First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy

Abstract

A new concept to describe the quantum dynamics in complex systems is suggested. It extends established schemes based on the Dirac-Frenkel variation principle, e.g., the multi-configurational time-dependent Hartree (MCTDH) approach. The concept is based on a correlation-based von Neumann entropy (CvN-entropy) definition measuring the complexity of the wavefunction. Equations of motion are derived using a CvN-entropy constraint in the variational principle and result in a generally applicable effective Hamiltonian. It consists of the standard Hamilton operator and an additional nonlinear operator which limits the complexity of the wavefunction. Effectively, this nonlinear operator absorbs complex structures which are emerging in the wavefunction and allows one to introduce non-norm conserving equations of motion. Important aspects of the new concept are outlined studying the wave packet propagation on the diabatic B(2) potential energy surfaces of NO(2). First, it is demonstrated that during standard wave packet propagation the CvN-entropy increases strongly with time roughly independent of the coordinate systems employed. Second, one finds that employing CvN-entropy constrained MCTDH propagation yields improved wave function accuracy on longer time scales while compromising on the short time accuracy. Third, the loss of the wavefunction's norm is directly related to the overlap with the exact wavefunction. This provides an error estimate available without knowing an exact reference.