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The European Physical Journal A

The Argyres-Kelley approach to the master equation and an extended theory of superradiance

P. Schwendimann

Published Sep 1, 1974• 5 citations
Publisher
DOI
10.1007/bf01677930

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A time-convolutionless expression for the quantal equation of motion for the linear response of a system in contact with a heat bath to an external, time-varying driving field is derived from the quantal Liouville equation of motion for the total system. This is done by renormalizing the memory effect by the method of Shibata, Takahashi and Hashitsume. It has a form convenient for the perturbational expansion. It is shown that this equation coincides with the time-convolution equation of Argyres and Kelley in their Markoffian approximation in the narrowing limit and in the lowest Born approximation for the system-bath interaction. This equation is expanded up to fourth order in powers of the system-bath interaction.
A master equation of a Laser system is presented from a dynamical point of .It is assumed that the Laser system is coupled with other independent subsystems.They p!ay a role as distinct reservoirs in our Laser system.As an application of this approach, the master equation is obtained for a system that corresponds to a Laser model considered by Scully-Lamb.The equation obtained heye includes the dynamical effect of an atomic system, i. e., atomic coherence. gl. IntroductionRecently various statistical mechanical theories have been developed by many authors in order to explain the properties of Laser systems.Especially, Haken et al.i) presented a model in which the Laser system is in contact with several independent heat reservoirs of different temperatures, undergoing irreversible processes among them.In particular, Weidlich and Haake2) showed the existence of the lasing state which might be considered as a revelation of the phase change in an open system by the method of a master equation similar to the Wangnness-Bloch equation of nuclear spin induction.In this theory the relaxation processes are lntroduced phenomenologica!ly in the master equation, without taking into account its detailed derivation from a microscopic point of view.On the other hand, Scully-Lamb3) independently developed a quantal theory of Laser, which is an extention of the famous semiclassic theory by Lamb, and obtained the statistical properties of radiation field of Laser systems.In g2, one of the purposes of this paper is presented.Here, from a dynamical point of view, a generalized master equation was setforth for a system coupled with several independent subsystems.Thus the discussion in g2 is analogous to Argyres' theory") for the relaxation of spin system, in wh!ch Wangness-Bloch equation was derived from a dynamical point of view.The second purpose of this paper is to present a generalized master equation corresponding to the Laser system considered by Scully-Lamb as described in g3.gZ. Derivation of the master equation Now let us consider the following system.The system with which we are mainly concerned shali be called A and is described by dynamical variables {ai}.