The Anthony J Leggett Institute for Condensed Matter Special Theory Seminar, Shu Hamanaka (Kyoto University, Japan), "Koopman Nonlinear Non-Hermitian Skin Effect"
- Sponsor
- Physics - The Anthony J Leggett Institute for Condensed Matter Theory
- Speaker
- Shu Hamanaka
- Contact
- Thierry Ramais
- ramais@illinois.edu
- Views
- 172
- Originating Calendar
- Physics - The Anthony J Leggett Institute for Condensed Matter Theory Seminar
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