Abstract

We obtain correct master equation for a driven non-degenerate quantum system subject to a time-dependent interaction with a reservoir. To derive this equation, we apply for the first time the relined mathematical technique of complex spectral decomposition to a general time-dependent N-level Friedrichs-Fano hamiltonian. A total hamiltonian has been exactly diagonalized in such a way that al each moment there appear discrete decaying (quasi) states, |ϕ_α(t)〉 (and$〈{\tilde{\varphi }}_{\text{α}}\left(t\right)|\ne |{\varphi }_{\text{α}}\left(t\right)〉$; α = 1,…,N that are related directly to the initial (quasi) energy states of a driven dynamical subsystem, but have got complex (quasi)energies E_α(t) = hω_α(t) due to dressing by a continuum, In fact, these generalized states are distributions and lay in the so-called rigged Hilbert space, so that the non-zero Imω_α are not in conflict with the fact that the total hamiltonian is hermitian in the initial (more narrow) Hilbert space of regular wavefunctions.

© 1996 IEEE