On variational approximations in quantum molecular dynamics

By Christian Lubich. 2004

68 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “…aim to determine an approximation Y ( t ) in a manifold M of low-rank tensors by restricting the dynamics of (11) to the tangent space T Y ( t ) M : As explained in [183], this approximation is closely related to the can Dirac-Frenkel-McLachlan variational principle in quantum molecular dynamics.”
Dynamical Low-Rank Approximation (2007, methodology): “We refer to [ 11, Theorem 4.1 ] for a related quasi-optimality result in a situation of a linear dieren tial equation with an unbounded operator.”
Mathematik in den Naturwissenschaften Leipzig Tensor-Product Approximation to Operators and Functions in High Dimensions (2007, background): “In recent papers modern methods of structured tensor-product approximations to some classes of multidimensional integral operators and operator-valued functions have been applied successfully (see [1, 14, 10, 2, 12, 13, 17, 19, 22] and references therein).”
Dynamical low-rank approximation: applications and numerical experiments (2008, methodology): “d (xd,t), and derived dierential equations for the functions k from minimizing the defect in the Schr¨odinger equation as in (11), which is now known as the Dirac-Frenkel time-dependent variational principle in the chemical physics literature; see, e.g., [3, 16 ].”
A Dynamical Low-Rank Approach to the Chemical Master Equation (2008, unknown): “, [30, 3, 25, 26] and references therein).”
The geometry of algorithms using hierarchical tensors (2013, methodology): “For example, [32] analyzes the multi-configuration time-dependent Hartree (MCTDH) method [1] for many-particle quantum dynamics by relating this method to a flow problem on the manifold of fixed-rank Tucker tensors (in an infinite-dimensional setting).”
Numerical solution of the Hartree-Fock equation by multilevel tensor-structured methods (2011, unknown): “6.1 Brief summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.2 Presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140”