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physica status solidi (b)

Green's Function Method in Thermo‐Field Dynamics: Applications to Plasma and Laser Heated Matter

Zhen Ye

Published Sep 1, 1993• 2 citations
Publisher

Abstract

Abstract This paper, on one hand, is an introduction to thermo‐field dynamics (TFD), on the other hand a derivation of some interesting features of Green's functions in the frame of thermo‐field dynamics. It is proved that in the language of TFD, Green's functions at finite temperature take a very simple form. Through the applications of TFD to many‐body systems it is shown that TFD is a straightforward method in dealing with finite temperature many‐body systems. As an application of Green's function method in TFD, we derive a Kogan‐type formula for the non‐equilibrium dynamic conductivity or laser‐pulse heated condensed matters, where electrons and ions are held at different temperatures.

DOI
10.1002/pssb.2221790114

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Cambridge University Press eBooks•Feb 19, 2009•0 citations
Abstract This paper, on one hand, is an introduction to thermo‐field dynamics (TFD), on the other hand a derivation of some interesting features of Green's functions in the frame of thermo‐field dynamics. It is proved that in the language of TFD, Green's functions at finite temperature take a very simple form. Through the applications of TFD to many‐body systems it is shown that TFD is a straightforward method in dealing with finite temperature many‐body systems. As an application of Green's function method in TFD, we derive a Kogan‐type formula for the non‐equilibrium dynamic conductivity or laser‐pulse heated condensed matters, where electrons and ions are held at different temperatures.
Among many proposed field theories for thermal phenomena, thermo-field dynamics (TFD) is very useful and simple tool to study non-equilibrium many-body systems, especially for a complicated system composed of several subsystems at different thermal equilibria. A complete perturbative calculation scheme in TFD for such systems is presented. In the TFD method, explicit investigation will be made of the energy loss rate (ELR) and resistivity of hot electrons in semiconductors. The ELR formula is shown to be different from that obtained by the Keldysh method. The possible ambiguity in the Keldysh method is discussed.
Abstract We develop a wave‐function‐based method for the simulation of quantum dynamics of systems with many degrees of freedom at finite temperature. The method is inspired by the ideas of Thermo Field Dynamics (TFD). As TFD, our method is based on the doubling of the system's degrees of freedom and thermal Bogoliubov transformation. As distinct from TFD, our method implements the doubling of thermalized degrees of freedom only, and relies upon the explicitly constructed generalized thermal Bogoliubov transformation, which is not restricted to fermionic and bosonic degrees of freedom. This renders the present approach computationally efficient and applicable to a large variety of systems.
Abstract This review provides the fundamental theoretical tools for the development of a complete wave‐function formalism for the study of time‐evolution of chemico‐physical systems at finite temperature. The methodology is based on the non‐equilibrium thermo‐field dynamics (NE‐TFD) representation of quantum mechanics, which is alternative to the commonly used density matrix representation. TFD concepts are extended and integrated with the tensor‐train (TT) numerical tools leading to a novel and powerful theoretical and computational framework for the study of complex quantum dynamical problems. In addition, NE‐TFD techniques are extended to enable the study of dissipative open systems via a new formulation of the hierarchical equations of motion (HEOM) fully integrated with TT methodologies. We demonstrate that the combination of the TFD machinery with computational advantages of TTs results in a powerful theoretical and computational framework for scrutinizing dynamics of complex multidimensional electron‐vibrational systems. We illustrate the validity and the computational advantages of the developed methodologies by applying them to the study of quantum coherence effects in the energy‐transfer processes in antenna systems, to the analysis of fingerprints of vibrational modes in electron‐transfer and charge‐transfer processes in various model and realistic multidimensional molecular systems, as well as to simulation of other fundamental models of physical chemistry. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Theoretical and Physical Chemistry > Statistical Mechanics
The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible to extract information from the system under study, such as the density of states, relaxation times and response functions. Despite its power and versatility, it is known as a laborious and sometimes cumbersome method. Here we introduce the equilibrium Green's functions and the equation-of-motion technique, exemplifying the method in discrete lattices of non-interacting electrons. We start with simple models, such as the two-site molecule, the infinite and semi-infinite one-dimensional chains, and the two-dimensional ladder. Numerical implementations are developed via the recursive Green's function, implemented in Julia, an open-source, efficient and easy-to-learn scientific language. We also present a new variation of the surface recursive Green's function method, which can be of interest when simulating simultaneously the properties of surface and bulk.
The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible to extract information from the system under study, such as the density of states, relaxation times and response functions. Despite its power and versatility, it is known as a laborious and sometimes cumbersome method. Here we introduce the equilibrium Green's functions and the equation-of-motion technique, exemplifying the method in discrete lattices of non-interacting electrons. We start with simple models, such as the two-site molecule, the infinite and semi-infinite one-dimensional chains, and the two-dimensional ladder. Numerical implementations are developed via the recursive Green's function, implemented in Julia, an open-source, efficient and easy-to-learn scientific language. We also present a new variation of the surface recursive Green's function method, which can be of interest when simulating simultaneously the properties of surface and bulk.
In Chapter 3, we introduced a simple but reasonable approximation for the nonequilibrium dynamics of a Bose-condensed gas based on a generalized GP equation coupled to a kinetic equation. In Chapters 4–7, we turn to the question of how to derive such coupled equations for the condensate and noncondensate components in a way that gives a deeper understanding of the ZNG theory. Chapters 4–7 involve an introduction to Green's functions and field theoretic techniques for nonequilibrium problems. These provide the natural language and formalism to deal with the many subtle aspects of a Bose-condensed gas at finite temperatures. These four chapters are fairly technical. This chapter is mainly based on Kadanoff and Baym (1962) and Imamović-Tomasović (2001). Readers who are not interested in these questions can go straight to Chapter 8, which begins the discussion of applications of the ZNG coupled equations given in Chapter 3. Overview of Green's function approach To derive a microscopic theory of the nonequilibrium behaviour of a dilute weakly interacting Bose-condensed gas at finite temperatures, there are several different approaches available in the literature. We will use the wellknown Kadanoff–Baym (KB) nonequilibrium Green's function method. The generalization of this formalism to a Bose-condensed system was first considered by Kane and Kadanoff (1965), whose goal was to derive the Landau two-fluid hydrodynamic equations for a system with a Bose broken symmetry. The general problem consists of how to calculate the nonequilibrium response of a system induced by an external (space- and time-dependent) perturbation. In response to such an external perturbation, many interesting physical phenomena appear, including the excitation of collective modes and various transport processes.