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arXiv · 1907.07734

An efficient spectral method for numerical time-dependent perturbation theory

Cyrille Lavigne·Paul Brumer
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Abstract

We develop the Fourier-Laplace Inversion of the Perturbation Theory (FLIPT), a novel numerically exact "black box" method to compute perturbative expansions of the density matrix with rigorous convergence conditions. Specifically, the FLIPT method is extremely well-suited to simulate multiphoton pulsed laser experiments with complex pulse shapes. The $n$-dimensional frequency integrals of the $n$-th order perturbative expansion are evaluated numerically using tensor products. The $N$ points discretized integrals are computed in $O(N^2)$ operations, a significant improvement over the $O(N^n)$ scaling of standard quadrature methods.

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Cyrille Lavigne, Paul Brumer. 2019-07-17. An efficient spectral method for numerical time-dependent perturbation theory. https://doi.org/10.1063/1.5121722

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