Emergence of a Wiener process as a result of the quantum mechanical interaction with a macroscopic medium

Raffaella Blasi, Hiromichi Nakazato, Mikio Namiki and Saverio Pascazio

Physica A: Statistical Mechanics and its Applications, 1997, vol. 245, issue 1, 189-211

Abstract: We analyze a modified version of the Coleman-Hepp model, which is able to take into account energy-exchange processes between the incoming particle and the linear array made up of N spin-12 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic (N → ∞) limit. In such and a limit a restricted portion of the total Hilbert space, the particle undergoes a sort of Brownian motion, while the free Hamiltonian of the spin array serves as a Wiener process. No partial trace is computed over the states of the spin system (which plays the role of “reservoir”). The mechanism of appearance of the stochastic process is discussed and contrasted to other noteworthy examples in the literature. The links with van Hove's “λ2T” limits are emphasized.

Keywords: Wiener process; Quantum statistical mechanics; Theory of quantum measurement (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:245:y:1997:i:1:p:189-211

DOI: 10.1016/S0378-4371(97)00043-5

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