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, In Press.
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.
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