Grainger College of Engineering, All Events

Abstract:

Non-Hermitian skin effects are conventionally understood as boundary localization of eigenstates in 

linear systems [1]. In realistic experimental platforms, however, nonlinearity is ubiquitous [2], and 

eigenstates are no longer well defined, raising a fundamental question of how skin effects should be 

characterized beyond the linear regime. Previous approaches have mainly focused on stationary 

solutions, reducing the problem to a spatial dynamical system at a fixed frequency [3, 4]. While 

successful in certain contexts, such approaches may probe a restricted subset of the full nonlinear 

dynamics, leaving the underlying nature of nonlinear skin effects obscured.

In this talk, I propose a Koopman-based characterization of nonlinear skin effects, in which 

localization is defined in terms of Koopman eigenfunctions in a lifted observable space, rather than 

physical states [5]. Using a minimal nonlinear extension of the Hatano-Nelson model, I show that 

dominant Koopman eigenfunctions localize sharply on higher-order observables, in stark contrast to 

linear skin effects confined to linear observables. This lifted-space localization governs the sensitivity 

to boundary amplitude perturbations, providing a distinct dynamical signature of the nonlinear skin 

effect. These results establish the Koopman framework as a natural setting in which skin effects unique 

to nonlinear non-Hermitian systems can be identified.

References:

[1] S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018).

[2] S. Wang et al., Phys. Rev. Lett. 134, 243805 (2025).

[3] C. Yuce, Physics Letters A 408, 127484 (2021); Phys. Rev. B 111, 054201 (2025).

[4] K. Kawabata and D. Nakamura, Phys. Rev. Lett. 135, 126610 (2025).

[5] S. Hamanaka, arXiv: 2601.03636

Zoom Link: https://illinois.zoom.us/my/icmt.seminar?pwd=ZU1KbnBLeXZLUmJKc0oyU205cDNDdz09

Meeting ID: 791 382 8328

Password: 106237