Study on the spectral zeta function of the Jaynes-Cummings model

Abstract

In this thesis, the spectral zeta function associated with the Jaynes-Cummings Hamiltonian is explored. The thesis first reviews the known results about the spectral properties of the JC Hamiltonian and then goes on to prove the analytic continuation of the JC spectral zeta function using summation formulas. This proof is completed in two parts, first the analytic continuation to Re(s) > 0 is shown followed by the analytic continuation to the entire complex plane. This proof involves analysing some hypergeometric functions arising naturally from the summation formulas used in the proof. Some possible areas where this proof might be applied in the future are discussed.