  In this work we reconsider the problem discussed by Caldeira and Leggett
(CL), and generalize their results for a quantum oscillator coupled bilinearly
to a reservoir with dense discrete spectrum of harmonic oscillators. We show
that for such systems dynamic evolution of any state of the CL Hamiltonian
consists of recurrence cycles with partial revivals of the initial state
amplitude. This revival or Loschmidt echo appears in each cycle due to reverse
(from the reservoir) transitions (not existing in the limit of a macroscopic
bath). Width and number of the Loschmidt echo components increase with the
recurrence cycle number, eventually leading to irregular, stochastic-like time
evolution. Standard for continuous spectrum thermal bath CL dynamics
dissipative dynamics (exponential decay) takes place only within the initial
cycle. In terms of the effective CL Hamiltonian, where the reservoir degrees of
freedom are integrated out, our results mean oscillatory (time periodic)
behavior of the effective mass. Only in the initial cycle, we found the known
for CL Hamiltonian exponential in time increase of the effective mass. We do
believe that the basic ideas inspiring our work can be applied to a large
variety of interesting nano-systems and molecular complexes.
