Related papers: Localization for the Anderson Model on Trees with …
We solve $O(n,1)$ nonlinear vector model on Bethe lattice and show that it exhibits a transition from ordered to disordered state for $0 \leq n < 1$. If the replica limit $n\to 0$ is taken carefully, the model is shown to reduce to the…
In this paper, we establish Anderson localization for a class of Jacobi matrices associated with skew shifts on $\mathbb{T}^{d}$, $d\geq3$.
We revisit the Anderson localization problem on Bethe lattices, putting in contact various aspects which have been previously only discussed separately. For the case of connectivity 3 we compute by the cavity method the density of states…
A metric phylogenetic tree relating a collection of taxa induces weighted rooted triples and weighted quartets for all subsets of three and four taxa, respectively. New intertaxon distances are defined that can be calculated from these…
We consider a system of two discrete quasiperiodic 1D particles as an operator on $\ell^2(\mathbb Z^2)$ and establish Anderson localization at large disorder, assuming the potential has no cosine-type symmetries. In the presence of…
We propose to observe Anderson localization of ultracold atoms in the presence of a random potential made of atoms of another species and trapped at the nodes of an optical lattice, with a filling factor less than unity. Such systems enable…
Let $\mathcal T_n$ denote the set of all labelled spanning trees of $K_n$. A family $\mathcal F \subset \mathcal T_n$ is $t$-intersecting if for all $A, B \in \mathcal F$ the trees $A$ and $B$ share at least $t$ edges. In this paper, we…
The necessary and sufficient conditions under which a given family $\mathcal{F}$ of subsets of finite set $X$ coincides with the family $\mathbf{B}_X$ of all balls generated by some ultrametric $d$ on $X$ are found. It is shown that the…
Anderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for {dynamical localization}. In the one-dimensional Hermitian Anderson model with uncorrelated diagonal…
We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional…
The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…
We consider a two dimensional magnetic Schroedinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate…
We study multi-particle interactive quantum disordered systems on a polynomially-growing countable connected graph (Z,E). The novelty is to give localization bounds uniform in finite or infinite volumes (subgraphs) in Z^N as well as for the…
I present the exact solution of a family of fragmented Bose-Hubbard models and represent the models as graphs in one-dimension, two-dimensions and three-dimensions with the condensates in the vertices. The models are solved by the algebraic…
We provide analytical solutions to the thermodynamic Bethe ansatz equations in the large and small density approximations. We extend results previously obtained for leading order behaviour of the scaling function of affine Toda field…
We suggest a two-matrix model depending on three (infinite) sets of parameters which interpolates between all the models proposed in arXiv:2206.13038, and defined there through $W$-representations. We also discuss further generalizations of…
We discuss the conditions under which an anomaly occurs in conductance and localization length of Anderson model on a lattice. Using the ladder hamiltonian and analytical calculation of average conductance we find the set of resonance…
Using a new technique, we prove a rich family of special cases of the matroid intersection conjecture. Roughly, we prove the conjecture for pairs of tame matroids which have a common decomposition by 2-separations into finite parts.
Motivated by online recommendation systems, we study a family of random forests. The vertices of the forest are labeled by integers. Each non-positive integer $i\le 0$ is the root of a tree. Vertices labeled by positive integers $n \ge 1$…
We propose a novel linearization of a constituent tree, together with a new locally normalized model. For each split point in a sentence, our model computes the normalizer on all spans ending with that split point, and then predicts a tree…