The present paper studies the formal aspects of the total-time-ordering-cumulant (TTOC) and the partial-time-ordering-cumulant (PTOC) relaxations of a quantum system, of few degrees of freedom, in weak interaction with a bath, both within and outside the Markovian limit. To this end, the general expressions connecting the matrix elements of the TTOC and PTOC relaxation superoperators with the bath correlation functions are determined. Special attention is paid to two particular cases: a system with a nonequidistant energy spectrum and a system with an equidistant energy spectrum. Discussions revolve mainly around the possibility of applying the secular approximation to the TTOC and PTOC master equations for the off-diagonal matrix elements of the reduceddensity operator of the system.
Given a quantum system of a few degrees of freedom in weak interaction with a bath, the expressions which connect its total-time-ordering-cumulant and partial-time-ordering-cumulant relaxation with the corresponding spectral line shapes of dipolar absorption are deduced. For simplicity we consider a system with a nondegenerate and nonequidistant energy spectrum. A special study in the cases of isolated resonances and of a weak interference effect between resonances is made.
A two-dimensional model is developed to approach the spectral properties of a diatomic polar molecule embedded in a monatomic crystal. This model introduces two rotational degrees of freedom in the limit of small amplitude oscillations. The first one describes the angular (planar) motion of the dipole moment of the molecule. The second one is connected to some collective motion of the nearest atom neighbors of this molecule (called the first shell). The remaining atoms of the crystal act as a thermal bath. This problem is treated first in a classical and then in a quantum version. The experimental data presently available (i.e., for CO molecules trapped in argon crystal) are compared to the theoretical results.
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