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We investigate the Coherence--Curvature Model (CCM), a dynamical ensemble of connected graphs governed by a Hamiltonian that couples algebraic connectivity, Ollivier-Ricci curvature, and an edge-density penalty. Using connected simulated…
We are honored to dedicate this article to Emmanuel Rashba on the occasion of his 95 birthday. In the ideal disorder-free situation, a two-dimensional band gap insulator has an activation energy for conductivity equal to half the band gap,…
A matching M is a dominating induced matching of a graph, if every edge of the graph is either in $M$ or has a common end-vertex with exactly one edge in $M$. The concept of complete dominating induced matching is introduced as graphs where…
We study common randomness generation problems where $n$ players aim to generate same sequences of random coin flips where some subsets of the players share an independent common coin which can be tossed multiple times, and there is a…
We study a set of scattering matrices of quantum graphs containing minimal number of passbands, i.e., maximal number of zero elements. The cases of even and odd vertex degree are considered. Using a solution of inverse scattering problem,…
We study the field concentration phenomenon between two closely spaced perfect conductors with imperfect bonding interfaces of low conductivity type. The boundary condition on these interfaces is given by a Robin-type boundary condition. We…
In this study, we explore the substructures of a hypergraph that lead us to linearly dependent rows (or columns) in the incidence matrix of the hypergraph. These substructures are closely related to the spectra of various hypergraph…
We study the blind centrality ranking problem, where our goal is to infer the eigenvector centrality ranking of nodes solely from nodal observations, i.e., without information about the topology of the network. We formalize these nodal…
We study the average probability that a discrete-time quantum walk finds a marked vertex on a graph. We first show that, for a regular graph, the spectrum of the transition matrix is determined by the weighted adjacency matrix of an…
For a given infinite connected graph $G=(V,E)$ and an arbitrary but fixed conductance function $c$, we study an associated graph Laplacian $\Delta_{c}$; it is a generalized difference operator where the differences are measured across the…
We construct a simple holographic model incorporating higher-order coupling terms for electron self-interactions. It can exhibit typical behavior of a Mott insulator, including a metal-insulator transition and a decrease in DC conductivity…
In recent work on equiangular lines, Jiang, Tidor, Yuan, Zhang, and Zhao showed that a connected bounded degree graph has sublinear second eigenvalue multiplicity. More generally they show that there cannot be too many eigenvalues near the…
The eccentricity matrix of a simple connected graph is obtained from the distance matrix by only keeping the largest distances for each row and each column, whereas the remaining entries become zero. This matrix is also called the…
The low-temperature conductivity of low-density, high-mobility, two-dimensional hole systems in GaAs was studied. We explicitly show that the metal-insulator transition, observed in these systems, is characterized by a well-defined critical…
We present a theoretical study of electronic transport in a hybrid junction consisting of an excitonic insulator sandwiched between a normal and a superconducting electrode. The normal region is described as a two-band semimetal and the…
We develop a theory of the conductance of a quantum dot connected to two leads by single-mode quantum point contacts. If the contacts are in the regime of perfect transmission, the conductance shows no Coulomb blockade oscillations as a…
Let $H$ be a $k$-edge-coloured graph and let $n$ be a positive integer. What is the maximum number of copies of $H$ in a $k$-edge-coloured complete graph on $n$ vertices? This paper studies the case $k=2$, which we call the…
We study the DC transport of finite graphene samples with random gap. Using Dirac fermions to describe the low-energy physics near the Dirac point, we employ a generalized Drude form for the conductivity. The latter is constant for a…
We investigate the universal properties of quantum transport in graphene nanowires that engender subtle universal conductance fluctuations. We present results for three of the main microscopic models that describe the sublattice of graphene…
In the core of the vortex of a superconductor, energy levels appear inside the gap. We discuss here through a random matrix approach how these levels are broadened by impurities. It is first shown that the level statistics is governed by an…