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TT: Fachverband Tiefe Temperaturen
TT 4: Topological Insulators
TT 4.11: Vortrag
Montag, 17. März 2025, 12:15–12:30, H33
Characterizing exceptional topology through tropical geometry — •Ayan Banerjee1, Rimika Jaiswal2, Madhusudan Manjunath3, and Awadhesh Narayan4 — 1Max Planck Institute for the Science of Light, Erlangen — 2University of California Santa Barbara, USA — 3Indian Institute of Technology Bombay, India — 4Indian Institute of Science, Bangalore
Non-Hermitian Hamiltonians describing open quantum systems have been widely explored in platforms ranging from photonics to electric circuits [1]. A defining feature of non-Hermitian systems is exceptional points (EPs), where both eigenvalues and eigenvectors coalesce. The study of EPs has become an exciting frontier at the crossroads of optics, photonics, acoustics, and quantum physics. Tropical geometry is an emerging field of mathematics at the interface between algebraic geometry and polyhedral geometry, with diverse applications to science [2]. Here, we introduce Newton’s polygon method and adopt the notion of a geometrical object known as amoeba in developing a unified tropical geometric framework to characterize different facets of non-Hermitian systems [3]. We introduce a framework linking tropical geometry to non-Hermitian physics, enabling the study of EPs, skin effects, and disorder properties.
[1] E.J.Bergholtz, J.C.Budich, F.K.Kunst, Rev.Mod.Phys.93, 015005 (2021).
[2] D.Maclagan, B.Sturmfels, Graduate Stud. Math.161, 75 (2009).
[3] A.Banerjee, R.Jaiswal, M.Manjunath, A.Narayan, Proc. Natl. Acad. Sci. U.S.A. 120, e2302572120 (2023).
Keywords: Non-Hermitian systems; Exceptional Points; Tropical Geometry; Newton Polygons; Non-Hermitian skin effect