Séminaire

Mardi 16 Mai 2023 à 11h00.

Low-rank analytical representation of operators for high-dimensional quantum dynamical simulations

''Grid-based approaches to quantum dynamics (molecules, electrons) imply the use of local operators, such as the the Potential Energy Surface (PES), in the form of multidimensional arrays (tensors). Arguably, the major bottleneck for decades now is to achieve a compact yet accurate low-rank approximation to these high-dimensional objects. Furthermore, explicit constraints to their functional form may exist as a result of the specific requirements of the algorithm with which they are interfaced. For instance, in the case of the Multiconfiguration Time-Dependent Hartree (MCTDH) approach to high-dimensional quantum dynamics, the so-called sum-of-products (SOP) form is a must. To tackle these problems, a plethora of methods have been developed. Roughly speaking, methods able to approximate any type of PES (vibrational, scattering, coupled states) could be divided into grid-based and grid-free ones. The former typically, though not necessarily, rely on a pre-existing PES routine. In contrast, the latter type of algorithms are able to yield the required SOP ansatz directly from a set of ab initio data. In this talk, we will present a comprehensive overview of our more recents developments in this direction. More specifically, we will discuss our approaches to obtain analytical SOP representations of low rank in Tucker and Canonical Polyadic forms.''