The models traditionally used for studying decoherence and dissipation, like Caldeira-Leggett’s, give a good description of the environment, but the uncoupled system is always considered to be very simple (i.e. an harmonic oscillator in most of the cases). We have studied the importance of the dynamics of the system, and we have established that for particles confined by a one-dimensional potential, the width of the eigenstates, given by the coupling to an ohmic environment, is always proportional to their quantum numbers. We have also found that in the two-dimensional case there are noticeable differences en the distribution of level widths according to the nature of the underlying classical mechanics (chaotic or integrable).
Nuclear Magnetic Resonance is a useful technique for the studies of decoherence. Lately, the phenomenon of spin echo has been studied in systems where the spin interact strongly (P. Levstein et al, J. Chem. Phys. 108 , 2718 (1998)). The experimental results indicate that the decoherence rate of these systems is independent of the coupling with the environment, and only fixed by the complexity of the system. We have tried to understand the experimental results from a model built on a one-particle system, whose underlying classical dynamics is fully chaotic, weakly coupled to a quenched environment. We have calculated the Loschmidt’s echo (the reconstruction of a local density after the time reversal of its evolution), in the presence of the perturbation. In a given regime of parameters, we obtain for such an echo an exponential decrease with a decoherence rate asymptotically given by the mean Lyapunov exponent of the classical system, thus independent of the strength of the perturbation. This result, in agreement with the experiments, has been also verified by various numerical simulations.
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