The heat kernel of the asymmetric quantum Rabi model
Abstract
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 TrotterKato 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2023
 DOI:
 10.1088/17518121/acfbc8
 arXiv:
 arXiv:2012.13595
 Bibcode:
 2023JPhA...56P5302R
 Keywords:

 asymmetric quantum Rabi model;
 heat kernel;
 partition function;
 spectral zeta;
 Mathematical Physics;
 47B93 (Primary) 35K08;
 11M36 (Secondary)
 EPrint:
 20 pages. Fixed errors in previous version and improved presentation