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arXiv:quant-ph/0106006

Decoherence : An irreversible Process

Roland L. Omnes

Published Jun 1, 2001• 14 citations
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Abstract

A wide-ranging theory of decoherence is derived from the quantum theory of irreversible processes, with specific results having for their main limitation the assumption of an exact pointer basis.
DOI
10.48550/arxiv.quant-ph/0106006

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A theory of the decoherence effect can be obtained by applying the projection method in the theory of irreversible processes. The procedure is shown specifically on a model, already general enough for covering all the previously known ones. Decoherence is found to be governed by a master equation, which is particulary simple when the existence of convenient collective observables yields a preferred basis for diagonalization. A criterion is given for the existence of such “microstable” observables. In the case of mechanical macroscopic bodies, this basis exits and is given by the position coordinates in ordinary three-dimensional space for the various parts of the bodies.
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The problem investigated in this paper is einselection, i. e. the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection method in the quantum theory of irreversible processes, which is general enough for giving reliable predictions. This approach leads to a definition (or redefinition) of the coupling with the environment involving only fluctuations. The range of application of perturbation calculus is then wide, resulting in a rather general master equation. Two distinct cases of decoherence are then found: (i) A ``degenerate'' case (already encountered with solvable models) where decoherence amounts essentially to approximate diagonalization; (ii) A general case where the einselected states are essentially classical. They are mixed states. Their density operators are proportional to microlocal projection operators (or ``quasi projectors'') which were previously introduced in the quantum expression of classical properties. It is found at various places that the main limitation in our understanding of decoherence is the lack of a systematic method for constructing collective observables.
The problem investigated in this paper is einselection, i.e., the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection method in the quantum theory of irreversible processes, which is general enough for giving reliable predictions. This approach leads to a definition (or redefinition) of the coupling with the environment involving only fluctuations. The range of application of perturbation calculus is then wide, resulting in a rather general master equation. Two distinct cases of decoherence are then found: (i) a ``degenerate'' case (already encountered with solvable models) where decoherence amounts essentially to approximate diagonalization; (ii) a general case where the einselected states are essentially classical. They are mixed states. Their density operators are proportional to microlocal projection operators (or ``quasiprojectors'') that were previously introduced in the quantum expression of classical properties. It is found at various places that the main limitation in our understanding of decoherence is the lack of a systematic method for constructing collective observables.