Cid Reyes Bustos

NTT Communication Science Laboratories · NTT Institute for Fundamental Mathematics

In this paper we introduce a Cayley-type graph for group-subgroup pairs and present some elementary properties of such graphs, including connectedness, their degree and partition structure, and vertex-transitivity. We relate these properties to those of the underlying group-subgroup pair. From the properties of the group, subgroup and generating se...

The purpose of the present paper is to study the exceptional eigenvalues of the asymmetric quantum Rabi models (AQRM), specifically, to determine the degeneracy of the exceptional eigenstates. Exceptional eigenvalues are labelled by certain integers and are considered to be remains of the eigenvalues of the uncoupled bosonic mode (i.e. the quantum...

In this paper we discuss a recently discovered continued fraction expansion \[ e = 3 - \cfrac{1}{4 - \cfrac{2}{5 - \cfrac{3}{6 - \cfrac{4}{7 - \cdots}}} }, \] and its convergence properties. We show that this expansion is a particular case of a continued fraction expansion of $e^n$, for positive integer power $n$, and more generally, it is a specia...

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 quantum light-matter interaction. The objective of the paper is to give an analytical formula of the heat kernel of the Hamiltonian explicitly by infinite series of iterate...

The non-commutative harmonic oscillator (NCHO) is a matrix valued differential operator introduced as a generalization of the quantum harmonic oscillator. The spectrum of the NCHO has remarkable properties, including the presence of a number theoretical structure such as modular forms, elliptic curves, Eichler cohomology observed in the special val...

The hidden symmetry of the asymmetric quantum Rabi model (AQRM) with a half-integral bias (ibQRM$_{\ell}$) was uncovered in recent studies by the explicit construction of operators $J_\ell$ commuting with the Hamiltonian. The existence of such symmetry has been widely believed to cause the degeneration of the spectrum, that is, crossings on the ene...

The quantum Rabi model (QRM) is widely recognized as an important model in quantum systems, particularly in quantum optics. The Hamiltonian $H_{\text{Rabi}}$ is known to have a parity decomposition $H_{\text{Rabi}} = H_{+} \oplus H_{-}$. In this paper, we give the explicit formulas for the propagator of the Schr\"odinger equation (integral kernel o...

The symmetric quantum Rabi model (QRM) is integrable due to a discrete $\mathbb{Z}_2$-symmetry of the Hamiltonian. This symmetry is generated by a known involution operator, measuring the parity of the eigenfunctions. An experimentally relevant modification of the QRM, the asymmetric (or biased) quantum Rabi model (AQRM) is no longer invariant unde...

In this paper we give the explicit formula for the heat kernel of the asymmetric quantum Rabi model. The method used here is an extension of the one recently used for the computation of the heat kernel of the (symmetric) quantum Rabi model. In addition, we present several results derived from the heat kernel formula, including formulas for the part...

The quantum Rabi model (QRM) is widely regarded as one of the fundamental models of quantum optics. One of its generalizations is the asymmetric quantum Rabi model (AQRM), obtained by introducing a symmetry-breaking term depending on a parameter 𝜀∈ℝ to the Hamiltonian of the QRM. The AQRM was shown to possess degeneracies in the spectrum for values...

The quantum Rabi model (QRM) is widely recognized as an important model in quantum systems, particularly in quantum optics. The Hamiltonian $H_{\text{Rabi}}$ is known to have a parity decomposition $H_{\text{Rabi}} = H_{+} \oplus H_{-}$. In this paper, we give the explicit formulas for the propagator of the Schr\"odinger equation (integral kernel o...

The aim of this article is to investigate certain family of (so-called constraint) polynomials which determine the quasi-exact spectrum of the asymmetric quantum Rabi model. The quantum Rabi model appears ubiquitously in various quantum systems and its potential applications include quantum computing and quantum cryptography. In (Wakayama, Symmetry...