tRecX -- an environment for solving time-dependent Schr\"odinger-like problems

TL;DR

tRecX is a versatile C++ software environment designed for solving complex time-dependent Schrödinger-like equations across various dimensions and coordinate systems, enabling advanced simulations in atomic, molecular, and computational physics.

Contribution

It introduces novel numerical methods like the time-dependent surface flux and exterior complex scaling, with a flexible, symbolic input system for large-scale ab initio calculations.

Findings

Effective computation of single and double emission spectra.

Supports large-scale, multi-dimensional simulations.

Integrates symbolic algebra for operator specification.

Abstract

TRecX is a C++ code for solving generalized inhomogeneous time-dependent Schr\"odinger-type equations $id\Psi/dt = H[t,\Psi] + \Phi$ in arbitrary dimensions and in a variety of coordinate systems. The operator $H[t,\Psi]$ may have simple non-linearities, as in Gross-Pitaevskii and Hartree(-Fock) problems. Primary application of tRecX has been non-perturbative strong-field single and double photo-electron emission in atomic and molecular physics. The code is designed for large-scale {\it ab initio} calculations, for exploring models, and for advanced teaching in computational physics. Distinctive numerical methods are the time-dependent surface flux method for the computation of single and double emission spectra and exterior complex scaling for absorption. Wave functions and operators are handled by tree-structures with the systematic use of recursion on the coarse-grain level. Numerical, analytic, and grid-based discretizations can be combined and are treated on the same abstract level. Operators are specified in the input using a script language including symbolic algebra. User-friendly in- and output, error safety, and documentation are integrated by design.