Related papers: Spectral transition model with the general contact…
The new representation formula for the spectral shift function due to F.Gesztesy and K.A.Makarov is considered. This formula is extended to the case of relatively trace class perturbations.
In these lecture notes I present a short review of nuclear shapes, shape coexistence and shape-phase transitions in the interacting boson model. In a study with random interactions it is shown that the appearance of regular spectral…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some…
In this paper, we study the controllability and stabilizability properties of the Kolmogorov forward equation of a continuous time Markov chain (CTMC) evolving on a finite state space, using the transition rates as the control parameters.…
We propose a modification of the Kuramoto model to account for the effective change in the coupling constant among the oscillators, as suggested by some experiments on Josephson junction, laser arrays and mechanical systems, where the…
Monitored quantum system have sparked great interest in recent years due to the possibility of observing measurement-induced phase transitions (MIPTs) in the full-counting statistics of the quantum trajectories associated with different…
We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the…
We study communities emerging from generalised random Lotka--Volterra dynamics with a large number of species with interactions determined by the degree of niche overlap. Each species is endowed with a number of traits, and competition…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
We discuss the effective donor/acceptor coupling for a bridged electron transfer system with a site-diagonal disorder of bridge energies. The average spectral properties of the system are discussed by using the Wegner model (Anderson's type…
Superexponential systems are characterized by a potential where dynamical degrees of freedom appear in both the base and the exponent of a power law. We explore the scattering dynamics of many-body systems governed by superexponential…
In this paper, we introduce a general framework for co-infection as cooperative SIR dynamics. We first solve analytically CGCG model [1] and then the generalized model in symmetric scenarios. We calculate transition points, order parameter,…
The increasing integration of power electronic devices is driving the development of more advanced tools and methods for the modeling, analysis, and control of modern power systems to cope with the different time-scale oscillations. In this…
Non Efimovian $N$-body resonances are investigated in the regime of a large two-body s wave scattering length. In view of a universal description of low-energy bound and quasi-bound states, a contact model is introduced. The modeling…
Methods from scattering theory are introduced to analyze random Schroedinger operators in one dimension by applying a volume cutoff to the potential. The key ingredient is the Lifshitz-Krein spectral shift function, which is related to the…
The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin coherent states formalism. In the first step, a classical analysis allows one to distinguish between four distinct regions in…
Lipkin model of arbitrary particle-number N is studied in terms of exact differential-operator representation of spin-operators from which we obtain the low-lying energy spectrum with the instanton method of quantum tunneling. Our new…
Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring…
We consider chains of $N$ harmonic oscillators in two dimensions coupled to two Langevin heat reservoirs at different temperatures - a classical model for heat conduction introduced by Lebowitz, Lieb, and Rieder \cite{RLL67}. We extend our…