A probabilistic representation of the ground state expectation of fractional powers of the boson number operator

Fumio Hiroshima, József Lorinczi, Toshimitsu Takaesu

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    We give a formula in terms of a joint Gibbs measure on Brownian paths and the measure of a random-time Poisson process of the ground state expectations of fractional (in fact, any real) powers of the boson number operator in the Nelson model. We use this representation to obtain tight two-sided bounds. As applications, we discuss the polaron and translation invariant Nelson models.

    Original languageEnglish
    Pages (from-to)437-447
    Number of pages11
    JournalJournal of Mathematical Analysis and Applications
    Volume395
    Issue number2
    DOIs
    Publication statusPublished - Nov 15 2012

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Applied Mathematics

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