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Survival of quantum effects after decoherence and relaxation


I will review our results on a mathematical dynamical theory for observables for open quantum nonlinear bosonic systems for a very general class of Hamiltonians. We argue that for open quantum nonlinear systems in the “deep” quasi-classical region, important quantum effects survive even after the decoherence and relaxation processes take place. Estimates are derived which demonstrate that for a wide class of nonlinear quantum dynamical systems interacting with the environment, and which are “close” to the corresponding classical systems, quantum effects still remain important and can be observed, for example, in the frequency Fourier spectrum of the dynamical observables and in the corresponding spectral density of the noise. These preliminary estimates are presented for Bose-Einstein condensates, low temperature mechanical resonators, and nonlinear optical systems prepared in large amplitude coherent states.