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The purely algebraic technique associated with the creation and annihilation operators to resolve the radial equation of Hydrogen-like atoms (HLA) for generating the bound energy spectrum and the corresponding wave functions is suitable for…
The theory of exact and of approximate solutions for non-autonomous linear differential equations forms a wide field with strong ties to physics and applied problems. This paper is meant as a stepping stone for an exploration of this…
Obtaining insight into the constituents of dark matter and their interactions with normal matter has inspired a wide range of experimental efforts. Several approaches, particularly those involving searches for ultralight bosonic dark matter…
A Kerr type solution in the Regge calculus is considered. It is assumed that the discrete general relativity, the Regge calculus, is quantized within the path integral approach. The only consequence of this approach used here is the…
The widely used large-scale diagonalization method using harmonic oscillator basis functions (an instance of the Rayleigh-Ritz method, also called a spectral method, configuration-interaction method, or ``exact diagonalization'' method) is…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
We propose a novel general approximation to transform and simplify the description of a complex fully-quantized system describing the interacting light and matter. The method has some similarities to the time-dependent Born-Oppenheimer…
In this work, we construct an alternative formulation to the traditional Algebraic Bethe ansatz for quantum integrable models derived from a generalised rational Gaudin algebra realised in terms of a collection of spins 1/2 coupled to a…
This article reviews theoretical methods developed in the last decade to understand cavity quantum electrodynamics in the ultrastrong-coupling regime, where the strength of the light-matter interaction becomes comparable to the photon…
We discuss the physics of the Rabi-Hubbard model describing large arrays of coupled cavities interacting with two level atoms via a Rabi non-linearity. We show that the inclusion of counter-rotating terms in the light-matter interaction,…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
We present a general framework to tackle quantum optics problems with giant atoms, i.e. quantum emitters each coupled {\it non-locally} to a structured photonic bath (typically a lattice) of any dimension. The theory encompasses the…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…
Long-range effective methods are ubiquitous in physics and in quantum theory, in particular. Furthermore, the reliability of such methods is higher when the nature of short-ranged interactions need not be modeled explicitly. This may be…
A detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided. In particular, the quantum Rabi model, the Dicke model, and a generalization of the latter to multiple modes are considered. We prove a…
We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…
The quantum Rabi model is a paradigmatic example of a minimal yet nontrivial light-matter interaction, whose spectrum is transcendental yet exhibits a number of regularities. Braak observed that the eigenvalues bunch or anti-bunch following…
The interplay of three light-matter interaction processes - rotating and counter-rotating interactions and two-photon relaxation of the light field - is a topic of interest in quantum optics and quantum information processing. In this work,…
We present three statistical descriptions for systems of classical particles and consider their extension to hybrid quantum-classical systems. The classical descriptions are ensembles on configuration space, ensembles on phase space, and a…
The effective description of the weak interaction between an emitter and a bosonic field as a sequence of two-body collisions provides a simple intuitive picture compared to traditional quantum optics methods as well as an effective…