On a model for quantum friction III. Ergodic properties of the spin-boson system
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In this paper, the authors investigated the dynamics of a 2-level atom coupled to a massless bosonic field at positive temperature and proved that, at small coupling, the combined quantum system approaches thermal equilibrium.Abstract:
We investigate the dynamics of a 2-level atom (or spin 1/2) coupled to a mass-less bosonic field at positive temperature. We prove that, at small coupling, the combined quantum system approaches thermal equilibrium. Moreover we establish that this approach is exponentially fast in time. We first reduce the question to a spectral problem for the Liouvillean, a self-adjoint operator naturally associated with the system. To compute this operator, we invoke Tomita-Takesaki theory. Once this is done we use complex deformation techniques to study its spectrum. The corresponding zero temperature model is also reviewed and compared. From a more philosophical point of view our results show that, contrary to the conventional wisdom, quantum dynamics can be simpler at positive than at zero temperature.read more
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Quantum electrodynamics of confined nonrelativistic particles
TL;DR: In this article, a system of finitely many nonrelativistic, quantum mechanical electrons bound to static nuclei is considered, and the electrons are minimally coupled to the quantized electromagnetic field; but an ultraviolet cutoff on the electromagnetic vector potential appearing in covariant derivatives, and interactions between the radiation field and electrons localized very far from the nuclei are turned off.
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Return to equilibrium
TL;DR: In this article, an atom with finitely many energy levels in contact with a heat bath consisting of photons (blackbody radiation) at a temperature T > 0 was studied, and it was shown that an arbitrary initial state that is normal with respect to the equilibrium state of the uncoupled system at temperature T converges to an equilibrium state at the same temperature, as time tends to +∞ (return to equilibrium).
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Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics
TL;DR: In this paper, a model for heat conduction consisting of a chain of non-linear oscillators coupled to two Hamiltonian heat reservoirs at different temperatures was studied and the authors established existence of a Liapunov function for the chain dynamics and showed exponentially fast convergence of the dynamics to a unique stationary state.
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Mathematical Theory of Non-Equilibrium Quantum Statistical Mechanics
TL;DR: In this paper, the authors review and further develop a mathematical framework for non-equilibrium quantum statistical mechanics and introduce notions of entropy production and heat fluxes, and study their properties in a model of a small finite quantum system coupled to several independent thermal reservoirs.
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On a model for quantum friction. II. Fermi's golden rule and dynamics at positive temperature
TL;DR: In this article, the dynamics of an N-level system linearly coupled to a field of massless bosons at positive temperature were investigated using complex deformation techniques, and time-dependent perturbation theory was developed.
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Dynamics of the dissipative two-state system
Anthony J. Leggett,Sudip Chakravarty,Alan T. Dorsey,Matthew P. A. Fisher,Anupam Garg,Wilhelm Zwerger +5 more
TL;DR: In this article, a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment is presented, and an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of dissipative environments to the spin-boson problem is given.