{"department":[{"_id":"296"},{"_id":"230"},{"_id":"15"},{"_id":"170"},{"_id":"35"}],"_id":"60959","date_created":"2025-08-20T09:46:13Z","quality_controlled":"1","publication_status":"accepted","publisher":"MDPI","language":[{"iso":"eng"}],"type":"journal_article","year":"2025","publication":"Dynamics","abstract":[{"text":"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 [Meyer, M.T.; Schindlmayr, A. J. Phys. B 2024, 57, 095001], 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.","lang":"eng"}],"author":[{"first_name":"Maximilian Tim","full_name":"Meyer, Maximilian Tim","orcid":"0009-0003-4899-0920","id":"77895","last_name":"Meyer"},{"first_name":"Arno","last_name":"Schindlmayr","id":"458","orcid":"0000-0002-4855-071X","full_name":"Schindlmayr, Arno"}],"publication_identifier":{"eissn":["2673-8716"]},"title":"Generalized Miller formulae for quantum anharmonic oscillators","article_type":"original","date_updated":"2025-08-20T09:47:08Z","citation":{"chicago":"Meyer, Maximilian Tim, and Arno Schindlmayr. “Generalized Miller Formulae for Quantum Anharmonic Oscillators.” <i>Dynamics</i>, n.d.","apa":"Meyer, M. T., &#38; Schindlmayr, A. (n.d.). Generalized Miller formulae for quantum anharmonic oscillators. <i>Dynamics</i>.","short":"M.T. Meyer, A. Schindlmayr, Dynamics (n.d.).","ama":"Meyer MT, Schindlmayr A. Generalized Miller formulae for quantum anharmonic oscillators. <i>Dynamics</i>.","mla":"Meyer, Maximilian Tim, and Arno Schindlmayr. “Generalized Miller Formulae for Quantum Anharmonic Oscillators.” <i>Dynamics</i>, MDPI.","bibtex":"@article{Meyer_Schindlmayr, title={Generalized Miller formulae for quantum anharmonic oscillators}, journal={Dynamics}, publisher={MDPI}, author={Meyer, Maximilian Tim and Schindlmayr, Arno} }","ieee":"M. T. Meyer and A. Schindlmayr, “Generalized Miller formulae for quantum anharmonic oscillators,” <i>Dynamics</i>."},"user_id":"458","status":"public"}