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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)
Level shift operators describe the second order displacement of eigenvalues under perturbation. They play a central role in resonance theory and ergodic theory of open quantum systems at positive temperatures. We exhibit intrinsic properties of level shift operators, properties which stem from the structure of open quantum systems at positive temperatures… (More)
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.
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)
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)
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 which are under the influence of some local, time-dependent external forces. We are interested in asymptotic properties of such systems, as Λ increases to all of R. It might… (More)
We study the stationary states of a quantum mechanical system describing an atom coupled to black-body radiation at positive temperature. The stationary states of the non-interacting system are given by product states, where the particle is in a bound state corresponding to an eigenvalue of the particle Hamiltonian, and the field is in its equilibrium… (More)
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)
We present a rigorous analysis of the phenomenon of decoherence for general N-level systems coupled to reservoirs of free massless bosonic fields. We apply our general results to the specific case of the qubit. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.