Spin-boson model through a Poisson-driven stochastic process

Masao Hirokawa, Fumio Hiroshima, József Lőrinczi

Research output: Contribution to journalArticle

5 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 - Jan 1 2014

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Bosons
Stochastic Processes
Siméon Denis Poisson
Ground State
Poisson Point Process
Functional Integral
Operator
Exponential Decay
Real Line
Integral Representation
Model
Discontinuity
Euclidean
Jump
Existence and Uniqueness
Fractional
Semigroup
Decay
Fluctuations
Moment

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Spin-boson model through a Poisson-driven stochastic process. / Hirokawa, Masao; Hiroshima, Fumio; Lőrinczi, József.

In: Mathematische Zeitschrift, Vol. 277, No. 3-4, 01.01.2014, p. 1165-1198.

Research output: Contribution to journalArticle

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