Infinite-range exterior complex scaling as a perfect absorber in time-dependent problems

Abstract

It is shown that exterior complex scaling provides for complete absorption of outgoing flux in numerical solutions of the time-dependent Schrödinger equation with strong infrared fields. This is demonstrated by computing high harmonic spectra and wave-function overlaps with the exact solution for a one-dimensional model system and by three-dimensional calculations for the H atom and a Ne atom model. We lay out the key ingredients for correct implementation and identify criteria for efficient discretization.

Calculation of Stark resonance parameters for valence orbitals of the water molecule

“…to guarantee smooth turn-on in this region. Small values of ∆r pose challenges for the automated finite-element method, since in the limit of ∆r → 0 one would need to implement the derivative discontinuity in the solution as discussed by Scrinzi [34]. We find stable results for the real and imaginary parts of the eigenenergies at the level of three significant digits for the range 10 < r s < 15 a.u.…”

“…Among the different techniques implemented to compute the resonance energies established methods are the complex scaling [28][29][30], and exterior complex scaling [31]; the latter was introduced as an extension of the former method. These have been widely used in scattering problems [29,30], and also in time-dependent Schrödinger equation problems for strong fields [32][33][34]. For our aim of studying the field ionization properties of H 2 O orbitals, we implement a modified exterior complex scaling technique in which the radial coordinates are extended into the complex plane by a phase factor, which is turned on gradually beyond some distance from the origin.…”

Perfect absorption in Schrödinger-like problems using non-equidistant complex grids

“…If one succeeds, one obtains a perfect absorber in the mathematical sense [1][2][3]. This can be proven for stationary Schrödinger operators with free or Coulomb-like asymptotics and it has been demonstrated numerically for an important class of linear Schrödinger operators involving time dependent interactions [2]. The method will be discussed in more detail below.…”

Stability of the time-dependent configuration-interaction-singles method in the attosecond and strong-field regimes: A study of basis sets and absorption methods

“…Beyond r absorb , the complex path is usually rotated by a specific angle θ into the complex plane. In the limit of an exact representation (infinite basis set), ECS yields exact Siegert energies for quasibound states [36] and can be used as a perfect absorber [39,60] without reflections.…”

“…The introduction of an absorbing boundary [36][37][38][39] in the form of complex absorbing potentials (CAP) [40], window functions [41], or complex scaling (CS) [42,43] is natural as one tries to keep the radial grid as small as possible. Absorbers are generally not perfect (i.e., reflection free) and introduce unphysical motion.…”