Related papers: Dispersion Relations and Wave Operators in Self-Si…
We establish several new relations between the discrete transition operator, the continuous Laplacian and the averaging operator associated with combinatorial and metric graphs. It is shown that these operators can be expressed through each…
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations.…
We introduce a new semi-relativistic quantum operator for the length of the worldline a particle traces out as it moves. In this article the operator is constructed in a heuristic way and some of its elementary properties are explored. The…
The paper aims to study the spectral properties of elliptic operators with highly inhomogeneous coefficients and related issues concerning wave propagation in high-contrast media. A unified approach to solving problems in bounded domains…
Spectral analysis has long been recognized as a fundamental tool for studying the existence, uniqueness, and qualitative behavior of solutions to semilinear elliptic and parabolic equations, as well as their long-time dynamics. In modern…
We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary…
Multi-configurational wave functions are known to describe electronic structure across a Born-Oppenheimer surface qualitatively correct. However, for quantitative reaction energies, dynamical correlation originating from the many…
Novel results for the self-consistent single-particle spectral function and self-energy are presented for non-degenerate one-component Coulomb systems at various densities and temperatures. The GW^0-method for the dynamical self-energy is…
The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response…
The following version of the Lumer-Phillips is proved: a surjective dissipative operator is m-dissipative and invertible. The result remains true if dissipative linear relations (i.e multivalued operators) are considered. The main purpose…
In this paper we examine the semiclassical behavior of the scattering data of a non-self-adjoint Dirac operator with a rapidly oscillating potential that is complex analytic in some neighborhood of the real line. Some of our results are…
We consider the cubic Schrodinger equation on the line, for which the scattering theory requires modifications due to long range effects. We revisit the construction of the modified wave operator, and recall the construction of its inverse,…
Motivated by potential theory on discrete spaces, we study a family of unbounded Hermitian operators in Hilbert space which generalize the usual graph-theoretic discrete Laplacian. These operators are discrete analogues of the classical…
We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of complex-valued half-densities over a connected compact manifold without boundary. The eigenvalues of the principal symbol are assumed to be…
We construct nonlinear coherent states for the Susskind-Glogower operators by the application of the displacement operator on the vacuum state. We also construct nonlinear coherent states as eigenfunctions of a Hamiltonian constructed with…
We calculate the dispersion relations of plasmonic waves propagating along a chain of semiconducting or metallic nanoparticles in the presence of both a static magnetic field ${\bf B}$ and a liquid crystalline host. The dispersion relations…
We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyse linear stability of the fundamental self--similar solution of the wave equation with a focusing…
We develop a second-microlocal calculus of pseudodifferential operators in the semiclassical setting. These operators test for Lagrangian regularity of semiclassical families of distributions on a manifold $X$ with respect to a Lagrangian…
We study semilinear non-local elliptic problems driven by spectral-type operators of the form $\psi(-L_{|D})$ in a bounded $C^{1,1}$ domain $D\subset \mathbb{R}^d$ with a nonhomogeneous boundary condition. Here $\psi$ is a Bernstein…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…