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

Raffaella Blasi, Hiromichi Nakazato, Mikio Namiki, Saverio Pascazio

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    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-1/2 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic (N → ∞) limit. In such a limit and 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.

    Original languageEnglish
    Pages (from-to)189-221
    Number of pages33
    JournalPhysica A: Statistical Mechanics and its Applications
    Volume245
    Issue number1-2
    Publication statusPublished - 1997 Oct 15

    Fingerprint

    Wiener Process
    Interaction
    Linear Array
    Weak Coupling
    Spin Systems
    stochastic processes
    interactions
    linear arrays
    Hilbert space
    Sort
    Brownian motion
    Stochastic Processes
    energy transfer
    Trace
    Partial
    Energy
    Model

    Keywords

    • Quantum statistical mechanics
    • Theory of quantum measurement
    • Wiener process

    ASJC Scopus subject areas

    • Mathematical Physics
    • Statistical and Nonlinear Physics

    Cite this

    Emergence of a Wiener process as a result of the quantum mechanical interaction with a macroscopic medium. / Blasi, Raffaella; Nakazato, Hiromichi; Namiki, Mikio; Pascazio, Saverio.

    In: Physica A: Statistical Mechanics and its Applications, Vol. 245, No. 1-2, 15.10.1997, p. 189-221.

    Research output: Contribution to journalArticle

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