SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 48: Dynamics and Chaos in Many-Body Systems I (joint session DY/TT)

DY 48.9: Vortrag

Donnerstag, 30. März 2023, 17:15–17:30, MOL 213

Universal correlations in chaotic many-body quantum states: lifting Berry’s Random Wave Model into Fock spaceRémy Dubertrand1, Juan-Diego Urbina2, Klaus Richter2, and •Florian Schöppl21Department of Mathematics, Physics and Electrical Engineering, Northumbria University, NE1 8ST Newcastle upon Tyne, United Kingdom — 2Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany

Using a semiclassical analysis based on Berry’s ansatz [1] we investigate the universal statistical features of eigenstate correlations in chaotic mesoscopic many-body quantum systems, focusing on Bose-Hubbard lattices, where the existence of a classical (mean-field) limit allows for the use of many-body semiclassical methods [2]

For this, we first have to lift Berry’s ansatz into the many-body space by expanding the microscopic correlations and the conjectured multivariant Gaussian distribution of expansion coefficients into the Fock space of quantum fields. Together with numerical evidence, which supports the extension to multi-point correlations of the known Gaussian distribution for a single expansion coefficient, the universality of eigenstate correlations can be extended well beyond random matrix theory, where these correlations are absent. Our results bring the correlation backbone of eigenfunctions into a precise signature of quantum chaos in many-body mesoscopic systems.
[1] M. V. Berry, Journal of Physics A: Mathematical and General 10, 2083 (1977) [2] K.Richter, J.D. Urbina, and S. Tomsovic. "Semiclassical roots of universality in many-body quantum chaos," (2022)

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