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 journal › Article

2 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

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Bosons
Fractional Powers
Ground state
Ground State
Polaron
Gibbs Measure
Operator
Poisson process
Fractional
Path
Invariant
Model

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

A probabilistic representation of the ground state expectation of fractional powers of the boson number operator. / Hiroshima, Fumio; Lorinczi, József; Takaesu, Toshimitsu.

In: Journal of Mathematical Analysis and Applications, Vol. 395, No. 2, 15.11.2012, p. 437-447.

Research output: Contribution to journal › Article

Hiroshima, F, Lorinczi, J & Takaesu, T 2012, 'A probabilistic representation of the ground state expectation of fractional powers of the boson number operator', Journal of Mathematical Analysis and Applications, vol. 395, no. 2, pp. 437-447. https://doi.org/10.1016/j.jmaa.2012.04.076
Hiroshima F, Lorinczi J, Takaesu T. A probabilistic representation of the ground state expectation of fractional powers of the boson number operator. Journal of Mathematical Analysis and Applications. 2012 Nov 15;395(2):437-447. https://doi.org/10.1016/j.jmaa.2012.04.076
Hiroshima, Fumio ; Lorinczi, József ; Takaesu, Toshimitsu. / A probabilistic representation of the ground state expectation of fractional powers of the boson number operator. In: Journal of Mathematical Analysis and Applications. 2012 ; Vol. 395, No. 2. pp. 437-447.
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