The heat kernel of the asymmetric quantum Rabi model

In this paper we derive an explicit formula for the heat kernel of the asymmetric quantum Rabi model, a symmetry breaking generalization of the quantum Rabi model (QRM). The method described here is the extension of a recently developed method for the heat kernel of the QRM that uses the Trotter-Kato product formula instead of path integrals or stochastic methods. In addition to the heat kernel formula, we give applications including the explicit formula for the partition function and the Weyl law for the distribution of the eigenvalues, obtained from the corresponding spectral zeta function.