Periodic Reporting for period 3 - FACT (Factorizing the wave function of large quantum systems)
Reporting period: 2022-09-01 to 2024-02-29
The goal of this action is to attack the many-particle wave function with a novel theoretical approach, known as the exact factorization. In this approach one writes the wavefunction of the full quantum system as a single product of subsystem-wavefunctions in such a way that the product is an exact representation of the complete wave function. No approximation is made in this first step. In the case of two subsystems (e.g. electrons and nuclei), one factor is a regular wavefunction, satisfying a standard Schrödinger equation, while the other factor is a conditional probability amplitude that satisfies a more complicated Schrödinger-like equation with a non-local, non-linear and non-Hermitian Hamiltonian. The above-mentioned standard techniques can then be employed for the subsystem-Schrödinger equations. In particular, different standard techniques can be applied to different subsystems. What makes the exact factorization distinct from other embedding schemes is the fact that the derivation of equations of motion for the subsystems is done without approximation. The same universal procedure can be applied to any interacting quantum system and to any subdivision of the system. This makes the exact factorization an extremely powerful and versatile tool. The objective of this action is to exploit the power of the method in various, particularly challenging situations such as solids with strong long-range correlations a well as molecular processes with strong non-adiabatic couplings.