[{"quality_controlled":"1","file_date_updated":"2025-08-28T12:27:05Z","isi":"1","citation":{"bibtex":"@article{Meyer_Schindlmayr_2025, title={Generalized Miller formulae for quantum anharmonic oscillators}, volume={5}, DOI={<a href=\"https://doi.org/10.3390/dynamics5030034\">10.3390/dynamics5030034</a>}, number={334}, journal={Dynamics}, publisher={MDPI}, author={Meyer, Maximilian Tim and Schindlmayr, Arno}, year={2025} }","ama":"Meyer MT, Schindlmayr A. Generalized Miller formulae for quantum anharmonic oscillators. <i>Dynamics</i>. 2025;5(3). doi:<a href=\"https://doi.org/10.3390/dynamics5030034\">10.3390/dynamics5030034</a>","mla":"Meyer, Maximilian Tim, and Arno Schindlmayr. “Generalized Miller Formulae for Quantum Anharmonic Oscillators.” <i>Dynamics</i>, vol. 5, no. 3, 34, MDPI, 2025, doi:<a href=\"https://doi.org/10.3390/dynamics5030034\">10.3390/dynamics5030034</a>.","chicago":"Meyer, Maximilian Tim, and Arno Schindlmayr. “Generalized Miller Formulae for Quantum Anharmonic Oscillators.” <i>Dynamics</i> 5, no. 3 (2025). <a href=\"https://doi.org/10.3390/dynamics5030034\">https://doi.org/10.3390/dynamics5030034</a>.","short":"M.T. Meyer, A. Schindlmayr, Dynamics 5 (2025).","ieee":"M. T. Meyer and A. Schindlmayr, “Generalized Miller formulae for quantum anharmonic oscillators,” <i>Dynamics</i>, vol. 5, no. 3, Art. no. 34, 2025, doi: <a href=\"https://doi.org/10.3390/dynamics5030034\">10.3390/dynamics5030034</a>.","apa":"Meyer, M. T., &#38; Schindlmayr, A. (2025). Generalized Miller formulae for quantum anharmonic oscillators. <i>Dynamics</i>, <i>5</i>(3), Article 34. <a href=\"https://doi.org/10.3390/dynamics5030034\">https://doi.org/10.3390/dynamics5030034</a>"},"oa":"1","external_id":{"isi":["001581270200001"]},"has_accepted_license":"1","status":"public","user_id":"458","ddc":["530"],"volume":5,"_id":"60959","publisher":"MDPI","abstract":[{"lang":"eng","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, 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."}],"issue":"3","publication":"Dynamics","type":"journal_article","department":[{"_id":"296"},{"_id":"230"},{"_id":"15"},{"_id":"170"},{"_id":"35"}],"file":[{"relation":"main_file","date_updated":"2025-08-28T12:27:05Z","file_name":"dynamics-05-00034.pdf","access_level":"open_access","file_size":375897,"title":"Generalized Miller formulae for quantum anharmonic oscillators","file_id":"61056","content_type":"application/pdf","creator":"schindlm","description":"Creative Commons Attribution 4.0 International Public License (CC BY 4.0)","date_created":"2025-08-28T12:23:26Z"}],"date_created":"2025-08-20T09:46:13Z","publication_status":"published","date_updated":"2025-10-10T07:29:36Z","article_type":"original","intvolume":"         5","year":"2025","title":"Generalized Miller formulae for quantum anharmonic oscillators","publication_identifier":{"eissn":["2673-8716"]},"author":[{"id":"77895","last_name":"Meyer","first_name":"Maximilian Tim","orcid":"0009-0003-4899-0920","full_name":"Meyer, Maximilian Tim"},{"id":"458","first_name":"Arno","orcid":"0000-0002-4855-071X","last_name":"Schindlmayr","full_name":"Schindlmayr, Arno"}],"doi":"10.3390/dynamics5030034","article_number":"34","language":[{"iso":"eng"}]}]