GHERYANI, S. ...et al., 2017. P(𝜙)1-process for the spin-boson model and a functional central limit theorem for associated additive functionals. Stochastics: An International Journal of Probability and Stochastic Processes, 89(6/7), pp. 1104-1115.
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.
This is an Accepted Manuscript of an article published by Taylor & Francis in An International Journal of Probability and Stochastic Processes on 4 September 2017, available online: http://www.tandfonline.com/10.1080/17442508.2017.1371177.