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The response part of the exchange-correlation potential of Kohn-Sham density functional theory plays a very important role, for example for the calculation of accurate band gaps and excitation energies. Here we analyze this part of the…
The multichannel scattering problem for the stationary Schr\"{o}dinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions and of the transition matrix relating the…
An important quantity in electronic systems is the quasiparticle scattering rate (QPSR). A related optical scattering rate (OSR) is routinely extracted from optical data, and, while it is not the same as the QPSR, it nevertheless displays…
We investigate a functional obtained by summing the squared differences of the integral of an Ito process over disjoint intervals. The limit of this sum is shown to converge in probability to two thirds the quadratic variation of the…
The restricted optical sum rule and its dependence on the temperature, a superconducting gap and the cutoff energy have been investigated. As known this sum rule depends on the cutoff energy and the relaxation rate even for a homogeneous…
A sum rule is derived for elastic scattering of hadrons at high energies which is in good agreement with experimental data on $p\bar{p}$ available upto the maximum energy $\sqrt{s} = 2 TeV$. Physically, our sum rule reflects the way…
1.An expression for the smoothed counting function in terms of the fractional derivatives of the delta-function is presented. 2. The Neumann-Dirichlet (ND) boundary problem is introduced via some elementary examples based on a functorial…
Theory of scattering of massive chiral fermions in bilayer graphene by radial symmetric potential is developed. It is shown that in the case when the electron wavelength is much larger than the radius of the potential the scattering…
Screening effects are important to understand various aspects of ion-solid interactions and, in particular, play a crucial role in the stopping of ions in solids. In this paper the phase shifts and scattering amplitudes for the…
We investigate the influence of technical parameters in dynamic electrical conductivity calculations by the Kubo-Greenwood formula on the value of the so-called sum rule. We propose a possible explanation of the slight overestimation of the…
For a scattering system $\{A_\Theta,A_0\}$ consisting of selfadjoint extensions $A_\Theta$ and $A_0$ of a symmetric operator $A$ with finite deficiency indices, the scattering matrix $\{S_\gT(\gl)\}$ and a spectral shift function…
We study the scattering problem, the Sturm-Liouville problem and the spectral problem with periodic or skew-periodic boundary conditions for the one-dimensional Schr\"odinger equation with an $n$-cell (finite periodic) potential. We give…
We consider the symmetry property of the inelastic overlap function and its relation to the reflective scattering mode appearance.
We discuss the possibility to extend the spectral action up to energy close to the Planck scale, taking also into account the gravitational effects given by graviton exchange. Including this contribution in the theory, the coupling constant…
In conventional scattering theory, to obtain an explicit result, one imposes a precondition that the distance between target and observer is infinite. With the help of this precondition, one can asymptotically replace the Hankel function…
The solution of the scattering problem based on the Lippmann-Schwinger equation requires in many cases a discretization of the spectrum in the continuum which does not respect the unitary equivalence of the S-matrix on the finite grid. We…
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…
In this paper we investigate the spectral and scattering theory for operators acting on topological crystals and on their perturbations. A special attention is paid to perturbations obtained by the addition of an infinite number of edges,…
We study the semi-classical behavior of the spectral function of the Schr\"{o}dinger operator with short range potential. We prove that the spectral function is a semi-classical Fourier integral operator quantizing the forward and backward…
We show that the delta function potential can be exploited along with perturbation theory to yield the result of certain infinite series. The idea is that any exactly soluble potential if coupled with a delta function potential remains…