Related papers: Localization for the Anderson Model on Trees with …
In this paper, we propose DeepTree, a novel method for modeling trees based on learning developmental rules for branching structures instead of manually defining them. We call our deep neural model situated latent because its behavior is…
We describe an integrable model, related to the Gaudin magnet, and its relation to the matrix model of Brezin, Itzykson, Parisi and Zuber. Relation is based on Bethe ansatz for the integrable model and its interpretation using orthogonal…
Fix a bounded $3$-polygon $(\Omega; x_1, x_2, x_3)$ with three marked boundary points $x_1, x_2, x_3\in\partial\Omega$ and suppose $(\Omega^{\delta}; x_1^{\delta}, x_2^{\delta}, x_3^{\delta})$ is an approximation of $(\Omega; x_1, x_2,…
We study the P"oschl-Teller equation in complex domain and deduce infinite families of TQ and Bethe ansatz equations, classified by four integers. In all these models the form of T is very simple, while Q can be explicitly written in terms…
The Anderson model serves to study the absence of wave propagation in a medium in the presence of impurities, and is one of the most studied examples in the theory of quantum disordered systems. In these notes we give a review of the…
Consider the d-dimensional lattice Z^d where each vertex is ``open'' or ``closed'' with probability p or 1-p, respectively. An open vertex v is connected by an edge to the closest open vertex w such that the dth co-ordinates of v and w…
A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice $\mathcal N=2$ supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified.…
In the present article, we discuss the role played by the interaction in the Anderson localization problem, for a system of interacting fermions in a one-dimensional disordered lattice, described by the Fermi Hubbard Hamiltonian, in…
Recently, the XXX spin chain with arbitrary boundary fields was successfully solved [1] via the off-diagonal Bethe ansatz method [2]. The correctness and the completeness of this solution were numerically verified by Nepomechie for one…
We prove a result of delocalization for the Anderson model on the regular tree (Bethe lattice). When the disorder is weak, it is known that large parts of the spectrum are a.s. purely absolutely continuous, and that the dynamical transport…
We discuss a model of random segmented wire, with linear segments of 2D wires joined by circular bends. The joining vertices act as scatterers on the propagating electron waves. The model leads to resonant Anderson localization when all…
We consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of…
We investigate, both experimentally and theoretically, possible routes towards Anderson-like localization of Bose-Einstein condensates in disordered potentials. The dependence of this quantum interference effect on the nonlinear…
In a recent work Povolotsky provided a three-parameter family of stochastic particle systems with zero-range interactions in one dimension which are integrable by coordinate Bethe ansatz. Using these results we obtain the corresponding…
Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We…
The location of the mobility edge is a long standing problem in Anderson localization. In this paper, we show that the effective confining potential introduced in the localization landscape (LL) theory predicts the onset of delocalization…
We study questions inspired by Erd\H os' celebrated distance problems with dot products in lieu of distances, and for more than a single pair of points. In particular, we study point configurations present in large finite point sets in the…
An exact solution of the model of fully packed loops of two colors on a square lattice has recently been proposed by Dei Cont and Nienhuis using the coordinate Bethe Ansatz approach. We point out here a simpler alternative, in which the…
Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the present work, we define and study a new subclass of tree-like…
We examine the problem of gauge-field localization in higher-dimensional gauge theories. In particular, we study a five-dimensional U(1) by lattice techniques and we find that gauge fields can indeed be localized. Two models are considered.…