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Title: A probabilistic representation of the ground state expectation of fractional powers of the boson number operator
Authors: Hiroshima, Fumio
Lorinczi, Jozsef
Takaesu, Toshimitsu
Keywords: Gibbs measure on path space
Random-time Poisson process
Ground state
Boson number operator
Nelson model
Issue Date: 2012
Publisher: © Elsevier Inc.
Citation: HIROSHIMA, 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
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.
Version: Accepted for publication
DOI: 10.1016/j.jmaa.2012.04.076
URI: https://dspace.lboro.ac.uk/2134/21955
Publisher Link: http://dx.doi.org/10.1016/j.jmaa.2012.04.076
ISSN: 0022-247X
Appears in Collections:Published Articles (Maths)

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