Related papers: Ballistic Transport for Periodic Jacobi Operators …
We consider a special class of periodic continued fractions (called alpha-fractions) and discuss the related algebraic and geometric problems. A classical description of the Jacobi variety of a hyperelliptic curve due to Jacobi naturally…
We consider the vertical motion of a free falling ball bouncing elastically on a racket moving in the vertical direction according to a regular $1$-periodic function $f$. For fixed coprime $p,q$ we study existence, stability in the sense of…
We consider a lattice equation modelling one-dimensional metamaterials formed by a discrete array of nonlinear resonators. We focus on periodic travelling waves due to the presence of a periodic force. The existence and uniqueness results…
In this article, we review some notions of ballistic transport from the mathematics and physics literature, describe their basic interrelations, and contrast them with other commonly studied notions of wave packet spread.
The study of the asymptotic distributions of zeros of generalized Jacobi polynomials with non real varying parameters, leads with quadratic differentials. In fact, the support of the limit measure of the root-counting measures sits on the…
We consider Jacobi matrices and Schrodinger operators that are reflectionless on an interval. We give a systematic development of a certain parametrization of this class, in terms of suitable spectral data, that is due to Marchenko. Then…
We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. It was previously shown that for a parameter set of positive Lebesgue density at the bifurcation, the maps possess…
We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide…
A comprehensive study of periodic trajectories of billiards within ellipsoids in $d$-dimensional Euclidean space is presented. The novelty of the approach is based on a relationship established between periodic billiard trajectories and…
We study several fundamental operators in harmonic analysis related to Jacobi expansions, including Riesz transforms, imaginary powers of the Jacobi operator, the Jacobi-Poisson semigroup maximal operator and Littlewood-Paley-Stein square…
We consider a set of measures on the real line and the corresponding system of multiple orthogonal polynomials (MOPs) of the first and second type. Under some very mild assumptions, which are satisfied by Angelesco systems, we define…
In this paper, we first develop a notion of dominated splitting for $\mathbb M(2,\mathbb C)$-sequences and show it is a stable property under $\|\cdot \|_\infty$-perturbation. Then we show an energy parameter belongs to the spectrum of a…
A geometric formulation of the linear beam dynamics in accelerator physics is presented. In particular, it is proved that the linear transverse and longitudinal dynamics can be interpret geometrically as an approximation to the Jacobi…
Weyl's displacement operators for position and momentum commute if the product of the elementary displacements equals Planck's constant. Then, their common eigenstates constitute the Zak basis, each state specified by two phase parameters.…
We prove the Zariski dense orbit conjecture in positive characteristic for regular self-maps of split semiabelian varieties.
We investigate the motion of charged particles in a turbulent electrostatic potential using guiding-center theory. By increasing the Larmor radius, the dynamics exhibit close-to-ballistic transport properties. The transition from diffusive…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
The Hubbard model describes interacting electrons on a lattice,a situation which occurs in various solid state materials and devices. The aim of the present paper is to briefly discuss this model and its applications in the study of…
A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In…
We consider the Boltzmann system corresponding to the motion of a billiard with a linear boundary under the influence of a gravitational field. We derive analytic conditions of Cayley's type for periodicity of its trajectories and provide…