Related papers: Leaky Quantum Graphs: A Review

A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…

Hamiltonian tridiagonal matrices characterized by multi-fractal spectral measures in the family of Iterated Function Systems can be constructed by a recursive technique here described. We prove that these Hamiltonians are almost-periodic.…

We study Hamiltonians with point interactions in spaces of vector-valued functions. Using some information from the theory of quantum graphs we describe a class of the operators which can be reduced to the direct sum of several…

We consider magnetic Schroedinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the underlying combinatorial graph and a certain Hill operator.…

We introduce a minimal set of physically motivated postulates that the Hamiltonian H of a continuous-time quantum walk should satisfy in order to properly represent the quantum counterpart of the classical random walk on a given graph. We…

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…

Quantum symmetry of graph $C^{*}$-algebras has been studied, under the consideration of different formulations, in the past few years. It is already known that the compact quantum group $(\underbrace{C(S^{1})*C(S^{1})*\cdots…

Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…

The Hamiltonian dynamics of spherically symmetric massive thin shells in the general relativity is studied. Two different constraint dynamical systems representing this dynamics have been described recently; the relation of these two…

We consider a quantum mechanical particle living on a graph and discuss the behaviour of its wavefunction at graph vertices. In addition to the standard (or delta type) boundary conditions with continuous wavefunctions, we investigate two…

Charges associated with gauge symmetries are defined on boundaries of spacetimes. But these constructions typically involve divergent quantities when considering asymptotic boundaries. Different prescriptions exist to address this problem,…

Owing to their interesting spectral properties, the synthetic crystals over lattices other than regular Euclidean lattices, such as hyperbolic and fractal ones, have attracted renewed attention, especially from materials and meta-materials…

We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.

We propose an experiment to test the non-classicality of the gravitational interaction. We consider two optomechanical systems that are perfectly isolated, except for a weak gravitational coupling. If a suitable resonance condition is…

In this paper, we introduce the comaximal graph $\Gamma(L)$ of a finite-dimensional Lie algebra $L$, whose vertices are the nontrivial proper Lie subalgebras of $L$ over a field $\mathbb{F}$, and two vertices $A$ and $B$ are adjacent if and…

This paper is a direct continuation of an earlier work, where we studied Erd\"os-R\'enyi random graphs perturbed by an interaction Hamiltonian favouring the formation of short cycles. Here, we generalize these results. We keep the same…

A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…

We consider symmetric powers of a graph. In particular, we show that the spectra of the symmetric square of strongly regular graphs with the same parameters are equal. We also provide some bounds on the spectra of the symmetric squares of…

The level structure of nuclei offers a large amount and variety of information to improve our knowledge of the strong interaction and of mesoscopic quantum systems. Gamma spectroscopy is a powerful tool to perform such studies: modern gamma…

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…