Related papers: Local Friedel sum rule on graphs
This work explores the spectra of quantum graphs where the Schr\"odinger operator on the edges is equipped with a potential. The scattering approach, which was originally introduced for the potential free case, is extended to this case and…
The planar-diagrammatic technique of large-$N$ random matrices is extended to evaluate averages over the circular ensemble of unitary matrices. It is then applied to study transport through a disordered metallic ``grain'', attached through…
We study planar "vertex" models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including dimer model, and 1-2 model, which we will define. We express the local…
Scanning gate microscopy images from measurements made in the vicinity of quantum point contacts were originally interpreted in terms of current flow. Some recent work has analytically connected the local density of states to conductance…
Consider a `dense' Erd\H{o}s--R\'enyi random graph model $G=G_{n,M}$ with $n$ vertices and $M$ edges, where we assume the edge density $M/\binom{n}{2}$ is bounded away from 0 and 1. Fix $k=k(n)$ with $k/n$ bounded away from 0 and~1, and let…
We numerically analyze the transmission through a thin disordered wire of finite length attached to perfect leads, by making use of banded random Hamiltonian matrices. We compare the Landauer and the Thouless conductances, and find that…
In finite graphs, finite-order tangles offer an abstract description of highly connected substructures. In infinite graphs, infinite-order tangles compactify the graphs in the same way the ends compactify connected locally finite graphs.…
Competition among exchange interactions is able to induce novel spin correlations on a bipartite lattice without geometrical frustration. A prototype example is the spiral spin liquid, which is a correlated paramagnetic state characterized…
Let $\Gamma$ be a locally finite graph, $L$ the normalized Laplacian of $\Gamma$. If $\Gamma$ is uniformy locally finite, i.e. if each vertex has no more than $d$ adjacent vertices, then the matrix of $L$ (with respect to the standard…
We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a…
The eccentricity matrix of a simple connected graph is derived from its distance matrix by preserving the largest non-zero distance in each row and column, while the other entries are set to zero. This article examines the…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…
We address the problem of determining a natural local neighbourhood or "cluster" associated to a given seed vertex in an undirected graph. We formulate the task in terms of absorption times of random walks from other vertices to the vertex…
We study the transport properties of three Luttinger liquid wires (with possibly different interaction strength), connected through a Y-junction, within the scattering state formalism. We first formulate the problem in current algebra…
Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their…
We investigate the question how `small' a graph can be, if it contains all members of a given class of locally finite graphs as subgraphs or induced subgraphs. More precisely, we give necessary and sufficient conditions for the existence of…
Electron scattering in the monolayer graphene with short-range impurities modelled by the annular well with a band-asymmetric potential has been considered. Band-asymmetry of the potential resulted in the mass (gap) perturbation in the…
We present the results of detailed theoretical investigations of changes in local density of total electronic surface states in 2D anisotropic atomic semiconductor lattice in vicinity of impurity atom for a wide range of applied bias…
We compute explicitly (modulo solutions of certain algebraic equations) the spectra of infinite graphs obtained by attaching one or several infinite paths to some vertices of certain finite graphs. The main result concerns a canonical form…
Elastic scattering in a quantum wire has several novel features not seen in 1D, 2D or 3D. In this work we consider a single channel quantum wire as its application is inevitable in making devices based on quantum interference effects. We…