QuDPy-FDGF: A Python-Based Tool for Computing Ultrafast Nonlinear Optical Responses Using Frequency Domain Green's Functions
Abstract
We present QuDPy-FDGF, an open-source Python framework that evaluates Liouville-space pathways as hybrid chains of time propagators and frequency-domain Green's functions. Frequency-resolved intervals are computed directly through shifted linear systems, without time propagation followed by a Fourier transform, while other intervals may remain in the time domain. A model-agnostic block interface separates the physical model from pathway construction, numerical propagation, and detection. The released implementation provides an explicit dense Liouville-space backend for reference calculations and a sector-resolved sparse backend using matrix-free generator actions, Krylov time propagation, and generalized minimal residual (GMRES) resolvent solves. Its observable layer reuses propagated pathway responses to evaluate operator expectation values, action-detected readout interactions, instantaneous jump rates, and integrated mean jump counts. The framework is assessed on an analytically solvable open two-level system and on two examples of increasing complexity: the complete third-order rephasing response, with its eight sequences, of a thermally initialized anisotropic Heisenberg (XXZ) spin chain with unequal excitation sectors, and two coupled dissipative anharmonic modes whose spectra depend on the detected observable, with the fifth-order double-quantum response of their closed limit. The calculations reproduce the analytical two-level response, check the matrix-free sparse evaluation against the dense assembly of the generator, and recover the harmonic-limit cancellation of the fifth-order signal when the required three-excitation manifold is retained. QuDPy-FDGF therefore provides a unified framework for pathway- and observable-resolved nonlinear spectroscopy in finite or truncated Hilbert spaces with unitary or Markovian Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) dynamics.
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BibTeX
@misc{desmarais2026qudpyfdgf,
title = {{QuDPy-FDGF: A Python-Based Tool for Computing Ultrafast Nonlinear Optical Responses Using Frequency Domain Green's Functions}},
author = {Mathieu Desmarais and Simón Paiva-Ortega and Félix Brunell and Eric R. Bittner and Hao Li and Carlos Silva-Acuña},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30398},
eprint = {2610.30398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30398},
}
RIS
TY - UNPB
TI - QuDPy-FDGF: A Python-Based Tool for Computing Ultrafast Nonlinear Optical Responses Using Frequency Domain Green's Functions
AU - Mathieu Desmarais
AU - Simón Paiva-Ortega
AU - Félix Brunell
AU - Eric R. Bittner
AU - Hao Li
AU - Carlos Silva-Acuña
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30398
UR - https://arxiv.org/abs/2610.30398
AB - We present QuDPy-FDGF, an open-source Python framework that evaluates Liouville-space pathways as hybrid chains of time propagators and frequency-domain Green's functions. Frequency-resolved intervals are computed directly through shifted linear systems, without time propagation followed by a Fourier transform, while other intervals may remain in the time domain. A model-agnostic block interface separates the physical model from pathway construction, numerical propagation, and detection. The released implementation provides an explicit dense Liouville-space backend for reference calculations and a sector-resolved sparse backend using matrix-free generator actions, Krylov time propagation, and generalized minimal residual (GMRES) resolvent solves. Its observable layer reuses propagated pathway responses to evaluate operator expectation values, action-detected readout interactions, instantaneous jump rates, and integrated mean jump counts. The framework is assessed on an analytically solvable open two-level system and on two examples of increasing complexity: the complete third-order rephasing response, with its eight sequences, of a thermally initialized anisotropic Heisenberg (XXZ) spin chain with unequal excitation sectors, and two coupled dissipative anharmonic modes whose spectra depend on the detected observable, with the fifth-order double-quantum response of their closed limit. The calculations reproduce the analytical two-level response, check the matrix-free sparse evaluation against the dense assembly of the generator, and recover the harmonic-limit cancellation of the fifth-order signal when the required three-excitation manifold is retained. QuDPy-FDGF therefore provides a unified framework for pathway- and observable-resolved nonlinear spectroscopy in finite or truncated Hilbert spaces with unitary or Markovian Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) dynamics.
ER -