P(𝜙)₁-process for the spin-boson model and a functional central limit theorem for associated additive functionals

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.

Keywords:

• Spin-boson model
• ground state
• functional central limit theorem

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.