Hybrid surface-flux method for extraction of the ionization amplitude from the calculated wave function

Abstract

A method is proposed for extracting ionization amplitudes from the solution of the timedependent Schrödinger equation (TDSE) describing a system in a time-dependent external field.The method is a hybrid of two earlier developed methods, the time-dependent surface flux (t-SURFF) method and the method using the propagated wavepacket as the source term in a timeindependent driven Schrödinger equation with the field-free Hamiltonian. It is demonstrated that the method combines the advantages of the parent ones and allows the extraction of ionization amplitudes by solving the TDSE within a small spatial domain (with the boundary conditions provided by exterior complex scaling) and a time interval, not exceeding the external field pulse duration.

Solution of the Schrödinger equation using exterior complex scaling and fast Fourier transform

“…7 shows δ(k) for SO-FFT at t max = 20 a.u. The error increasing as compared to that of E-SURFF ( Fig.6(b)) is mainly caused by the error of the approximate integration rule for the time integration of the probability amplitude flux [14]. In the Fig.…”

“…The implementation of the E-SURFF approach [17] and its generalization known as t&E-SURFF [14] both require the solution of the SSE with the right-hand side of the form…”

“…The technique is based upon the splitting of the scaled kinetic energy operator to the spatially homogeneous part (for which a step may be performed by means of FFT) and the absorbing term (which can be handled with the help of the finite difference). The approach under proposal has been tested through a calculation of continuum spectrum amplitudes for the model system by t&E-SURFF method [14]. For the purpose of the iterative solution of the stationary Schrodinger equation (SSE) (which is necessary for the accomplishing of the E-SURFF part of the t&E-SURFF scheme) we suggest the FFT-based preconditioner.…”

Linewidths and energy shifts of the electron-impurity resonant states in quantum wells with infinite barriers

“…It was rigorously established for the description of resonance characteristics in the early seventies [53][54][55][56]. Since then, many quantum scattering problems in nuclear and atomic physics have been studied by this technique [57][58][59][60][61][62][63]. In semiconductor physics, a feasibility of complex-scaling calculations of the electron-hole nonradiative linewidths was firstly demonstrated in Ref.…”

Numerical time-of-flight analysis of the strong-field photoeffect

“…Albeit a mathematical trick in the first place, this provides the opportunity to study the build-up of the photoelectron spectrum in a time-resolved way. In [32], the integrand itself has been investigated, which, however, is highly oscillatory. Instead, we introduce a Gaussian time window in the integrand,…”