Related papers: Trace formulas for Schr\"odinger operators on star…
In this mostly expository note, we prove explicit formulas for the traces of Hecke operators on spaces of cusp forms fixed by Atkin-Lehner involutions, which are suitable for efficient implementation. In addition, we correct a couple of…
An explicit derivation of dispersion relations and spectra for periodic Schr\"{o}dinger operators on carbon nano-structures (including graphen and all types of single-wall nano-tubes) is provided.
In this paper we establish spectral comparison results for Schr\"odinger operators on a certain class of infinite quantum graphs, using recent results obtained in the finite setting. We also show that new features do appear on infinite…
This paper extends the trace formulas of [5] with perturbations in normed ideals of $B(H)$ to multivariate functions of commuting contractions admitting a dilation to commuting normal contractions.
We prove that the so-called first trace formula holds for all Schr\"odinger operators on the line with real-valued integrable potentials.
We introduce a method of computing biquandle brackets of oriented knots and links using a type of decorated trivalent spatial graphs we call trace diagrams. We identify algebraic conditions on the biquandle bracket coefficients for moving…
We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on…
We prove new formulae for the wave operators for a Friedrichs scattering system with a rank one perturbation, and we derive a topological version of Levinson's theorem for this model.
The spectrum of the evolution Operator associated with a nonlinear stochastic flow with additive noise is evaluated by diagonalization in a polynomial basis. The method works for arbitrary noise strength. In the weak noise limit we…
This paper gives combinatorial formulas for discrete series constants, both stable and unstable, on real reductive groups. It also carries out one step of the comparison of the topological trace formula for Hecke operators with Arthur's…
The study of the scattering data for a star-shape network of LC-transmission lines is transformed into the scattering analysis of a Schr\"odinger operator on the same graph. The boundary conditions coming from the Kirchhoff rules ensure the…
Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…
A method based on Rayleigh-Schroedinger perturbation theory is developed that allows to obtain high-order series expansions for ground-state properties of quantum lattice models. The approach is capable of treating both lattice geometries…
Koplienko gave a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class $\mathcal{B}_2(\mathcal{H})$. Recently Gesztesy, Pushnitski and Simon gave an alternative proof of the trace formula when the…
For a star-shaped graph, we introduce special characters and study their properties. We decompose special characters into odd and even parts and study their evolution under reflections. We apply the obtained formulas to prove that the…
We consider the difference $f(-\Delta +V)-f(-\Delta)$ of functions of Schr\"odinger operators in $L^2(\mathbb R^d)$ and provide conditions under which this difference is trace class. We are particularly interested in non-smooth functions…
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…
We establish Plemelj-Smithies formulas for determinants in different algebras of operators. In particular we define a Poincar\'e type determinant for operators on the torus $\Tn$ and deduce formulas for determinants of periodic…
The goal of the paper is to establish cubature formulas on combinatorial graphs. Two types of cubature formulas are developed. Cubature formulas of the first type are exact on spaces of variational splines on graphs. Since badlimited…
We give a proof of a formula for the trace of self-braidings (in an arbitrary channel) in UMTCs which first appeared in the context of rational conformal field theories (CFTs). The trace is another invariant for UMTCs which depends only on…