Related papers: Dirac particles on periodic quantum graphs
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 consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the…
We investigate nonlinear Dirac equations on a periodic quantum graph $G$ and develop a variational approach to the existence and multiplicity of bound states. After introducing the Dirac operator on $G$ with a $\mathbb Z^{d}$-periodic…
The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a randomly chosen momentum belongs to the spectrum of the periodic…
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…
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…
Quantum graphs and their experimental counterparts, microwave networks, are ideally suited to study the spectral statistics of chaotic systems. The graph spectrum is obtained from the zeros of a secular determinant derived from energy and…
It has been found that quantum corrections can substantially affect the classical results of tracking for trajectories close to the separatrix. Hence the development of a basic formalism for obtaining the quantum maps for any particle beam…
We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circulant graphs with standard vertex conditions maintain…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We study the dependence of the spectral gap (the first positive…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
We present quantum graphs with remarkably regular spectral characteristics. We call them {\it regular quantum graphs}. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
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 address the problem of identifying families of discrete models naturally flowing in continuum limit to relativistic quantum field theories. We call them Dirac graphs. In this work, we require the graphs to obey spectrality property,…
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $\sigma$--model…
Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…
Quantum graphs were introduced to model free electrons in organic molecules using a self-adjoint Hamiltonian on a network of intervals. A second graph quantization describes wave propagation on a graph by specifying scattering matrices at…