ELFT HÍRADÓ

[Nagy Attila <sem-admin AT szfki.hu>]

SZFI Seminar

DOMINIK SULZ

University of Tübingen (host: Legeza Örs)

_MANY-BODY QUANTUM DYNAMICS USING TREE TENSOR NETWORKS_

Tuesday, 28 May 2024, 13:00, KFKI Campus, Bldg. 1, 2nd floor, Conference 
Room

In many applications, it is of interest to numerically solve high-order 
tensor differential equations, e.g. the many-body Schrödinger equation 
in quantum physics or discretized high-dimensional time-dependent 
partial differential equations. Tree tensor networks (TTNs) turned out 
to be a promising ansatz to overcome the so-called "curse of 
dimensionality'' as they are an efficient hierarchical data sparse 
format to approximate tensors. Based on the dynamical low-rank 
approximation, several novel time integration methods for TTNs have been 
proposed in the last few years. In a recursion from the leaves up to the 
root, all nodes are updated by only solving small matrix-/tensor 
differential equations. The proposed methods are robust even in the 
presence of small singular values. Further properties like 
rank-adaptivity, norm and energy preservation and error behaviour are 
mathematically are discussed.

The talk intends to give an overview of the latest results for dynamical 
low-rank approximations. Further, the different time integration methods 
and their applicability to many-body quantum systems are discussed. 
Numerical experiments validate the theoretical results and show several 
applications from quantum physics.

MINDEN ÉRDEKLŐDŐT SZÍVESEN LÁTUNK! - EVERYONE IS WELCOME TO ATTEND.

Attila Nagy
sem-admin AT szfki.hu