Related papers: Completeness of generalized transmission eigenstat…
In this paper, we prove that Linearization Stability of Einstein Field Equations is a Generic Property in the sense that within the class $\mathcal{V}$ of space-times which admit a compact Cauchy hypersurface of constant mean curvature, the…
In recent years, unified correspondence has been developed as a generalized Sahlqvist theory which applies uniformly to all signatures of normal and regular (distributive) lattice expansions. This includes a general definition of the…
A number of authors have proposed stochastic versions of the Schr\"odinger equation, either as effective evolution equations for open quantum systems or as alternative theories with an intrinsic collapse mechanism. We discuss here two…
In this paper we present new solutions of the non-linear Schr\"oodinger equation proposed by Nobre, Rego-Monteiro and Tsallis for the free particle, obtained from different Lie symmetry reductions. Analytical expressions for the wave…
We report a systematic improvement to calculate the conductivity which associates to the anomaly of the propagation of surface acoustic waves at $\nu={1/2}$ above a two-dimensional electron gas. We try to resolve the discrepancy between…
We study generic semilinear Schr\"odinger systems which may be written in Hamiltonian form. In the presence of a single gauge invariance, the components of a solution may exchange mass between them while preserving the total mass. We…
In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. The transmission interfaces may join the domain boundary in a general way independent of the location…
An universal form of kinetic equation for open systems is considered which naturally unifies classical and quantum cases and allows to extend concept of wave function to open quantum systems. Corresponding stochastic Schr\"{o}dinger…
We introduce a new exactly integrable potential for the Schr\"odinger equation for which the solution of the problem may be expressed in terms of the Gauss hypergeometric functions. This is a potential step with variable height and…
This letter constructs, making use of the on-shell spinor-helicity formalism, a possible ultraviolet completion of gravity following a "bottom-up" approach. The assumptions of locality, unitarity and causality i) require an infinite tower…
We obtain scattering for the 3D Zakharov system with non-radial small data in the energy space with angular regularity of degree one. The main ingredient is a generalized Strichartz estimate for the Schr\"odinger equation in the space of…
We present a new approach to solve a Schr\"odinger Equation autonomous at infinity, by identifying the relation between the arrangement of the spectrum of the concerned operator and the behavior of the nonlinearity at zero and at infinity.…
We consider Schr\"odinger operators in $\ell^2(\Z)$ whose potentials are defined via continuous sampling along the orbits of a homeomorphism on a compact metric space. We show that for each non-atomic ergodic measure $\mu$, there is a dense…
A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schr\"odinger equation. The local symmetries of the potential are encoded into…
Let $\Omega\subseteq\mathbb R^n$ be a non-empty open set for which the Sobolev embedding $H_0^2(\Omega)\longrightarrow L^2(\Omega)$ is compact, and let $V\in L^\infty(\Omega)$ be a potential taking only positive real values and satisfying…
The elliptic-matrix quantum Olshanetsky-Perelomov problem is introduced for arbitrary root systems by means of an elliptic generalization of the Dunkl operators. Its equivalence with the double affine generalization of the…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
We consider the linearised vacuum Einstein equations around a Kerr exterior solution and present a scheme to prove elliptic $L^2(\mathbb{S}^2)$-estimates for the linearised curvature quantities in the equations. The scheme employs the…
We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for the bound states of generalized versions of the trigonometric and hyperbolic P\"oschl-Teller potentials. These new solvable potentials…
We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the…