of decoherence for general N −level systems coupled to reservoirs. The latter are described by free massless bosonic fields. We apply our general results to the specific cases of the qubit and the quantum register. We compare our results with the explicitly solvable case of systems whose interaction with the… (More)

- M. Merkli, I. M. Sigal
- 1999

In this paper we further develop a general theory of metastable states resulting from perturbation of unstable eigenvalues. We apply this theory to many-body Schrödinger operators and to the problem of quasiclassical tunneling.

This note is dedicated to H. Ezawa on the occasion of his 70 th birthday, with respect and affection. 1 Time-dependent thermodynamic processes In this note we describe some results concerning non-relativistic quantum systems at positive temperature and density confined to macroscopically large regions, Λ, of physical space R 3 which are under the influence… (More)

We study a small quantum system (e.g. a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states, parametrized by two numbers T1, T2 (" reservoir temperatures "). If T1 = T2, then these states are non-equilibrium,… (More)

The general theory of simple transport processes between quantum mechanical reservoirs is reviewed and extended. We focus on thermoelectric phenomena, involving exchange of energy and particles. The theory is illustrated on the example of two reservoirs of free fermions coupled through a local interaction. We construct a stationary state and determine… (More)

- Marco Merkli
- 2000

The method of positive commutators, developed for zero temperature problems over the last twenty years, has been an essential tool in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive temperatures, i.e. to non-equilibrium quantum statistical mechanics. We use the positive commutator technique to give an… (More)

The property of " return to equilibrium " is established for a class of quantum-mechanical models describing interactions of a (toy) atom with black-body radiation, or of a spin with a heat bath of scalar bosons, under the assumption that the interaction strength is sufficiently weak. For models describing the first class of systems, our upper bound on the… (More)

A quantum system S interacts in a successive way with elements E of a chain of identical independent quantum subsystems. Each interaction lasts for a duration τ and is governed by a fixed coupling between S and E. We show that the system, initially in any state close to a reference state, approaches a repeated interaction asymptotic state in the limit of… (More)

Let Ψ n be a product of n independent, identically distributed random matrices M , with the properties that Ψ n is bounded in n, and that M has a deterministic (constant) invariant vector. Assuming that the probability of M having only the simple eigenvalue 1 on the unit circle does not vanish, we show that Ψ n is the sum of a fluctuating and a decaying… (More)