Quantum dynamical effects as a singular perturbation for observables in open quasi-classical nonlinear mesoscopic systems

摘要

We review our results on a mathematical dynamical theory for observables foropen many-body quantum nonlinear bosonic systems for a very general class ofHamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonianprovide a singular "quantum" perturbation for observables in some "mesoscopic"region of parameters. In particular, quantum effects result in secular terms inthe dynamical evolution, that grow in time. We argue that even for open quantumnonlinear systems in the deep quasi-classical region, these quantum effects cansurvive after decoherence and relaxation processes take place. We demonstratethat these quantum effects in open quantum systems can be observed, forexample, in the frequency Fourier spectrum of the dynamical observables, or inthe corresponding spectral density of noise. Estimates are presented forBose-Einstein condensates, low temperature mechanical resonators, and nonlinearoptical systems prepared in large amplitude coherent states. In particular, weshow that for Bose-Einstein condensate systems the characteristic time ofdeviation of quantum dynamics for observables from the corresponding classicaldynamics coincides with the characteristic time-scale of the well-known quantumnonlinear effect of phase diffusion.