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Thermal Field Theory in Non-Equilibrium States

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

Conventional transport theory is not really applicable to non-equilibrium systems which exhibit strong quantum effects. We present two different approaches to overcome this problem. Firstly we point out how transport equations may be derived that incorporate a nontrivial spectral function as a typical quantum effect, and test this approach in a toy model of a strongly interacting degenerate plasma. Secondly we explore a path to include non-equilibrium effects into quantum field theory through momentum mixing transformations in Fock space. Although the two approaches are completely orthogonal, they lead to the same coherent conclusion. Dedicated to the memory of Hiroomi Umezawa, Friend and mentor, Who had the vision to unify Quantum field theory and statistical mechanics. GSI-Preprint 95-69 Invited contribution to the Umezawa Memorial Volume of Int.J.Mod.Phys. B

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Conventional transport theory is not really applicable to non-equilibrium systems which exhibit strong quantum effects. We present two different approaches to overcome this problem. Firstly we point out how transport equations may be derived that incorporate a nontrivial spectral function as a typical quantum effect, and test this approach in a toy model of a strongly interacting degenerate plasma. Secondly we explore a path to include non-equilibrium effects into quantum field theory through momentum mixing transformations in Fock space. Although the two approaches are completely orthogonal, they lead to the same coherent conclusion. Dedicated to the memory of Hiroomi Umezawa, Friend and mentor, Who had the vision to unify Quantum field theory and statistical mechanics. GSI-Preprint 95-69 Invited contribution to the Umezawa Memorial Volume of Int.J.Mod.Phys. B
The description of thermal or non-equilibrium systems necessitates a quantum field theory which differs from the usual approach in two aspects: 1.The Hilbert space is doubled; 2.Stable quasi-particles do not exist in interacting systems. A mini-review of these two aspects is given from a practical viewpoint including two applications. For thermal states it is shown how infrared divergences occuring in perturbative quasi-particle theories are avoided, whereas for non-equilibrium states a memory effect is shown to arise in the thermalization.
We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multiplier representation, the q -spectral properties and the methods for a direct calculation of the two-time q Green's functions and the related q -spectral density ( q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q=1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q -induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q -induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the q grand-partition function.
The book is devoted to the fundamental aspects of the non-equilibrium statistical mechanics of many-particle systems. The concept of Zubarev's approach, which generalizes the notion of Gibbs' ensembles, and introduces a nonequilibrium statistical operator, providing an adequate basis for dealing with strongly correlated systems that are governed by nonperturbative phenomena, such as the formation of bound states, quantum condensates and the instability of the vacuum. Besides a general introduction to the formalism, this book contains contributions devoted to the applications of Zubarev's method to the solution of modern problems in different fields of physics: transport theory, hydrodynamics, high-energy physics, quark-gluon plasma and hadron production in heavy-ion collisions. The book provides valuable information for researchers and students in these fields, requiring powerful concepts to solve fundamental problems of non-equilibrium phenomena in strongly
We investigate the potential of a quantum Boltzmann equation without momentum conservation, i.e., a kinetic equation for the local distribution function, for describing correlated electron systems out of equilibrium. The equation can be derived either for the dynamics of well-defined quasi- particles, neglecting the momentum conservation of the scattering in the spirit of dynamical mean field theory (DMFT), or, equivalently, as the quantum Boltzmann equation for the local occupied density of states in non-equilibrium DMFT. The approach may thus be applied even in cases where well-defined quasiparticles do not exist, with the main assumption that the spectral function remains rigid under the non-equilibrium evolution. We compare the result of the Boltzmann equation to non-equilibrium DMFT for the case of photo-carrier relaxation in Mott insulators, where processes on very different timescales emerge, i.e., impact ionization, intra-Hubbard-band thermalization, and full thermalization. Since the Boltzmann without momentum conservation is much simpler, it may allow us to simulate more complicated systems, whole devices, and much longer times.
In this paper we study the dynamical properties of a dissipative two-state fermionic system embedded in a phonon bath at finite temperature. The non-equilibrium thermo field dynamics, a real time formalism of thermal quantum field theory, is employed to formulate time dependent energy renormalization and derive transport equations. The renormalization procedures derived in this paper replace the on-shell energy definitions in stationary situations and thus can be used in any situations. The procedure reduces to that of equilibrium situations when there is no time dependence. We show that in a system where there are many coupled stages (with multi-components) quantum fluctuations among these states cannot be eliminated so that the long time limit of non-equilibrium theory does not exactly reproduce an equilibrium theory. The procedures and conclusions obtained also apply to more general systems with multi-components.
Quantum field theory is the application of quantum mechanics to systems with infinitely many degrees of freedom. This 2007 textbook presents quantum field theoretical applications to systems out of equilibrium. It introduces the real-time approach to non-equilibrium statistical mechanics and the quantum field theory of non-equilibrium states in general. It offers two ways of learning how to study non-equilibrium states of many-body systems: the mathematical canonical way and an easy intuitive way using Feynman diagrams. The latter provides an easy introduction to the powerful functional methods of field theory, and the use of Feynman diagrams to study classical stochastic dynamics is considered in detail. The developed real-time technique is applied to study numerous phenomena in many-body systems. Complete with numerous exercises to aid self-study, this textbook is suitable for graduate students in statistical mechanics and condensed matter physics.