The purpose of this paper is to study the exceptional eigenvalues of the asymmetric
quantum Rabi models (AQRMs), specifically, to determine the degeneracy of their …

We collect here 100 open conjectures on congruences made by the author, some of which
have never been published. This is a new edition of the author's preprint arXiv: 0911.5665 …

In this paper we study some sophisticated supercongruences involving dual sequences. For
n= 0, 1, 2,… define dn (x)=∑ k= 0 n (nk)(xk) 2 k and sn (x)=∑ k= 0 n (nk)(xk)(x+ kk)=∑ k= 0 …

In the standard normalization, the eigenvalues of the quantum harmonic oscillator are given
by positive half-integers with the Hermite functions as eigenfunctions. Thus, its spectral zeta …

The quantum Rabi model (QRM) is widely recognized as a particularly important model in
quantum optics. It is considered to be the simplest and most fundamental system describing …

The quantum Rabi model (QRM) is widely recognized as an important model in quantum
systems, particularly in quantum optics. The Hamiltonian H Rabi is known to have a parity …

The purpose of the present paper is to study the number theoretic properties of the special
values of the spectral zeta functions of the non-commutative harmonic oscillator (NcHO) …

The initial aim of the present paper is to provide a complete description of the eigenvalue
problem for the non-commutative harmonic oscillator (NcHO), which is defined by a (two-by …

The aim of the present paper is to understand the spectral problem of the quantum Rabi
model in terms of Lie algebra representations of $\mathfrak {s}{{\mathfrak {l}} _ {2}}(\mathbb …

Abstract In 2006, Kimoto and Wakayama discussed one kind of Apéry-like numbers which
occurs in a representation of the special value of the spectral zeta function, and proposed a …