# An efficient spectral method for numerical time-dependent perturbation theory

## TL;DR

The paper introduces FLIPT, a fast and exact spectral method for calculating time-dependent perturbation expansions of the density matrix, optimized for complex laser pulse simulations.

## Contribution

It presents FLIPT, a novel spectral approach that efficiently computes perturbative expansions with rigorous convergence, reducing computational complexity for high-dimensional integrals.

## Key findings

- FLIPT achieves $O(N^2)$ complexity for n-dimensional integrals.
- The method is highly suitable for simulating complex multiphoton laser experiments.
- FLIPT provides numerically exact results with rigorous convergence guarantees.

## 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.