Theory of Moment Propagation for Quantum Dynamics in Single-Particle Description

Abstract

We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle wave functions as generally done in time-dependent density functional theory, we describe an approach for reducing the high computational cost of simulating the quantum dynamics. The equation of motion is given for the moments by deriving analytical expressions for the first-order and second-order time derivatives of the moments, and a numerical scheme is developed for performing quantum dynamics by expanding the moments in the Taylor series as done in classical molecular dynamics simulation. We propose a few numerical approaches using this theoretical formalism on a simple one-dimensional model system, for which an analytically exact solution can be derived. Application of the approaches to an anharmonic system is also discussed to illustrate their generality. We also discuss the use of an artificial neural network model to circumvent the numerical evaluation of the second-order time derivatives of the moments, as analogously done in the context of classical molecular dynamics simulations.

References in corpus (5)

• A comparative study of different machine learning methods for dissipative quantum dynamics
• Electronic Excitation Response of DNA to High-energy Proton Radiation in Water
• Propagation of maximally localized Wannier functions in real-time TDDFT
• First-Principles Demonstration of Non-adiabatic Thouless Pumping of Electrons in A Molecular System
• Molecular Control of Floquet Topological Phase in Non-adiabatic Thouless Pumping