Related papers: Spectral filtering in quantum Y-junction
This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems.…
There exists a simple relationship between a quantum-mechanical bound-state wave function and that of nearby scattering states, when the scattering energy is extrapolated to that of the bound state. This relationship is demonstrated…
It is known that the spin structure on a Riemannian manifold can be extended to noncommutative geometry using the notion of a spectral triple. For finite geometries, the corresponding finite spectral triples are completely described in…
In order to obtain perfect state transfer between two sites in a network of interacting qubits, their corresponding vertices in the underlying graph must satisfy a combinatorial property called strong cospectrality. Here we determine the…
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…
We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional curved strip. We impose the Dirichlet and Neumann boundary conditions on opposite sides of the strip. The existence of the…
We investigate the scattering of a point particle from n non-overlapping, disconnected hard disks which are fixed in the two-dimensional plane and study the connection between the spectral properties of the quantum-mechanical scattering…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
We study direct and inverse scattering problem for systems of interacting particles, having web-like structure. Such systems consist of a finite number of semi-infinite chains attached to the central part formed by a finite number of…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz hypersurface. They…
We consider a realistic model for calculating the cross-spectral density of partially coherent beams from an x-ray undulator in a modern storage ring. This two-point coherence function is seen to have a speckled structure associated with…
We show how in PT-symmetric 2J-level quantum systems the assumption of an upside-down symmetry (or duality) of their spectra simplifies their classification based on the non-equivalent pairwise mergers of the energy levels.
The spectral properties of non-self-adjoint extensions $A_{[B]}$ of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in…
In the paper the one-dimensional one-center scattering problem with the initial potential $\alpha |x|^{-1}$ on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as…
The spectrum of planar N=6 superconformal Chern-Simons theory, dual to type IIA superstring theory on $AdS_4 \times CP^3$, is accessible at finite coupling using integrability. Starting from the results of [arXiv:1403.1859], we study in…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
The description of electron current through a splitting is a mathematical problem of electron transport in quantum networks. For quantum networks constructed on the interface of narrow-gap semiconductors the relevant scattering problem for…
A nonlinear scattering transform is studied for the two-dimensional Schrodinger equation at zero energy with a radial potential. First explicit examples are presented, both theoretically and computationally, of potentials with nontrivial…