Spectral zeta function and ground state of quantum Rabi model

TL;DR

This paper investigates the spectral zeta function of the quantum Rabi Hamiltonian, showing its convergence to the Riemann zeta function at strong coupling and constructing the ground state path measure on a discontinuous path space.

Contribution

It introduces a novel analysis of the spectral zeta function's behavior and constructs the ground state path measure for the quantum Rabi model.

Findings

Spectral zeta function converges to Riemann zeta function as coupling increases

Constructed the ground state path measure on a discontinuous path space

Provided applications of the constructed path measure

Abstract

The spectral zeta function of the quantum Rabi Hamiltonian is considered. It is shown that the spectral zeta function converges to the Riemann zeta function as the coupling constant goes to infinity. Moreover the path measure associated with the ground state of the quantum Rabi Hamiltonian is constructed on a discontinuous path space, and several applications are shown.