Displaying similar documents to “Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics”

An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics

Dajana Conte, Christian Lubich (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper gives an error analysis of the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of multi-particle time-dependent Schrödinger equations. The MCTDH method approximates the multivariate wave function by a linear combination of products of univariate functions and replaces the high-dimensional linear Schrödinger equation by a coupled system of ordinary differential equations and low-dimensional nonlinear partial differential equations. The main...

Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation

François Castella, Guillaume Dujardin (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we study the linear Schrödinger equation over the -dimensional torus, with small values of the perturbing potential. We consider numerical approximations of the associated solutions obtained by a symplectic splitting method (to discretize the time variable) in combination with the Fast Fourier Transform algorithm (to discretize the space variable). In this fully discrete setting, we prove that the regularity of the initial datum is preserved over long times,  times that...