Göttingen 2025 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 5: Theory of Machine Learning (joint session MP/AKPIK)

MP 5.1: Vortrag

Mittwoch, 2. April 2025, 13:45–14:05, ZHG001

Time Series Analysis of machine learned Quantum Systems — •Kai-Hendrik Henk and Wolfgang Paul — Martin-Luther-Universität Halle-Wittenberg, Halle(Saale), Deutschland

The Rayleigh-Ritz variation principle is a proven way to find ground states and energies for bound quantum systems in the Schrödinger picture. Advances in machine learning and neural networks make it possible to extend it from an analytical search from a subspace of the complete Hilbert space to the a numerical search in the almost complete Hilbert space. Here, we extend the Rayleigh-Ritz principle to Nelson’s stochastic mechanics formulation of non-relativistic quantum mechanics, and propose an algorithm to find the osmotic velocities u(x), which contain the information of a quantum systems in this picture (Phys. Rev. A 108, 062412). Motivated by experiments by the Aspelmeyer group at the University of Vienna using quantum levitodynamics (see for example Nature 595, 373-377 (2021)), we apply the algorithm to the harmonic oscillator, the Gaussian and the Lorentzian potential and analyze them using methods from time series analysis and phase portraits.

References: Henk, K.-H., and Paul, W. Machine learning quantum mechanical ground states based on stochastic mechanics. Phys. Rev. A 108 (Dec 2023), 062412

Keywords: Time Series Analysis; Nelson; Stochastic Mechanics; Phase Space; Oscillator