Abstract
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.
Acknowledgements
We gratefully thank the anonymous referee for constructive comments which greatly have improved the manuscript. JL thanks IHES, Bures-sur-Yvette, for a visiting fellowship, where part of this paper has been written. SG and AM thank Tunis El Manar University for a visiting grant to Loughborough University, where this work began.
Notes
No potential conflict of interest was reported by the authors.