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DY: Fachverband Dynamik und Statistische Physik

DY 59: Quantum Chaos and Coherent Dynamics (joint session DY/TT)

DY 59.11: Vortrag

Freitag, 13. März 2026, 12:30–12:45, HÜL/S186

Refinements of the Eigenstate Thermalization Hypothesis — •Elisa Vallini¹, Laura Foini², and Silvia Pappalardi¹ — ¹University of Cologne, Köln, Germany — ²Université Paris-Saclay, France

Understanding how isolated quantum many-body systems reach thermal equilibrium is a central question in nonequilibrium physics. The Eigenstate Thermalization Hypothesis (ETH) provides a powerful framework by linking thermalization to the statistical properties of matrix elements of physical observables in the energy eigenbasis.

In this talk, I will present our recent work, in which we revisit and clarify in detail the ideas that have led to the formulation of full ETH, a generalization of the ETH ansatz that captures multi-point correlation functions. Specifically, using tools from free probability, we explore the implications of local rotational invariance, a property that emerges from the statistical invariance of observables under random basis transformations induced by small perturbations of the Hamiltonian.

This approach allows us to analytically characterize subleading corrections to matrix-element correlations, thereby refining the ETH ansatz. Finally, I will show numerical results from non-integrable Floquet systems that support our analytical predictions.

Keywords: Eigenstate Thermalization Hypothesis; Free Probability; Local Rotational Invariance; Higher-order correlations