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Physica A Statistical Mechanics and its Applications

A variation principle in the quantum theory of irreversible processes formulated in a superspace

Masakazu Ichiyanagi

Published Sep 1, 1986• 1 citation
Publisher
DOI
10.1016/0378-4371(86)90097-x

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•Dec 1, 2018•0 citations
A method is proposed for investigating nonequilibrium processes in an arbitrary system under an action of external perturbations. We formulate a new quantum mechanical variation principle, which is valid beyond linear irreversible processes. The definition of our variation functional is made on the basis of our recognition of the importance of a change in the internal energy of the system. In this article, we go beyond the theory of Nakano by developing our new variation principle in the framework of the closed-time-path method by Schwinger. The relationship of the thermodynamical stability criterion to the exact solution of transport problems is discussed.
A reformulation in a superspace is given for Van Hove and Janner’s perturbation theory based on the two-resolvent method for nonequilibrium quantum statistical mechanics. This is attained by introducing an ordered superoperator in the superspace. As an application of our formalism, the derivation of an asymptotic generalized master equation in a Markovian form is given. Further, it is investigated how a quantum subdynamics theory similar to the Brussels school’s one can be formally constructed. Our subdynamics theory is formulated on every eigenspace of a superoperator (the ss-Hamiltonian) of which the eigenvalue is related to the intrinsic parameter E of Van Hove and Janner’s generalized master equation.
Symmetry principles have played a crucial role in the development of modern physics and underpin our most fundamental theories of nature. The present thesis is concerned with the analysis of symmetries in the context of quantum information theory. Whenever a quantum mechanical system interacts with its environment it is subjected to decoherence, a process that is typically irreversible and most generally treated abstractly using the concept of quantum operations. If there is an underlying symmetry principle, additional structures emerge. The central question we address is, What are the consequences of global or local gauge symmetry on the structure of many-body quantum processes?This leads us to a diagrammatic framework of decomposing quantum operations into terms that respond to the symmetry principle in particular ways and respect the causal structures involved. We present two core applications. First, we address the interplay between irreversibility and repeatable use of coherent resources under symmetry constraints. Second, we give an information-theoretic perspective on gauging globally symmetric dynamics to a local symmetry applicable even in the presence of irreversibility and thus it goes beyond the usual Lagrangian formulation. Finally, we analyse the departure from conservation laws under symmetric dynamics subject to decoherence.