Related papers: Inverse scattering on the quantum graph -- Edge mo…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
We define scattering data for the Newton equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some $\alpha\in (0,1]$. We provide estimates on the scattering solutions and scattering data and…
The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…
We show that the spectrum of the Schrodinger operator on a finite, metric graph determines uniquely the connectivity matrix and the bond lengths, provided that the lengths are non-commensurate and the connectivity is simple (no parallel…
Scattering theory for p-forms on manifolds with cylindrical ends has a direct interpretation in terms of cohomology. Using the Hodge isomorphism,the scattering matrix at low energy may be regarded as operator on the cohomology of the…
Resonant scattering of electrons with low energies (as compared to the bandwidth) on a single neutral short-range impurity in graphene is analyzed theoretically, taking into account the valley degeneracy. Resonances dramatically increase…
In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a…
We analytically calculate the energy spectrum of a circular graphene quantum dot with radius R subjected to a perpendicular magnetic field B by applying the infinite-mass boundary condition. We can retrieve well-known limits for the cases…
We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions…
We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation. A scattering transform is a deep convolution network computed with a cascade of…
We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in…
Aspects of of plane wave electromagnetic scattering by a radially inhomogeneous sphere is discussed. The vector problem is reduced to two scalar radial `Schr\"odinger-like' equations, and a connection with time-independent potential…
We study the resonant scattering for discrete time quantum walks on graphs with some tails. In our arguments, we reduce the study of resonances to the perturbation of eigenvalues of a finite rank matrix associated with the internal graph.…
Random band matrices relevant for open chaotic systems are introduced and studied. The scattering model based on such matrices may serve for the description of preequilibrium chaotic scattering. In the limit of a large number of open…
We address the two-dimensional band-structure of graphene above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the…
The $J$-matrix inverse scattering approach can be used as an alternative to a conventional $R$-matrix in analyzing scattering phase shifts and extracting resonance energies and widths from experimental data. A great advantage of the…
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…
We discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links, assuming that the vertex coupling is manifestly non-invariant with respect to the time…
In this paper we consider the inverse scattering problem for the Schr{\"o}dinger operator with short-range electric potential. We prove in dimension n $\geq$ 2 that the knowledge of the scattering operator determines the electric potential…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…