Perspective: Interactions and Nonlinearity in Non-Hermitian Physics

Quantum Physics [Submitted on 13 Mar 2026] Perspective: Interactions and Nonlinearity in Non-Hermitian Physics Federico Roccati, Federico Balducci For decades, Hermiticity was considered an immutable axiom of quantum mechanics, essential for ensuring real energies and unitary evolution. This perspective has shifted radically, driven by the realization that non-Hermitian Hamiltonians provide a powerful effective description of open quantum systems, granting access to unique phenomena such as Exceptional Points and the Non-Hermitian Skin Effect. In this Perspective, we chart the trajectory of this field, moving from its established foundations in single-particle, linear models to the emerging frontier of interacting many-body systems. We first clarify the physical origins of non-Hermitian dynamics, distinguishing between mean-field approximations, conditional "no-click" evolution, and exact Liouvillian dynamics. We then focus on the rich phenomenology arising from the interplay of non-Hermiticity and interactions. We discuss interaction-induced topological phases, the generalization of skin effects to the many-body Hilbert space, and the distinct signatures of dissipative quantum chaos and complexity. Finally, we highlight collective phenomena in nonlinear regimes, including skin solitons and dissipative phase transitions. We also comment on measurement-induced entanglement transitions and their relation to non-Hermitian spectra and topology. By synthesizing these diverse developments, we provide a roadmap for the future of non-Hermitian physics. Comments: 11 pages, no figures. Manuscript submitted to the inaugural issue of the journal Nonequilibrium Physics (NP) Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Cite as: arXiv:2603.13526 [quant-ph]   (or arXiv:2603.13526v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.13526 Focus to learn more Submission history From: Federico Roccati [view email] [v1] Fri, 13 Mar 2026 19:00:00 UTC (33 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.mes-hall References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)