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A probabilistic representation of the ground state expectation of fractional powers of the boson number operator
journal contributionposted on 2016-07-11, 15:33 authored by Fumio Hiroshima, Jozsef Lorinczi, Toshimitsu Takaesu
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.
- Mathematical Sciences
Published inJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Pages437 - 447 (11)
CitationHIROSHIMA, F., LORINCZI, J. and 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, 395 (2), pp.437-447
Publisher© Elsevier Inc.
- AM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/