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Spin-boson model through a Poisson-driven stochastic process

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journal contribution
posted on 07.06.2016, 11:57 by Masao Hirokawa, Fumio Hiroshima, Jozsef Lorinczi
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

MATHEMATISCHE ZEITSCHRIFT

Volume

277

Issue

3-4

Pages

1165 - 1198 (34)

Citation

HIROKAWA, M., HIROSHIMA, F. and LORINCZI, J., 2014. Spin-boson model through a Poisson-driven stochastic process. Mathematische Zeitschrift, 277 (3-4), pp.1165-1198

Publisher

© Springer Heidelberg

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

2014

Notes

The final publication is available at Springer via http://dx.doi.org/10.1007/s00209-014-1299-1

ISSN

0025-5874

eISSN

1432-1823

Language

en