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Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain

Valeria Banica (2003)

Journées équations aux dérivées partielles

We concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound from below the blow-up rate for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than ( T - t ) - 1 , the expected one. Moreover, we state that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.

Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain

Valeria Banica (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than ( T - t ) - 1 , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.

Remarks on the Fundamental Solution to Schrödinger Equation with Variable Coefficients

Kenichi Ito, Shu Nakamura (2012)

Annales de l’institut Fourier

We consider Schrödinger operators H on ℝ n with variable coefficients. Let H 0 = - 1 2 ▵ be the free Schrödinger operator and we suppose H is a “short-range” perturbation of H 0 . Then, under the nontrapping condition, we show that the time evolution operator: e - i t H can be written as a product of the free evolution operator e - i t H 0 and a Fourier integral operator W ( t ) which is associated to the canonical relation given by the classical mechanical scattering. We also prove a similar result for the wave operators. These results...

Scattering theory for 3-particle systems in constant magnetic fields : dispersive case

Christian Gérard, Izabella Łaba (1996)

Annales de l'institut Fourier

We develop a scattering theory for quantum systems of three charged particles in a constant magnetic field. For such systems, we generalize our earlier results in that we make no additional assumptions on the electric charges of subsystems. The main difficulty is the analysis of the scattering channels corresponding to the motion of the bound states of the neutral subsystems in the directions transversal to the field. The effective kinetic energy of this motion is given by certain dispersive Hamiltonians;...

Schrödinger operator with magnetic field in domain with corners

Virginie Bonnaillie Noël (2005)

Journées Équations aux dérivées partielles

We present here a simplified version of results obtained with F. Alouges, M. Dauge, B. Helffer and G. Vial (cf [4, 7, 9]). We analyze the Schrödinger operator with magnetic field in an infinite sector. This study allows to determine accurate approximation of the low-lying eigenpairs of the Schrödinger operator in domains with corners. We complete this analysis with numerical experiments.

s∗-compressibility of the discrete Hartree-Fock equation

Heinz-Jürgen Flad, Reinhold Schneider (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...

s∗-compressibility of the discrete Hartree-Fock equation

Heinz-Jürgen Flad, Reinhold Schneider (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...

Currently displaying 221 – 240 of 317