Perfect quantum wire structures are attractive candidates for low threshold lasers and high speed electronic devices because of the nature of the density of states and eigenfunctions. In this letter, we discuss the effect of structural disorder on the density of states as well as on the localization length of these eigenstates. We find that significant changes in the density of states and eigen...

We propose a framework for supersymmetric Dirac operators to have threshold energies. We apply the obtained results to magnetic Dirac operators with positive mass in order to investigate the asymptotic behaviors at infinity of the threshold eigenfunctions. It turns out that the results of most of the existing works on the zero modes of the Weyl-Dirac operators remain to hold for the threshold e...

Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic mechanical differential equation the presence of Dunkl operator-based deformation and investigate solutions for two important problems three-dimensional spatial space. To end, after introducing mechanics, examine Dunkl–Klein–Gordon oscillator with Cartesian spherical coord...

We present a framework for calculating low-dimensional bases to represent image irradiance from surfaces with isotropic reflectance under arbitrary illumination. By representing the illumination and the bidirectional reflectance distribution function (BRDF) in frequency space, a model for the image irradiance is derived. This model is then reduced in dimensionality by analytically constructing ...

In this paper we prove that the level sets of the first non–constant eigenfunction of the Neumann Laplacian on a convex planar domain have only finitely many connected components. This problem is motivated, in part, by the “hot spots” conjecture of J. Rauch. ∗Supported in part by NSF Grant # 9700585-DMS

A theorem is proved to the effect that a wave function for a set of N spins,, which is a product of single-spin wave functions and which is an eigenstate of the square of the total spin S*, must be a state with the maximum possible value of S* and of S 3 z being an arbitrary direction. This theorem has z been applied in a separate work by the authors to show strikingly that the imposition of sy...

At short distances, energy eigenfunctions of chaotic systems have spatial correlations that are well described by assuming a microcanonical density in phase space for the corresponding Wigner function. However, this is not correct on large scales. The correct correlation function is in turn needed to get the correct formula for the root-mean-square value of the off-diagonal matrix elements of s...

An ion moving in a constant magnetic field is considered as the generic example of two-dimensional topological (Chern-Simons) theory. The eigenfunctions for the generic particle are determined by solving Schrödinger’s equation in the secular and non-secular forms of the theory, corresponding to the inclusion and non-inclusion respectively in the Lagrangian of the particle’s kinetic energy. A no...

We present a proof of the explicit formula for asymptotically free eigenfunctions $$B_N$$ q-Toda operator which was conjectured by first and third authors. This can be regarded as branching from eigenfunction restricted to $$A_{N-1}$$ eigenfunctions. The is given contiguity relation recursion coefficients.

On the canonical 2-sphere and for Schrödinger eigenfunctions, we obtain a simple geometric criterion on potential under which can improve, near given point every $$p\ne 6$$ , Sogge’s estimates by power of eigenvalue. This be formulated in terms critical points Radon transform it is independent choice eigenfunctions.