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A probabilistic representation of the ground state expectation of fractional powers of the boson number operator

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journal contribution
posted on 11.07.2016, 15:33 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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Volume

395

Issue

2

Pages

437 - 447 (11)

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

Publisher

© Elsevier Inc.

Version

AM (Accepted Manuscript)

Publisher statement

This 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/

Publication date

2012

ISSN

0022-247X

Language

en