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P (Φ)₁-process for the spin-boson model and a functional central limit theorem for associated additive functionals
journal contributionposted on 2020-04-21, 14:35 authored 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.
- Mathematical Sciences
Pages1104 - 1115
PublisherTaylor & Francis
- AM (Accepted Manuscript)
Rights holder© Informa UK Limited, trading as Taylor & Francis Group
Publisher statementThis 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.