Generalized Coleman-Hepp model and quantum coherence

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Abstract
The modified Coleman-Hepp model proposed recently by Nakazato and Pascazio [Phys. Rev. Lett. 70, 1 (1993)] is further generalized so that an ultrarelativistic particle interacts with a linear array of N spins, each of generic magnitude s rather than 1/2. We study the evolution of an appropriately defined measure C(t) of quantum coherence, with t being time, and elucidate the roles played by N and s on the process of decoherence. It is shown that N and s appear in the form of the product Ns in C(∞) at zero temperature, but not in general. It is also noted that the effect of temperature shows up only for s≥1. We study the temperature dependence of C(∞) in detail, and point out in particular that it is not necessarily a monotonic function of temperature. The limiting cases of s→∞ and/or N→∞ are also considered to investigate how the present model tends to a boson model, that is, a model in which the spins are replaced by harmonic oscillators.