Spin-Boson Model through a Poisson-Driven Stochastic Process

TL;DR

This paper introduces a novel functional integral approach to the spin-boson model using Poisson-driven stochastic processes, enabling detailed analysis of ground state properties and decay behaviors.

Contribution

It develops a new method for representing the spin-boson Hamiltonian via Poisson point processes and constructs Gibbs measures, advancing understanding of ground state characteristics.

Findings

Proves existence and uniqueness of the ground state.

Shows super-exponential decay of boson number.

Derives moments and fluctuations of the field operator.

Abstract

We give a functional integral representation of the semigroup generated by the spin-boson Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a method of constructing Gibbs path measures indexed by the full real line which can be applied also to more general stochastic processes with jump discontinuities. Using these tools we then show existence and uniqueness of the ground state of the spin-boson, and analyze ground state properties. In particular, we prove super-exponential decay of the number of bosons, Gaussian decay of the field operators, derive expressions for the positive integer, fractional and exponential moments of the field operator, and discuss the field fluctuations in the ground state.