Spin-boson model through a Poisson-driven stochastic process

Masao Hirokawa, Fumio Hiroshima, József Lőrinczi

    Research output: Contribution to journalArticlepeer-review

    16 Citations (Scopus)

    Abstract

    We give a functional integral representation of the semigroup generated by the spin-boson Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a method of constructing Gibbs path measures indexed by the full real line which can be applied also to more general stochastic processes with jump discontinuities. Using these tools we then show existence and uniqueness of the ground state of the spin-boson, and analyze ground state properties. In particular, we prove super-exponential decay of the number of bosons, Gaussian decay of the field operators, derive expressions for the positive integer, fractional and exponential moments of the field operator, and discuss the field fluctuations in the ground state.

    Original languageEnglish
    Pages (from-to)1165-1198
    Number of pages34
    JournalMathematische Zeitschrift
    Volume277
    Issue number3-4
    DOIs
    Publication statusPublished - Aug 2014

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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