O. Koch, C. Lubich:

"Analysis and time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics";

in: "ASC Report 04/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

We discuss existence, regularity and numerical approximation of

the solution to the multi-configuration time-dependent Hartree-Fock (MCTDHF)

equations in quantum dynamics. This method approximates the highdimensional

solution to the time-dependent electronic Schršodinger equation 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 timedependent

variational principle, consist of a coupled system of low-dimensional

nonlinear partial differential equations and ordinary differential equations. We

show that the MCTDHF equations have a global solution in the Sobolev space

H2 if the initial data has the same regularity. Moreover, we investigate the

convergence of a time integrator based on splitting of the vector field. First

order convergence in the H1 norm and second order convergence in L2 are

established

http://www.asc.tuwien.ac.at/preprint/2008/asc04x2008.pdf

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