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physica status solidi (b)

On the Nonstationary Processes in Exciton Systems

E. A. Hadžiselimović, Momir Marinković, Bratislav S. Tosic

Published Aug 1, 1980• 2 citations
Publisher

Abstract

Abstract In consequence of the nonconservation of excitons, the excitation number operator as well as the exciton pair creation and annihilation operators are expressed as functions of time and of the corresponding stationary operators. The nonstationary pair correlation processes and the nonstationary excitation density fluctuation processes are analysed using the nonstationary operators. It is found that the nonstationary pair correlations are characterized by a specific kind of dissipation that is linearly proportional with time. In contradistinction to stationary processes, the corresponding nonstationary ones, lead to elementary excitations having a double energy: E (nonstationary) = 2E (stationary). It is shown that in contrast to exciton density fluctuations, pair correlations have a tendency of localization related to a lattice point. It is also shown that the exciton non‐statinoary pair correlations are in many respect similar to the density fluctuations that take place in the crystal due to a near slow neutron passage. Finally, a general method for the evaluation of the correlation function, applicable even in the case when the Green's function has a n‐th order pole, is developed in the Appendix.

DOI
10.1002/pssb.2221000206

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•Jul 27, 2017•0 citations
Abstract In consequence of the nonconservation of excitons, the excitation number operator as well as the exciton pair creation and annihilation operators are expressed as functions of time and of the corresponding stationary operators. The nonstationary pair correlation processes and the nonstationary excitation density fluctuation processes are analysed using the nonstationary operators. It is found that the nonstationary pair correlations are characterized by a specific kind of dissipation that is linearly proportional with time. In contradistinction to stationary processes, the corresponding nonstationary ones, lead to elementary excitations having a double energy: E (nonstationary) = 2E (stationary). It is shown that in contrast to exciton density fluctuations, pair correlations have a tendency of localization related to a lattice point. It is also shown that the exciton non‐statinoary pair correlations are in many respect similar to the density fluctuations that take place in the crystal due to a near slow neutron passage. Finally, a general method for the evaluation of the correlation function, applicable even in the case when the Green's function has a n‐th order pole, is developed in the Appendix.
Abstract The equations of motion of a two‐level system and a harmonic oscillator coupled to a dissipative system are discussed; the dissipative system is assumed to consist of a large number of radiation oscillators. Special equations for the determination of the correlation functions of the fluctuation forces are derived under the condition of large time values, for which the atomic system has “forgotten” its initial state. The expectation values of the correlation functions are connected with the damping constant and the population operator of the excited state of the atomic system is in thermal equilibrium. Taking into account the influence of the coherent radiation field on the atomic system, the basic equations for the treatment of the nonstationary Raman scattering by polaritons are derived; the temporal range of validity is discussed. Using a time‐dependent “variable” Fourier transformation, the nonstationary time‐ and spacedependent spectral densities are related to the correlation functions of the fields; here the Wiener‐Khintchine theorem is applied in a nonstationary form. The limiting cases of the stationary scattering process as well as the usually introduced correlators of the slowly varying amplitudes are discussed.
Based on the general theory of the non-equilibrium statistical mechanics, we have discussed the influences of waves on the relaxation processes in macroscopic systems, especially. about the non-exponential asymptotic behaviour of the correlation functions.Because, how to select the representation is important for discussing the dissipative processes in non-equilibrium statistical mechanics, it is desirable to start from the elementary excitation representation. Using the Basic idea of C* algebra theory, we have developed a method for operator expansion, and employed it to express the flow operators in second quantized elementary excitation representation. Taking the residual interaction between the elementary excitations as perturbation in the calculation of the resolvent of the Liouville operator, and using the method of projection operator, a general expression of the non-exponential decaying part of the correlation functions have been obtained.By analysing the procedure of treating the elementary excitation spectrum, we devided the residual interaction into two parts. For pure dissipative mode, taking into account the linear interaction, the main terms of the non-exponential decaying part(t(-d/2) term) were obtained. Detailed analysis shows that, the non-linear interaction (mode-mode coupling) is very small, and leads to a relatively faster decaying process (t(-d) or so), hence it can be neglected.This article emphasizes that, for the wave processes, the local fluctuation correlation, the particle self-correlation and the transport processes are different in nature. Their relative magnitudes (relative to the corresponding quasi-particle parts) may also be quite different.With these general results, we have analysed briefly the relaxation processes in liquid, and made some discussion about the so called mode-mode coupling theory.
Abstract The structural dependence of the longitudinal and transversal relaxation times of a two‐level‐system on the transition frequency ω0 and the temperature of the coupled dissipative system has been derived. The fluctuation operators are explicitely given in dependence on the operators and the constants of the dissipative and the two‐level‐system; the corresponding fluctuation correlators have been calculated. If additionally a time‐dependent external force F(t) acts on the system, then the fluctuation correlators depend on the temporal behavior of this force. Due to this effect the run of nonstationary processes which are initiated by quantum noise (e.g., scattering processes) is affected. These considerations have been applied to the case of spontaneous anti‐Stokes Raman scattering with biharmonic vibrational excitation by ultra‐short light pulses. The strength of the external force, which gives rise to an appreciable time dependence of the correlators, has been estimated.
Equations for correlation functions in nonequilibrium systems are derived using a generalization of the diagrammatic Keldysh method. The four field operators of the correlation function are ordered on a time contour that consists of four axes extending from -\ensuremath{\infty} to +\ensuremath{\infty} and from +\ensuremath{\infty} to -\ensuremath{\infty} (doubled Keldysh contour). For those correlation functions that may be considered as correlation functions of one-particle Green-functions' fluctuations, a closed system of equations is obtained in the case of weak interaction of the particles with the scattering system. Its structure may be related to the Langevin approach: on the left-hand side a linear operator acts on each of two pairs of the correlation-function arguments, each of these two operators being just the operator of the linearized quantum kinetic equation. The expression for the right-hand side of this equation is derived. It has the meaning of the correlation function of extraneous Langevin sources, and the equation may be called the quantum Boltzmann-Langevin equation. In the quasi-classical limit it reduces to the usual Boltzmann-Langevin equation for the particles' distribution-function fluctuations. Possible applications of the method are discussed.
Abstract Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η+ of a generating functional eW=TrU(t0+τ,t0)CS/TrU(t0+τ,t0)C. (In the non-interacting case this yields the n-particle Green’s function as a permanent/determinant of single-particle Green’s functions.) These variational relations yield a symmetric set of multi-particle Green’s function equations. Cumulants and the Linked Cluster Theorem are discussed and the Random Phase Approximation (RPA) is derived variationally. Schwinger’s variational differential formulation of perturbation theories for the Green’s function, self-energy, vertex operator, and also shielded potential perturbation theory, are reviewed. The Langreth Algebra arises from analytic continuation of integration of products of Green’s functions in imaginary time to the real-time axis with time-ordering along the integration contour in the complex time plane. An account of the Generalized Kadanoff-Baym Ansatz is presented.