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Progress of Theoretical Physics

Non-Equilibrium Thermo Field Dynamics

Toshihico Arimitsu, Hiroomi Umezawa

Published Jan 1, 1987• 157 citations
Publisher

Abstract

A fundamental framework for the construction of a quantum field theory for open systems, which will be called non-equilibrium thermo field dynamics (NETFD), is built upon two concepts. One is the thermal state in the thermal-Liouville space, by which the quasi-particle superoperator is introduced generally from the thermal state condition. The other is the coarse graining which is realized by projecting out some partial space from the complete thermal-Liouville space, and by which the dissipation is introduced. Most properties of the usual quantum field theory (e.g., the operator formalism, the time-ordered formulation of the Green’s functions, the Feynman diagram method in real time, etc.) are preserved in NETFD. The entropy for the nonequilibrium state can be also introduced in NETFD.

DOI
10.1143/ptp.77.32

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A fundamental framework for the construction of a quantum field theory for open systems, which will be called non-equilibrium thermo field dynamics (NETFD), is built upon two concepts. One is the thermal state in the thermal-Liouville space, by which the quasi-particle superoperator is introduced generally from the thermal state condition. The other is the coarse graining which is realized by projecting out some partial space from the complete thermal-Liouville space, and by which the dissipation is introduced. Most properties of the usual quantum field theory (e.g., the operator formalism, the time-ordered formulation of the Green’s functions, the Feynman diagram method in real time, etc.) are preserved in NETFD. The entropy for the nonequilibrium state can be also introduced in NETFD.
The generating functional formulation of non-equilibrium thermo field dynamics (NETFD) is given. The results are compared with those obtained by Schwinger who introduced the forward and backward time axes in order to include the dissipation effect. The relation of NETFD to other closed time-path formalisms is also given. As NETFD is an operator formalism of quantum field theory for non-equilibrium situations, one can say that the usual Green's function formalisms are well founded by NETFD through the comparison given in this paper.
A fundamental framework of thermo field dynamics (TFD), including non-equilibrium situations as well as equilibrium stuations, is formulated through a compact axiomatic form, in which no reference to reservoirs is needed, by considering quantum fields. The semi-free quantum fields in TFD are constructed in a way parallel to that of the usual quantum field theory without thermal degrees of freedom, i.e. in terms of orthonormalization relations among wave functions, the sum rule for wave functions, the divisor operator and the particle-antiparticle conjugation (C-conjugation).
The framework of the canonical operator formalism for dissipative and/or stochastic quantum systems named non-equilibrium thermo field dynamics (NETFD) is presented in a self-contained manner. As an application of the formalism, a model of noisy-channel which is under the influence of spatially correlated quantum Brownian motion is investigated within the framework of NETFD. It is shown that errors due to spatially correlated noises can be corrected by the quantum error-correction code and error-correction procedure prepared for those for independent noises.