Self-induced avalanches in relaxing media

A theory of boson avalanches (self-induced waves) has been constructed with allowance for longitudinal relaxation. It is shown that inclusion of longitudinal relaxation requires a completely different approach to the theory of superradiance than that taken previously. For the first time an equation is derived for an avalanche with allowance for longitudinal and transverse relaxation. Numerical solution of this equation makes It possible to establish all the distinctive features of a coherent self-induced wave under the conditions of the action of relaxation mechanisms. An inversion effect is found to occur in the action of longitudinal and transverse relaxation on the delay parameter of a self-induced wave, i.e., the superradiance delay time. Analytic expressions are found of the ensemble-averaged delay time of an avalanche and the relative fluctuations of the delay time as a function of irreversible phase relaxation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 81–86, September, 1986.