From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis

By Christian Lubich. 2008

504 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Numerical Analysis

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In Atomic and Molecular Physics, and Optics

In Numerical Analysis

Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “The efﬁcient and robust numerical integration of (12) is crucial to the success of dynamical low-rank methods; apart from the references above, this aspect has been discussed in [184,185].”
O(dlog N)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling (2011, background): “In computational molecular dynamics such methods have been known for a long time as hierarchical or binary cascadic multi-configuration tensor methods (see [1, 33] for further details).”
Tensor-Train Decomposition (2011, background): “An efficient representation of a tensor (by tensor we mean only an array with d indices) by a small number of parameters may give us an opportunity and ability to work with d-dimensional problems, with d being as high as 10, 100, or even 1000 (such problems appear in quantum molecular dynamics [28, ”
Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen (2013, background): “Dass diese Formate von praktischer Bedeutung sind, wird allein dadurch belegt, dass sie in der Quantenmechanik schon seit längerer Zeit verwendet werden [6, 68, 80, 89, 106, 108].”
Quantics-TT Collocation Approximation of Parameter-Dependent and Stochastic Elliptic PDEs (2010, unknown): “AMS Subject Classification: 65F30, 65F50, 65N35, 65F10 Key words: elliptic equations, stochastic PDEs, the Karhunen-Loève expansion, separable approximation, quantics-TT tensors, preconditioners, tensor-truncated iteration.”
Quantized-TT-Cayley transform to compute dynamics and spectrum of high-dimensional Hamiltonians (2011, background): “AMS Subject Classification: 65F30, 65F50, 65N35, 65F10 Key words: High-dimensional problems, rank structured tensor approximation, quantized representation of vectors, matrix valued functions, Cayley transform, model reduction, molecular dynamics.”
The geometry of algorithms using hierarchical tensors (2013, methodology): “A smooth manifold structure underlies this analysis; see also [34] for related methods.”
Geometric Structures in Tensor Representations (Final Release) (2013, unknown): “5, we give a formalisation in this framework of the multi–configuration time–dependent Hartree MCTDH method (see [25]) in tensor Banach spaces.”
DMRG Approach to Fast Linear Algebra in the TT-Format (2011, background): “Tensors arise naturally in high-dimensional problems, for example, in quantum chemistry [1, 2], ﬁnancial mathematics [3, 4] and many others.”
Efficient time-stepping scheme for dynamics on TT-manifolds (2012, unknown): “We refer the reader to the book [22] for more details.”
Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors (2013, methodology): “In the context of the time-dependent Schrödinger equation, the approach is known as the Dirac–Frenkel time-dependent variational principle [20].”
QTT approximation of elliptic solution operators in higher dimensions (2011, background): “Such applications include the computation of vibrational ground state for quantum molecular dynamics problems [24, 26], and solution of stochastic partial differential equations [25].”