相关论文: Spectrum of periodic chain graphs with time-revers…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
We show how arbitrary unit cells of periodic materials can be represented as graphs whose nodes represent atoms and whose weighted edges represent tunneling connections between atoms. Further, we present methods to calculate the band…
The spectral properties of disordered fully-connected graphs with a special type of the node-node interactions are investigated. The approximate analytical expression for the ensemble-averaged spectral density for the Hamiltonian defined on…
Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…
We characterize the graphs with loops whose degree sequences have no repeated values and find their adjacency spectrum. In the case of simple graphs, such graphs are called anti-regular graphs and are examples of threshold graphs. The…
The spectral gap for Laplace operators on metric graphs is investigated in relation to graph's connectivity, in particular what happens if an edge is added to (or deleted from) a graph. It is shown that in contrast to discrete graphs…
We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dead ends. The first kind are transfer operators acting on…
We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with…
Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
We establish an upper bound on the spectral gap for compact quantum graphs which depends only on the diameter and total number of vertices. This bound is asymptotically sharp for pumpkin chains with number of edges tending to infinity.
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
We investigate the spectrum of the non-backtracking matrix of a graph. In particular, we show how to obtain eigenvectors of the non-backtracking matrix in terms of eigenvectors of a smaller matrix. Furthermore, we find an expression for the…
Let $\Gamma$ be an arbitrary $\mathbb{Z}^n$-periodic metric graph, which does not coincide with a line. We consider the Hamiltonian $\mathcal{H}_\varepsilon$ on $\Gamma$ with the action $-\varepsilon^{-1}{\mathrm{d}^2/\mathrm{d} x^2}$ on…
For vertex and edge connectivity we construct infinitely many pairs of regular graphs with the same spectrum, but with different connectivity.
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that…
Banded random matrices were introduced as a more realistic alternative to full random matrices for describing the spectral statistics of heavy nuclei. Initially considered by Wigner, they have since become a paradigmatic model for…