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Condensed Matter Physics

APPLICATION OF NETFD TO THE SYSTEM OF A LOCALIZED-ELECTRON AND PHONONS

Arimitsu, Arimitsu

Published Jan 1, 2000• 0 citations
Publisher

Abstract

The optical absorption spectrum in an analytically solvable model of a localized-electron and phonons is investigated using the operator algebra in NonEquilibrium Thermo Field Dynamics (NETFD).The position and the curvature of the adiabatic potentials for the ground and for the excited electronic states are assumed to differ from each other.The structures of the absorption spectra are investigated for various situations including the cases of slow modulation and of fast one.The method of NETFD is explained in order to be self-contained in solving the problem.

DOI
10.5488/cmp.3.1.103

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The optical absorption spectrum in an analytically solvable model of a localized-electron and phonons is investigated using the operator algebra in NonEquilibrium Thermo Field Dynamics (NETFD).The position and the curvature of the adiabatic potentials for the ground and for the excited electronic states are assumed to differ from each other.The structures of the absorption spectra are investigated for various situations including the cases of slow modulation and of fast one.The method of NETFD is explained in order to be self-contained in solving the problem.
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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 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.
We address the question whether observables of an exactly solvable model of electrons coupled to (optical) phonons relax into large time stationary state values and investigate if the asymptotic expectation values can be computed using a stationary density matrix. Two initial nonequilibrium situations are considered. A sudden quench of the electron-phonon coupling, starting from the noninteracting canonical equilibrium at temperature TTT in the electron as well as in the phonon subsystems, leads to a rather simple dynamics. A richer time evolution emerges if the initial state is taken as the product of the phonon vacuum and the filled Fermi sea supplemented by a highly excited additional electron. Our model has a natural set of constants of motion, with as many elements as degrees of freedom. In accordance with earlier studies of such type of models, we find that expectation values which become stationary can be described by the density matrix of a generalized Gibbs ensemble which differs from that of a canonical ensemble. For the model at hand, it appears to be evident that the eigenmode occupancy operators should be used in the construction of the stationary density matrix.