In this review we discuss quantum phase transitions and the mapping between symmetry breaking of electronic structure con® gurations at the large-dimension limit and mean-® eld theory of phase transitions. We show that the ® nite size scaling method can be used for the calculations of the critical parameters of the few-body Schr È odinger equation. In this approach, the ® nite size corresponds ...

The three-dimensional Schr/Sdinger equation inverse scattering problem with a nonspherically-symmetric potential is related to the filtering problem of computing the linear leastsquares estimate of the three-dimensional random field on the surface of a sphere from noisy observations inside the sphere. The relation consists of associating an estimation problem with the inverse scattering problem...

Tuncay Aktosun Department of Mathematics North Dakota State University Fargo, ND 58105 Martin Klaus Department of Mathematics Virginia Polytechnic Institute and State University Blacksburg, VA 24061 Cornelis van der Mee Department of Mathematics University of Cagliari Cagliari, Italy Abstract: In this review paper, the generalized Schr odinger equation d2 =dx2 + k2 = [ikP (x) +Q(x)] is conside...

In this paper, we present the main issues and the modelling approaches for the simulation of nanoscale MOSFETs in which transport is dominated by ballistic electrons. We show that is indeed possible to compute in an accurate way the density of states in the channel in the case of quantum confinement without solving the complete two-dimensional Schr€ odinger equation. We are developing modelling...

The strongly coupled nonlinear Schr odinger equations are studied numerically to gain insight into an increasingly complex family of collision interactions. Speci cally, the case of apparent repulsion between soliton solutions are considered in terms of phase velocity, relative shift, and apparent trajectory. Both elastic and inelastic collisions are discussed. −→∞ ∞←− anisotropic e ects on por...

The purpose of the study was to identify subjective experiences that are characteristic of schizophrenia. A questionnaire for self-assessment of disturbances in several cognitive-perceptual areas (the Eppendorf Schizophrenia Inventory) was constructed and administered to first episode schizophrenia patients (SCHf; n = 45), negative-syndrome schizophrenia patients (SCHn; n = 45), remitted schizo...

The one particle sector of the simplest one dimensional quantum lattice gas automaton has been observed to simulate both the (relativistic) Dirac and (nonrelativistic) Schrodinger equations, in di erent continuum limits. By analyzing the discrete analogues of plane waves in this sector we nd conserved quantities corresponding to energy and momentum. We show that the Klein paradox obtains so th...

As a prelude to a truly non-perturbative evaluation of the e ective potential in terms of lattice QCD, the one loop e ective potential for a non-Abelian gauge con guration is calculated using the background eld method. Through a non-trivial correlation between the space and color orientations the new background eld avoids the possible coordinate singularity, DetBa i = 0, observed recently by Ke...

A framework that naturally uni es smoothing and enhancement processes is presented. We generalize the linear and nonlinear scale spaces in the complex domain, by combining the di usion equation with the simpli ed schrodinger equation. A fundamental solution for the linear case is developed. Preliminary analysis of the complex di usion shows that the generalized di usion has properties of both ...

Marseille Cedex 9 France One-dimensional quantum scattering for potentials de ned as measures Charles-Antoine GUERIN1 Abstract We generalize the basic one-dimensional scattering formalism to potentials de ned as measures and retrieve the classical results that hold for smooth potentials. We introduce a set of generalized eigenfunctions for the corresponding Schr odinger operator and study thei...