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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Exactly solvable quantum macroscopic motions and decoherence mechanism based on many quantum-mechanical space theory

T. Kobayashi

Published Feb 1, 1996• 2 citations
Publisher
DOI
10.1007/bf02724647

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•Jan 1, 1996•0 citations
We revisit the quantum decoherence problem of the center of mass motion of a macroscopic object, which is modelled as a one-dimensional atom chain. Induced by the coupling of the center of mass (C.M) motion with the inner degrees of freedom, this inner-environment-induced decoherence is reflected by the localization of the C.M wave packet. We show that, the C.M motion is coupled to the inner states only when the chain has interaction with the external potential. This result provides a realistic mechanism for the analysis of the inner-environment-induced localization of a macroscopic object.
We analyze a modified version of the 'AgBr' Hamiltonian, solve exactly the equations of motion in terms of SU(2) coherent states, and study the weak-coupling, macroscopic limit of the model, obtaining an exponential behavior at all times. The asymptotic dominance of the exponential behavior is representative of a purely stochastic evolution and can be derived quantum mechanically in the so-called van Hove's limit (which is a weak-coupling, macroscopic limit). At the same time, a temporal behavior of the exponential type, yielding a 'probability dissipation' is closely related to dephasing ('decoherence') effects and one can expect a close connection with a dissipative and irreversible behavior. We stress the central relevance of the problem of dissipation to the quantum measurement theory and to the general topic of decoherence.