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P (Φ)₁-process for the spin-boson model and a functional central limit theorem for associated additive functionals

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journal contribution
posted on 21.04.2020, 14:35 by Soumaya Gheryani, Fumio Hiroshima, Jozsef Lorinczi, Achref Majid, Habib Ouerdiane
We construct a random process with stationary increments associated to the Hamiltonian of the spin-boson model consisting of a component describing the spin and a component given by a Schwartz distribution-valued Ornstein-Uhlenbeck process describing the boson field. We use a path integral representation of the Hamiltonian to prove a functional central limit theorem for additive functionals, and derive explicit expressions of the diffusion constant for specific functionals.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Stochastics

Volume

89

Issue

6-7

Pages

1104 - 1115

Publisher

Taylor & Francis

Version

AM (Accepted Manuscript)

Rights holder

© Informa UK Limited, trading as Taylor & Francis Group

Publisher statement

This is an Accepted Manuscript of an article published by Taylor & Francis in Stochastics on 4 September 2017, available online: http://www.tandfonline.com/10.1080/17442508.2017.1371177.

Acceptance date

21/08/2017

Publication date

2017-09-04

Copyright date

2017

ISSN

1744-2508

eISSN

1744-2516

Language

en

Depositor

Dr Jozsef Lorinczi. Deposit date: 18 April 2020

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