All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2

Displaying 21 – 40 of 40

Showing per page

Numerical Analysis of the Adiabatic Variable Method for the Approximation of the Nuclear Hamiltonian

Yvon Maday, Gabriel Turinici (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Many problems in quantum chemistry deal with the computation of fundamental or excited states of molecules and lead to the resolution of eigenvalue problems. One of the major difficulties in these computations lies in the very large dimension of the systems to be solved. Indeed these eigenfunctions depend on 3n variables where n stands for the number of particles (electrons and/or nucleari) in the molecule. In order to diminish the size of the systems to be solved, the chemists have proposed...

Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models

Eric Cancès, Rachida Chakir, Yvon Maday (2012)

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

In this article, we provide a priorierror estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the...

Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models

Eric Cancès, Rachida Chakir, Yvon Maday (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the...

Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics

Othmar Koch, Christian Lubich (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We discuss the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of the time-dependent Schrödinger equation in quantum molecular dynamics. This method approximates the high-dimensional nuclear wave function by a linear combination of products of functions depending only on a single degree of freedom. The equations of motion, obtained via the Dirac-Frenkel time-dependent variational principle, consist of a coupled system of low-dimensional nonlinear partial differential...

The smooth continuation method in optimal control with an application to quantum systems

Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system...

The smooth continuation method in optimal control with an application to quantum systems

Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system...

Currently displaying 21 – 40 of 40

Previous Page 2