Development of a general time-dependent absorbing potential for the constrained adiabatic trajectory method

TL;DR

This paper introduces a general time-dependent absorbing potential for the constrained adiabatic trajectory method, enabling efficient solutions of the time-dependent Schrödinger equation with improved boundary condition handling.

Contribution

A new general form of the absorbing potential is derived, allowing flexible boundary conditions and enabling multi-step propagation to reduce Fourier basis size.

Findings

Successfully applied to H2+ molecular ion under laser pulse

Absorbing potential reduces boundary reflection errors

Multi-step propagation improves computational efficiency

Abstract

The Constrained Adiabatic Trajectory Method (CATM) allows us to compute solutions of the time-dependent Schr\"odinger equation using the Floquet formalism and Fourier decomposition, using matrix manipulation within a non-orthogonal basis set, provided that suitable constraints can be applied to the initial conditions for the Floquet eigenstate. A general form is derived for the inherent absorbing potential, which can reproduce any dispersed boundary conditions. This new artificial potential acting over an additional time interval transforms any wavefunction into a desired state, with an error involving exponentially decreasing factors. Thus a CATM propagation can be separated into several steps to limit the size of the required Fourier basis. This approach is illustrated by some calculations for the $H_2^+$ molecular ion illuminated by a laser pulse.