We consider the transient dynamics and asymptotic behaviour of a dissipative multilevel quantum system, consisting of a particle in an asymmetric double well potential. The environment is the thermal bath described by the Caldeira-Leggett model with Ohmic spectral density. The time evolution of the system is studied through the populations, the diagonal elements of the reduced density matrix of the system, in the Discrete Variable Representation (i.e. in a spatially localized basis): they are the solution of a Markovian approximated master equation, derived, in the strong coupling regime, from a discretized double path integral with the Feynman-Vernon influence functional.
First we evaluate the populations by varying the damping constant i.e. the strength of the coupling with the environment. At higher damping we find a delayed dynamics, due to the quantum Zeno effect. In particular we observe that the population of the metastable state, located in the higher well, reaches its maximum value at later times as the the coupling strength is increased.
As a second step, we study the mean escape time (MET) from the metastable state, varying both the bath's temperature and coupling strength. We find that for weaker damping the MET exhibits, as a function of the temperature, a nonmonotonic behavior, which resembles the noise enhanced stability (NES) phenomenon observed in several nonlinear classical systems. Conversely, increasing the coupling strength, the MET becomes independent of the temperature (quantum Zeno effect).
We conclude our study considering the presence of an external periodical driving force. We study the time evolution of all populations as a function of the amplitude A and frequency \(\nu\) of the periodical signal, in different damping/temperature regimes. We also analyze the combined effect of the thermal noise and external driving on the long-time behaviour of the system. In particular, we find that both the energy and asymptotic population of the metastable state exhibit a nonmonotonic behaviour as functions of the frequency \(\nu\).