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