@article{60959,
  abstract     = {{Miller's rule originated as an empirical relation between the nonlinear and linear optical coefficients of materials. It is now accepted as a useful tool for guiding experiments and computational materials discovery, but its theoretical foundation had long been limited to a derivation for the classical Lorentz model with a weak anharmonic perturbation. Recently, we developed a mathematical framework which enabled us to prove that Miller's rule is equally valid for quantum anharmonic oscillators, despite different dynamics due to zero-point fluctuations and further quantum-mechanical effects. However, our previous derivation applied only to one-dimensional oscillators and to the special case of second- and third-harmonic generation in a monochromatic electric field. Here we extend the proof to three-dimensional quantum anharmonic oscillators and also treat all orders of the nonlinear response to an arbitrary multi-frequency field. This makes the results applicable to a much larger range of physical systems and nonlinear optical processes. The obtained generalized Miller formulae rigorously express all tensor elements of the frequency-dependent nonlinear susceptibilities in terms of the linear susceptibility and thus allow a computationally inexpensive quantitative prediction of arbitrary parametric frequency-mixing processes from a small initial dataset.}},
  author       = {{Meyer, Maximilian Tim and Schindlmayr, Arno}},
  issn         = {{2673-8716}},
  journal      = {{Dynamics}},
  number       = {{3}},
  publisher    = {{MDPI}},
  title        = {{{Generalized Miller formulae for quantum anharmonic oscillators}}},
  doi          = {{10.3390/dynamics5030034}},
  volume       = {{5}},
  year         = {{2025}},
}