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We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is…
We study general models of random fields associated with non-local equations in time and space. We discuss the properties of the corresponding angular power spectrum and find asymptotic results in terms of random time changes.
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
We describe the resonant interaction of an atom with a strongly focused light beam by expanding the field in multipole waves. For a classical field, or when the field is described by a coherent state, we find that both intensity pattern and…
A disordered structure embedding an active gain material and able to lase is called random laser (RL). The RL spectrum may appear either like a set of sharp resonances or like a smooth line superimposed to the fluorescence. A recent letter…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behaviour between an ordered, large-world and a disordered, small-world behaviour. Using the ergodic Pachner flips…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
The last two decades have witnessed the discovery of a myriad of new and unexpected hadrons. The future holds more surprises for us, thanks to new-generation experiments. Understanding the signals and determining the properties of the…
The emission spectra of many pi-conjugated polymers and oligomers contain side-band replicas with apparent frequencies that do not match the Raman active mode frequencies. Using a time dependent model we show that in such many mode systems,…
The classical model of an oscillator linearly coupled to a string captures, for a low price in technique, many general features of more realistic models for describing a particle interacting with a field or an atom in a electromagnetic…
A coupling-constant definition is given based on the compositeness property of some particle states with respect to the elementary states of other particles. It is applied in the context of the vector-spin-1/2-particle interaction vertices…
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…
The hierarchy between the mass parameter of the Higgs boson and larger mass scales becomes ever more puzzling as experiments explore higher energies. Neutral naturalness is the umbrella term for symmetry-based explanations for these…
We present here a relation of different types of Friedrichs models and their use in the description and comprehension of resonance phenomena. We first discuss the basic Friedrichs model and obtain its resonance in the case that this is…
We study "circular net" (discrete orthogonal net) equations for angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of Lagrangian density. There are…
A completely microscopic beyond mean-field approach has been elaborated to overcome some intrinsic limitations of self-consistent mean-field schemes applied to nuclear systems, such as the incapability to produce some properties of…
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…
We present a general framework that enables one to model high-order interaction among entangled dynamical systems, via hypergraphs. Several relevant processes can be ideally traced back to the proposed scheme. We shall here solely elaborate…