Multilayer formulation of the multiconfiguration time-dependent Hartree theory

By Haobin Wang, M. Thoss. 2003

853 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Moreover, the so called multilayer multi-configuration time-dependent Hartree method (MLMCTDH) introduced in [267] makes use of a decomposition based on general trees instead of binary trees.”
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].”
Quantum dynamics simulations using Gaussian wavepackets: the vMCG method (2015, methodology): “The full power of the MCTDH method for solving the TDSE is seen in the multilayer variant, ML-MCTDH [43].”
Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances (2012, methodology): “In computational molecular dynamics such methods are known for longer time as hierarchical or binary cascadic multi-configuration methods (MCTDH) used in combination with the Tucker tensor format (see [2, 99, 68] for further details).”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “The HT decompositions lead naturally to a distributed Tucker decomposi8 The HT model was developed independently, from a different perspective, in the chemistry community under the name MultiLayer Multi-Configurational Time-Dependent Hartree method (ML-MCTDH) [275].”
Dynamical Tensor Approximation (2010, methodology): “The dynamical tensor approximation approach for the Tucker format can be extended to the hierarchical tensor format described in [2, 5, 13, 18], which has only cubic scaling with N .”
The geometry of algorithms using hierarchical tensors (2013, background): “In particular, the HT format has its analogue in the multilayer version of MCDTH of [22].”
O(dlog N)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling (2011, methodology): “In computational molecular dynamics such methods are known for longer time as hierarchical or binary cascadic multi-configuration methods to be used in the framework of the Tucker tensor format (see [1, 45, 33] for further”
Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors (2013, methodology): “5) were already used in the quantum chemists community [32]; see also [20, p.”
QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations (2011, background): “the matrix product states (MPS) in DMRG quantum computations [46, 43, 44]).”