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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 result of this paper yields an L2 error bound of the MCTDH approximation in terms of a best-approximation error bound in a stronger norm and of lower bounds of singular values of matrix unfoldings of the coefficient tensor. This result permits us to establish convergence of the MCTDH method to the exact wave function under appropriate conditions on the approximability of the wave function, and it points to reasons for possible failure in other cases.
@article{M2AN_2010__44_4_759_0,
author = {Conte, Dajana and Lubich, Christian},
title = {An error analysis of the multi-configuration time-dependent {Hartree} method of quantum dynamics},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {759--780},
publisher = {EDP-Sciences},
volume = {44},
number = {4},
year = {2010},
doi = {10.1051/m2an/2010018},
mrnumber = {2683582},
zbl = {1192.81125},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010018/}
}
TY - JOUR AU - Conte, Dajana AU - Lubich, Christian TI - An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2010 SP - 759 EP - 780 VL - 44 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010018/ DO - 10.1051/m2an/2010018 LA - en ID - M2AN_2010__44_4_759_0 ER -
%0 Journal Article %A Conte, Dajana %A Lubich, Christian %T An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2010 %P 759-780 %V 44 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010018/ %R 10.1051/m2an/2010018 %G en %F M2AN_2010__44_4_759_0
Conte, Dajana; Lubich, Christian. An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 4, pp. 759-780. doi: 10.1051/m2an/2010018
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