Abstract:
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.