Related papers: Zero resonances for localised potentials
The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact…
We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…
Many fractional quantum Hall wave functions are known to be unique and highest-density zero modes of certain "pseudopotential" Hamiltonians. Examples include the Read-Rezayi series (in particular, the Laughlin, Moore-Read and Read-Rezayi…
We investigate correlations among various parameters in the solution space of minimal supersymmetric grand unification. In particular the extent to which the top quark Yukawa coupling exhibits fixed point behavior is discussed and we…
We provide a short proof of the convergence of the Born series on asymptotically conic manifolds, at sufficiently high energy. The potential is allowed to have multiple Coulomb singularities. This is handled using powerful semiclassical…
We discuss the resonances of Hamiltonians with constant electric field in one dimension in the limit of small field. These resonances occur near the real axis, near zeros of the analytic continuation of a reflection coefficient for…
The determination of renormalized parameters in model Hamiltonians is discussed. A simple model of a 3d compound is studied, and it is shown how higher states can be projected out, resulting in a simpler model with renormalized parameters.…
Light-front Hamiltonian for Yukawa type models is determined without the framework of canonical light-front formalism. Special attention is given to the contribution of zero modes.
We propose a method to construct localized single particle wave functions using imaginary time projection and thereby determine lattice Hamiltonian parameters. We apply the method to a specific disordered potential generated by an optical…
Resonances are uniquely characterized by their complex pole locations and the corresponding residues. In practice, however, resonances are typically identified experimentally as structures in invariant mass distributions, with branching…
We study two uncoupled oscillators, horizontal and vertical, residing in rectilinear polygons (with only vertical and horizontal sides) and impacting elastically from their boundary. The main purpose of the article is to analyze the…
We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…
The quantization of superconducting transmission-line resonators is usually introduced phenomenologically by modeling the resonator as an effective LC circuit and imposing canonical commutation relations on macroscopic variables such as…
Photons, i.e. the basic energy quanta of monochromatic waves, are highly non-localised and occupy all available space in one dimension. This non-local property can complicate the modelling of the quantised electromagnetic field in the…
We consider a Riemannian cylinder endowed with a closed potential 1-form A and study the magnetic Laplacian with magnetic Neumann boundary conditions associated with those data. We establish a sharp lower bound for the first eigenvalue and…
A local magnetic equilibrium model is presented, with finite aspect ratio and up-down asymmetrically shaped cross section, that depends on eight free parameters. In contrast with other local equilibria, which provide simple magnetic-surface…
We describe a method for the accurate calculation of bound-state and resonance energies for one-dimensional potentials. We calculate the shape resonances for symmetric two-barrier potentials and compare them with those coming from the…
We investigate the stability with respect to homogenization of classes of integrals arising in the control-theoretic interpretation of some Hamilton-Jacobi equations. The prototypical case is the homogenization of energies with a Lagrangian…
In this paper, we construct isospectral Hamiltonians without shape invariant potentials for the relativistic quantum mechanical potentials such as the Dirac Oscillator and Hydrogen-like atom.
We present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological Coupled-Mode Theory. We calculate the…