Mathematical and Numerical Methods for Complex Quantum Systems

The Multilayer Multiconfiguration Time-Dependent Hartree Theory

Haobin Wang

New Mexico State University

The multilayer multi-configuration time-dependent Hartree (MCTDH) theory is a particularly powerful tool to simulate quantum dynamics in large systems. This rigorous quantum approach is based on an efficient representation of the functional in a time-dependent variational calculation, which recursively expand the wave function in several (or many) dynamically contracted layers. Mathematically, the method belongs to the general class of hierarchical tensor decomposition. In this talk I will outline the derivation of the theory, the scaling of the method, and application of the theory to some model reactions that have interesting many-body quantum effects.