Non-Markovian effects in dynamics of exciton-polariton Bose condensates
Formation of exciton-polariton condensate due to incoherent pumping of an excitonic reservoir is considered. The condensate dynamics is governed by a system of stochastic integro-differential equations of Langevin's type corresponding to the model developed by Elistratov and Lozovik . Attention is concentrated on non-Markovian interaction of the condensate with the excitonic and photonic reservoirs. It is shown that dynamical memory caused by the non-Markovian interaction qualitatively changes the condensate behavior as compared to the Markovian regime. In particular, it diminishes the threshold of pumping strength for the condensate emergence. Also, it is found that the non-Markovian regime leads to relaxation oscillations corresponding to population exchange between the condensate and the excitonic reservoir. Increasing of incoherent pumping strength leads to chaos of relaxation oscillations that is accompanied by random-like transitions between the lower and upper polaritonic states.