Related papers: Massive Modes for Quantum Graphs
We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…
We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that when a quantum network is described by such a graph, the network is efficiently controllable, in…
In this paper we study the spectral gap of the path graph and illustrate an interesting effect which has been described recently in the continuous setting. More explicitly, in the large-volume limit and in the presence of a certain external…
Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand…
Connectivity is a fundamental property of quantum graphs, previously studied in the operator system model for matrix quantum graphs and via graph homomorphisms in the quantum adjacency matrix model. In this paper, we develop an algebraic…
We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
We present an infinite sequence of finite graphs with trivial automorphism group and non-trivial quantum automorphism group. These are the first known examples of graphs with this property. Moreover, to the best of our knowledge, these are…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
The existence of quasinormal modes (QNMs) for waves propagating on pure de Sitter space has been called into question in several works. We definitively prove the existence of quasinormal modes for massless and massive scalar fields in all…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
An important unanswered question in quantum field theory is to understand precisely under which conditions scale invariance implies invariance under the full conformal group. While the general answer in two dimensions has been known for…
One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale…
In this paper, we examine the behavior of modes of the Kerr geometry when the mode's frequency is purely imaginary. We demonstrate that quasinormal modes must be polynomial in nature if their frequency is purely imaginary, and present a…
We formulate N-fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix 2-fold supersymmetric quantum mechanical systems. We find that there are two inequivalent such systems,…
The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on…
With appropriate notions of Hermitian vector bundles and connections over weighted graphs which we allow to be locally infinite, we prove Feynman-Kac-type representations for the corresponding semigroups and derive several applications…
We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on…
We examine supersymmetric theories with approximately conformal sectors. Without an IR cutoff the theory has a continuum of modes, which are often referred to as "unparticles." Making use of the AdS/CFT correspondence we find that in the…
A field $k$ is called large if every irreducible $k$-curve with a $k$-rational smooth point has infinitely many $k$-points. Let $k$ be a perfect large field and let $f \in k[x]$. Consider the evaluation map $f_k: k \to k$. Assume that $f_k$…