Theoretical seminar | 26 November 2025

Thermalization of closed many body systems is at the heart of fundamental quantum concepts like many body localization, eigenstate thermalization hypothesis, and quantum computers since several decades. More recently it also entered the world of classical many body systems through light propagation in nonlinear photonic multimode waveguides and waveguide networks, relating to such observations as e.g. spatial beam self cleaning.

I will introduce concepts of quantifying thermalization, which are tied up to measuring time scales (aka length scales in photonic waveguide applications). The paradoxical upshot is that easy-to-measure scales are footing on the concept of ergodicity and may quickly lead to ambiguous non-universal assessments [1-3]. On the other side stands the universal and unambiguous concept of Lyapunov time scales, which are however much harder to be measured [4-8].

I will present results which show that Lyapunov spectra scale in distinct ways for different classes of systems, depending on the type of weak coupling network between modes of a decoupled limit (e.g. low intensity light, or weak coupling in wave guide arrays) [4-8]. These results establish for the first time the existence of different thermalization universality classes in many body physics.

Main paper/arXiv, related to the seminar, and other references

[1] Mithun Thudiyangal, Carlo Danieli, Yagmur Kati and Sergej Flach, Dynamical Glass Phase and Ergodization Times in Classical Josephson Junction Chains, Phys. Rev. Lett. 122
054102 (2019)
[2] Carlo Danieli, Thudiyangal Mithun, Yagmur Kati, David K. Campbell and Sergej Flach, Dynamical glass in weakly non-integrable Klein-Gordon chains, Phys. Rev. E 100 032217
(2019)
[3] T. Mithun, C. Danieli, M. V. Fistul, B. L. Altshuler and S. Flach, Fragile Many Body Ergodicity From Action Diffusion, Phys. Rev. E 104, 014218 (2021)
[4] Merab Malishava and Sergej Flach, Lyapunov spectrum scaling for classical many-body dynamics close to integrability, Phys. Rev. Lett. 128, 134102 (2022)
[5] Merab Malishava and Sergej Flach, Thermalization dynamics of macroscopic weakly nonintegrable maps, Chaos 32, 063113 (2022)
[6] Gabriel Lando and Sergej Flach, Thermalization Slowing-Down in Multidimensional Josephson Junction Networks, Phys. Rev. E 108 , L062301 (2023).
[7] X. Zhang, G. M. Lando, B. Dietz, S. Flach, Observation of prethermalization in weakly nonintegrable unitary maps , Low Temp Phys 51, 870 (2025).
[8] Weihua Zhang, Gabriel M. Lando, Barbara Dietz and Sergej Flach, Thermalization Universality-Class Transition Induced by Anderson Localization, Phys. Rev. Res. 6
L012064 (2024).