The Spectral Shift Function of a Compactly Supported Potential and Wegner Estimates
نویسندگان
چکیده
We analyze the spectral shift function (SSF) of a Schrödinger operator due to a compactly supported potential. We give a bound on the integral of the SSF with respect to a bounded compactly supported function. It is based on the control of the singular values of the difference of two Schrödinger semigroups. As an application we improve some earlier results on the regularity of the integrated density of states.
منابع مشابه
Collocation Method using Compactly Supported Radial Basis Function for Solving Volterra's Population Model
In this paper, indirect collocation approach based on compactly supported radial basis function (CSRBF) is applied for solving Volterra's population model. The method reduces the solution of this problem to the solution of a system of algebraic equations. Volterra's model is a non-linear integro-differential equation where the integral term represents the effect of toxin. To solve the pr...
متن کاملElectronic Spectral Line Shape of a Diatomic Molecule
The electronic absorption spectral line shape of a diatomic molecule with harmonic potential curves is calculated using the time correlation function formalism. Both the equilibrium shift and the frequency shift of the two linking electronic states ate taken into account. The spectrum is also calculated using the cumulated expansion which is related to the correlation function of the time-d...
متن کاملLarge Amplitude Vibration Analysis of Graphene Sheets as Resonant Mass Sensors Using Mixed Pseudo-Spectral and Integral Quadrature Methods
The present paper investigates the potential application of graphene sheets with attached nanoparticles as resonant sensors by introducing a nonlocal shear deformation plate model. To take into account an elastic connection between the nanoplate and the attached nanoparticle, the nanoparticle is considered as a mass-spring system. Then, a combination of pseudo-spectral and integral quadrature m...
متن کاملUniform convergence of spectral shift functions
The spectral shift function ξL(E) for a Schrödinger operator restricted to a finite cube of length L in multi-dimensional Euclidean space, with Dirichlet boundary conditions, counts the number of eigenvalues less than or equal to E ∈ R created by a perturbation potential V . We study the behavior of this function ξL(E) as L→∞ for the case of a compactly-supported and bounded potential V . After...
متن کاملWegner Estimate for Discrete Alloy-type Models
We study discrete alloy type random Schrödinger operators on `(Z). Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of...
متن کامل