The heat kernel of the asymmetric quantum Rabi model

TL;DR

This paper derives an explicit heat kernel formula for the asymmetric quantum Rabi model, enabling precise calculations of the partition function and eigenvalue distribution without using path integrals or stochastic methods.

Contribution

It extends existing methods to derive the heat kernel of the AQRM, providing explicit formulas and applications like the partition function and eigenvalue distribution.

Findings

Explicit heat kernel formula for AQRM

Derived partition function and spectral zeta function

Established Weyl law for eigenvalue distribution

Abstract

In this paper we derive an explicit formula for the heat kernel of the asymmetric quantum Rabi model (AQRM), a symmetry breaking generalization of the quantum Rabi model (QRM). The method described here is an extension of the recently developed one for the heat kernel of the QRM based on the Trotter-Kato formula. In particular, the method is not based on path integrals or stochastic methods. In addition to the heat kernel formula, we present applications including the explicit formula for the partition function and the Weyl law for the distribution of the eigenvalues, obtained from the analytic continuation of the corresponding spectral zeta function.