We consider a general class of discrete nonlinear Schrödinger equations (DNLS) on the lattice hZ with mesh size h > 0. In the continuum limit when h → 0, we prove that the limiting dynamics are given by a nonlinear Schrödinger equation (NLS) on R with the fractional Laplacian (− ) as dispersive symbol. In particular, we obtain that fractional powers 1 2 < α < 1 arise from long-range lattice int...

The fractional diffusion equation is derived from the master equation of continuous time random walks (CTRWs) via a straightforward application of the GnedenkoKolmogorov limit theorem. The Cauchy problem for the fractional diffusion equation is solved in various important and general cases. The meaning of the proper diffusion limit for CTRWs is discussed.

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...

The paper is devoted to the dissipative Schrödinger-Poisson system. We indicate conditions in terms of the Schrödinger-Poisson data which guarantee the uniqueness of the solution. Moreover, it is shown that if the system is sufficiently small shrunken, then it always admits a unique solution.

Carbon nanotube field-effect transistors (CNTFETs) have been studied in recent years as a potential alternative to CMOS devices, because of the capability of ballistic transport. In order to account for the ballistic transport we solved the coupled Poisson and Schrödinger equations for the analysis these devices. Conventionally the coupled Schrödinger-Poisson equation is solved iteratively, by ...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

A Drift-Diffusion-Schrödinger-Poisson system is presented, which models the transport of a quasi bidimensional electron gas confined in a nanostructure. We prove the existence of a unique solution to this nonlinear system. The proof makes use of some a priori estimates due to the physical structure of the problem, and also involves the resolution of a quasistatic Schrödinger-Poisson system.

interaction and correlation effects in quantum dots play a fundamental role in defining both their equilibrium and transport properties. numerical methods are commonly employed to study such systems. in this paper we investigate the numerical calculation of quantum transport of electrons in spherical centered defect ingaas/algaas quantum dot (scdqd). the simulation is based on the imaginary time...