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NONEQUILIBRIUM STEADY STATES FOR A HARMONIC OSCILLATOR INTERACTING WITH TWO BOSE FIELDS - STOCHASTIC LIMIT APPROACH AND C* ALGEBRAIC APPROACH

S. TASAKI, Luigi Accardi

Published Mar 1, 2006• 1 citation
Publisher

Abstract

Recently, nonequilibrium steady states (NESS) are intensively studied by several methods.In this article, NESS of a harmonic oscillator interacting with two freeboson reservoirs at different temperatures and/or chemical potentials are studied by the stochastic limit approach and the C* algebraic approach.Their interrelation is investigated as well.

DOI
10.1142/9789812774491_0028

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The fluctuations of macroscopic observables in quantum systems which are in a nonequilibrium steady state are studied rigorously in the thermodynamic limit. In particular, the nonequilibrium steady state (NESS) of a quantum spin system that is composed of two infinite reservoirs at different temperatures coupled in a bounded region is considered. Under suitable assumptions on the interaction and the asymptotics of the fluctuations, a nonequilibrium central limit theorem for the fluctuations of the NESS expectation value of the empirical average of observables is proven by showing the analyticity of the corresponding moment generating function in a neighbourhood of the origin using the cluster expansion method. Furthermore, the large deviation principle is proven for a class of observables by establishing the existence and differentiability of the corresponding moment generating function.
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The quasi-static evolution of steady states far from equilibrium is investigated from the point of view of quantum statistical mechanics. As a concrete example of a thermodynamic system, a two-level quantum dot coupled to several reservoirs of free fermions at different temperatures is considered. A novel adiabatic theorem for unbounded and nonnormal generators of evolution is proven and applied to study the quasi-static evolution of the nonequilibrium steady state (NESS) of the coupled system. © Birkhäuser Verlag Basel/Switzerland 2007.
This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state (NESS) conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures T 1 > T 2. For constant bilinear inter-oscillator coupling studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary temperatures even for strong coupling. We find that the valid entanglement criterion in general is not a function of the bath temperature difference, in contrast to thermal transport in the same NESS setting [1]. Thus lowering the temperature of one of the thermal baths does not necessarily help to safeguard the entanglement between the oscillators. Indeed, quantum entanglement will disappear if any one of the thermal baths has a temperature higher than the critical temperature T c, defined as the temperature above which quantum entanglement vanishes. With the Langevin equations derived we give a full display of how entanglement dynamics in this system depends on T 1, T 2, the inter-oscillator coupling and the system-bath coupling strengths. For weak oscillator-bath coupling the critical temperature T c is about the order of the inverse oscillator frequency, but for strong oscillator-bath coupling it will depend on the bath cutoff frequency. We conclude that in most realistic circumstances, for bosonic systems in NESS with constant bilinear coupling, ‘hot entanglement’ is largely a fiction.