An efficient parallel method for relaxing to the minimum action wavefunction

TL;DR

This paper introduces a highly efficient, parallelizable numerical method for relaxing trial wavefunctions to minimize propagation error in solving the time-dependent Schrödinger equation, suitable for complex Hamiltonians.

Contribution

It presents a novel, trivially parallelizable relaxation method that integrates with multigrid techniques for rapid convergence in wavefunction propagation.

Findings

Method achieves rapid convergence even for non-positive definite Hamiltonians

Parallelization simplifies implementation and enhances computational efficiency

Compatible with multigrid methods for improved accuracy

Abstract

Efficient and accurate numerical propagation of the time dependent Schroedinger equation is a problem with applications across a wide range of physics. This paper develops an efficient, trivially parallelizeable method for relaxing a trial wavefunction toward a variationally optimum propagated wavefunction which minimizes the propagation error relative to a platonic wavefunction which obeys the time dependent Schroedinger equation exactly. This method is shown to be well suited for incorporation with multigrid methods, yielding rapid convergence to a minimum action solution even for Hamiltonians which are not positive definite.