Related papers: Local Friedel sum rule on graphs
We define direct sums and a corresponding notion of connectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
We define the Schr\"odinger equation with focusing, cubic nonlinearity on one-vertex graphs. We prove global well-posedness in the energy domain and conservation laws for some self-adjoint boundary conditions at the vertex, i.e. Kirchhoff…
A recent development in graph-minor theory is to study local separators, vertex-sets that separate graphs locally but not necessarily globally. The local separators of a graph roughly correspond to the genuine separators of its local…
We expose an interesting connection between the distribution of local spectral density of states arising in the theory of disordered systems and the notion of superstatistics introduced by Beck and Cohen and recently incorporated in random…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
We study the spin-dependent scattering of charge carriers in a magnetized one dimensional Luttinger liquid from a localized non-homogeneous magnetic field, which might be brought about by the stray field of magnetic tip near a uniform…
One dimensional conductors are described by Luttinger liquid theory, which predicts a power-law suppression of the density of states near the Fermi level. The scaling exponent is non-universal in the general case, but is predicted to be…
Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation…
Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a…
We consider a Schr\"odinger particle on a graph consisting of $\,N\,$ links joined at a single point. Each link supports a real locally integrable potential $\,V_j\,$; the self--adjointness is ensured by the $\,\delta\,$ type boundary…
By applying the Kramers-Kronig dispersion relation to the transmission amplitude a direct connection of the conductance with the density of states is given in quantum scattering systems connected to two one-channel leads. Using this method…
Random pure states of multi-partite quantum systems, associated with arbitrary graphs, are investigated. Each vertex of the graph represents a generic interaction between subsystems, described by a random unitary matrix distributed…
The Local Structure Theorem (LST) for Graph Minors roughly states that for every $H$-minor-free graph $G$ that contains a sufficiently large wall $W$, there is a small vertex subset $A,$ whose removal yields a graph that admits an "almost…
Using the semi-classical Boltzmann theory, we calculate the conductivity as function of the carrier density. As usually, we include the scattering from charged impurities, but conclude that the estimated impurity density is too low in order…
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…
In the framework of scattering theory, we show how the scattering matrix can be related to the projection on the bound states by an index map of K-theory. Pairings with appropriate cyclic cocyles lead naturally to a topological version of…
Mesoscopic systems and large molecules are often modeled by graphs of one-dimensional wires, connected at vertices. In this paper we discuss the solutions of the Schr\"odinger equation on such graphs, which have been named "quantum…
We use two variational techniques to prove upper bounds for sums of the lowest several eigenvalues of matrices associated with finite, simple, combinatorial graphs. These include estimates for the adjacency matrix of a graph and for both…
The scattering phase, defined as $ \log \det S ( \lambda ) / 2\pi i $ where $ S ( \lambda ) $ is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely…