Gaussian-process-regression-based method for the localization of exceptional points in complex resonance spectra

Resonances in open quantum systems depending on at least two controllable parameters can show the phenomenon of exceptional points (EPs), where not only the eigenvalues but also the eigenvectors of two or more resonances coalesce. Their exact localization in the parameter space is challenging, in pa...

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Bibliographic Details
Published in:Machine learning: science and technology 2024-03, Vol.5 (1), p.15045
Main Authors: Egenlauf, Patrick, Rommel, Patric, Main, Jörg
Format: Article
Language:English
Subjects:
Algorithms
Computation
Controllability
Copper oxides
Eigenvalues
Eigenvectors
exceptional points
Excitation spectra
Excitons
excitons in external fields
Gaussian process
Gaussian process regression
Localization
Machine learning
Parameters
Regression models
Resonance
Valence band
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Summary:Resonances in open quantum systems depending on at least two controllable parameters can show the phenomenon of exceptional points (EPs), where not only the eigenvalues but also the eigenvectors of two or more resonances coalesce. Their exact localization in the parameter space is challenging, in particular in systems, where the computation of the quantum spectra and resonances is numerically very expensive. We introduce an efficient machine learning algorithm to find EPs based on Gaussian process regression (GPR). The GPR-model is trained with an initial set of eigenvalue pairs belonging to an EP and used for a first estimation of the EP position via a numerically cheap root search. The estimate is then improved iteratively by adding selected exact eigenvalue pairs as training points to the GPR-model. The GPR-based method is developed and tested on a simple low-dimensional matrix model and then applied to a challenging real physical system, viz., the localization of EPs in the resonance spectra of excitons in cuprous oxide in external electric and magnetic fields. The precise computation of EPs, by taking into account the complete valence band structure and central-cell corrections of the crystal, can be the basis for the experimental observation of EPs in this system.
ISSN:2632-2153
2632-2153
DOI:10.1088/2632-2153/ad2e16