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Journal of Physics Condensed Matter

The energy loss rate and dynamical resistivity of hot electrons in semiconductors

Ziwen Ye

Published Sep 20, 1993• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0953-8984/5/38/007

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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 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.
We present a comprehensive review of the most fundamental and practical aspects of thermo-field dynamics (TFD), including some of the most recent developments in the field. To make TFD fully consistent, some suitable changes in the structure of the thermal doublets and the Bogoliubov transformation matrices have been made. A close comparison between TFD and the Schwinger-Keldysh closed time path formalism (SKF) is presented. We find that TFD and SKF are in many ways the same in form; in particular, the two approaches are identical in stationary situations. However, TFD and SKF are quite different in time-dependent nonequilibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theory. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynman diagram recipes, which we will present. We will show that the calculations of two-point functions are simplified, instead of being complicated, by the matrix nature of the formalism. We will present some explicit calculations using TFD, including space-time inhomogeneous situations and the vacuum polarization in equilibrium relativistic QED.
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This paper is a review on the structure of thermo field dynamics (TFD) in which the basic concepts such as the thermal doublets, the quasi-particles and the self-consistent renormalization are presented in detail. A strong emphasis is put on the computational scheme. A detailed structure of this scheme is illustrated by the one-loop calculation in a non-equilibrium time-dependent process. A detailed account of the one-loop calculation has never been reported anywhere. The role of the self-consistent renormalization is explained. The equilibrium TFD is obtained as the long-time limit of non-equilibrium TFD.
This paper has two aims: to provide a physical background of thermo field dynamics (TFD) and to present a review of the recent development of TFD. Macroscopic and thermal phenomena are considered from the unified viewpoint of microscopic quantum field theory. The concepts in quantum field theory such as renormalization and quasi-particles force us to take account of the time-dependence of the trace sum which has been ignored in the usual treatment of thermal situation. It is within this context that we review TFD. The applications of TFD to time-dependent non-equilibrium phenomena (the reservoir model and the self-interacting field model), show that we can obtain the master equation as well as the dissipative coefficient from the self-consistent renormalization condition. At the same time it is also shown that the final Gibbs distribution and the temperature can be derived, which implies that we obtain the equilibrium theory from the non-equilibrium one at the long-time limit.
Thermo-field dynamics (TFD) is a method linking quantum information to statistical thermodynamics, focus directly on the state because the states in the tilde space in TFD play a role of tracer of the initial states by defining an extended density matrix described on the double Hilbert space. The study of quantum entanglement is more complicated, so the TFD method makes it easier, this is the subject of this paper. We use Thermo-field Dynamics method to study entanglement entropies and transition probability of a Photon-electron system between equilibrium with heat bath, and non-equilibrium, based on the dissipative von Neumann equation. Numerically, at the equilibrium and by controlling the system through temperature, we show that entanglement entropies verify the Nernst’s theorem. By increasing the quantization of a single-mode electromagnetic field, entanglement and transition probability decrease. At non-equilibrium, we show that entanglement entropies obey the second law of thermodynamics, and the emission of a photon decrease the probability of detecting the electron at a quantum level