Related papers: Ballistic Transport for Periodic Jacobi Operators …
We study Jacobi matrices that are uniformly approximated by periodic operators. We show that if the rate of approximation is sufficiently rapid, then the associated quantum dynamics are ballistic in a rather strong sense; namely, the…
We prove the existence of ballistic transport for a Schr\"odinger operator with a generic quasi-periodic potential in any dimension $d>1$.
In this paper, we show that one-dimensional discrete multi-frequency quasiperiodic Schr\"odinger operators with smooth potentials demonstrate ballistic motion on the set of energies on which the corresponding Schr\"odinger cocycles are…
We study the transport properties of Schr\"{o}dinger operators on $\mathbb{Z}^2$ with potentials that are periodic in one direction and compactly supported in the other. Such systems are known to produce surface states that are weakly…
We give a simple proof of Borg type uniqueness Theorems for periodic Jacobi operators with matrix valued coefficients.
Motivated by Open Problem 17 in Damanik-Fillman's manuscript , we study the decay rate of limit-periodic approximation such that ballistic transport persists in the limit-periodic setting. We show an exponential decay rate, roughly…
We begin the systematic study of the spectral theory of periodic Jacobi matrices on trees including a formal definition. The most significant result that appears here for the first time is that these operators have no singular continuous…
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical…
We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well known gap in the spectrum of the Laplacian on the upper half-plane with hyperbolic metric. We make some…
Banded bounded matrices, which represent non normal operators, of oscillatory type that admit a positive bidiagonal factorization are considered. To motivate the relevance of the oscillatory character the Favard theorem for Jacobi matrices…
We prove ballistic transport of all orders, that is, $\lVert x^m\mathrm{e}^{-\mathrm{i}tH}\psi\rVert\asymp t^m$, for the following models: the adjacency matrix on $\mathbb{Z}^d$, the Laplace operator on $\mathbb{R}^d$, periodic…
We theoretically study the motion of magnetic colloidal particles above a magnetic pattern and compare the predictions with Brownian dynamics simulations. The pattern consists of alternating square domains of positive and negative…
We consider the 1D periodic Jacobi matrices. The spectrum of this operator is purely absolutely continuous and consists of intervals separated by gaps. We solve the inverse problem (including characterization) in terms of vertical slits on…
Our main result asserts that a certain natural non-linear operator on Jacobi matrices built by a hyperbolic polynomial with real Julia set is a contraction in operator norm if the polynomial is sufficiently hyperbolic. This allows us to get…
We consider the periodic Jacobi operator $J$ with finitely supported perturbations on the half-lattice. We describe all eigenvalues and resonances of $J$ and give their properties. We solve the inverse resonance problem: we prove that the…
We introduce a function of the density of states for periodic Jacobi matrices on trees and prove a useful formula for it. This allows new, streamlined proofs of the gap labeling and Aomoto index theorems. We prove a version of this new…
It is shown that there exists a commuting diagram of mappings between dynamics of classical systems on one side and variational principles for geodesic lines in stationary spacetimes of general relativity on the other. The construction of…
We establish strong ballistic transport for a family of discrete quasiperiodic Schr\"odinger operators as a consequence of exponential dynamical localization for the dual family. The latter has been, essentially, shown by Jitomirskaya and…
A result of Borg--Hochstadt in the theory of periodic Jacobi matrices states that such a matrix has constant diagonals as long as all gaps in its spectrum are closed (have zero length). We suggest a quantitative version of this result by…
The effective dynamics of a slow classical system coupled to a fast chaotic environment is described by means of a Master equation. We show how this approach permits a very simple derivation of geometric magnetism.