Related papers: Spectral Properties of Quantum Circulant Graphs
In the past few decades, quantum algorithms have become a popular research area of both mathematicians and engineers. Among them, uniform mixing provides a uniform probability distribution of quantum information over time which attracts a…
A semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems. The approach is based on periodic orbit theory, the exact semiclassical trace…
We evaluate the variance of coefficients of the characteristic polynomial for binary quantum graphs using a dynamical approach. This is the first example where a spectral statistic can be evaluated in terms of periodic orbits for a system…
For non-Hermitian equilateral q-pointed star-shaped quantum graphs of paper I [Can. J. Phys. 90, 1287 (2012), arXiv 1205.5211] we show that due to certain dynamical aspects of the model as controlled by the external, rotation-symmetric…
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…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
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,…
The paper concerns the automorphism groups of Cayley graphs over cyclic groups which have a rational spectrum (rational circulant graphs for short). With the aid of the techniques of Schur rings it is shown that the problem is equivalent to…
Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the…
Studying the spectral theory of Schroedinger operator on metric graphs (also known as quantum graphs) is advantageous on its own as well as to demonstrate key concepts of general spectral theory. There are some excellent references for this…
Quantum graphs are an operator space generalization of classical graphs that have emerged in different branches of mathematics including operator theory, non-commutative topology and quantum information theory. In this paper, we obtain…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
We report on spectra of circuit-quantum-electrodynamics (QED) systems in an intermediate regime that lies between the ultrastrong and deep-strong-coupling regimes, which have been reported previously in the literature. Our experimental…
We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a $\delta$-coupling at the points where the rings touch. We start…
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…
Circulant graphs are a widely studied family of graphs whose members possess varying amounts of symmetry. Although considerable progress has been made in finding the automorphism groups of circulant graphs under certain restrictions, a…
This paper gives lower bounds on the spectral radius of vertex-transitive graphs, based on the number of ``prime cycles'' at a vertex. The bounds are obtained by constructing circuits in the graph that resemble ``cactus trees'', and…