Quantum Dynamical Effects as a Singular Perturbation for Observables in Open QuasiClassica.pdf

Quantum Dynamical Effects as a Singular Perturbation for Observables in Open Quasi-Classical Nonlinear Mesoscopic Systems G.P. Berman and D.A.R. Dalvit Theoretical Division, MS B213, Los Alamos 8 National Laboratory, Los Alamos, NM 87545, USA 0 0 2 F. Borgonovi n a Dipartimento di Matematica e Fisica, Universit´a Cattolica, J 9 via Musei 41, 25121 Brescia, Italy and 2 3 INFN, Sezione di Pavia, Italy v 4 (Dated: February 1, 2008) 2 0 Abstract 4 0 We review our results on a mathematical dynamical theory for observables for open many- 6 0 / body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that h p non-quadratic (nonlinear) terms in a Hamiltonian provide a singular “quantum” perturbation for - t n observables in some “mesoscopic” region of parameters. In particular, quantum effects result in a u secular terms in the dynamical evolution, that grow in time. We argue that even for open quan- q : v tum nonlinear systems in the deep quasi-classical region, these quantum effects can survive after i X decoherence and relaxation processes take place. We demonstrate that these quantum effects in r a open quantum systems can be observed, for example, in the frequency Fourier spectrum of the dynamical observables, or in the corresponding spectral density of noise. Estimates are presented