Research Seminar in Mathematics - Non-Hermitian Topology of Exceptional Points

Speaker

Marcus Bäcklund, Nordita.

Abstract

Exceptional points (EPs) are eigenvalue degeneracies where also the eigenvectors coalesce, leaving the parent operator/matrix non-diagonalizable to instead cast a Jordan block form. From a mathematical perspective, such matrices have been well-studied [1], while they have been almost completely neglected within the physics community due to the fundamental amendments of quantum mechanics constraining the theory to only include Hermitian operators. Recent years have, however, marked a paradigm shift where non-Hermitian operators have surfaced at the forefront also in physics research. These operators are highly relevant both in classical and quantum setups, where they can be used to model, e.g., gain and loss in optical systems, and open quantum systems, to mention just a few examples. This has resulted in a novel physical interpretation and application of these mathematical concepts, and furthermore a direct connection between EPs and various aspect of topology [2].

In this interdisciplinary talk, I will give a brief background on the last years progress within this rapidly developing field. As I intend to focus on my specific contributions [3-9], the above mentioned connection to topology will be central, and I will show how abstract, yet well-established, mathematical notions and techniques are given a novel interpretation in terms of theoretical physics. I will also comment on how this manifest in physics experiments, to complete the bridge between observational physics and abstract mathematics.

[1] T. Kato, Pertubration theory for linear operators, Vol 132 (Springer, 1966).

[2] E. J. Bergholtz, J. C. Budich,and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).

[3] J. Carlström, MS, J. C. Budich, and E. J. Bergholtz, Knotted non-Hermitian Metals, Phys. Rev. B 99, 161115 (2019).

[4] MS, L. Rødland, G. Arone, J. C. Budich, and E. J. Bergholtz, Hyperbolic nodal band structures and knot invariants, SciPoist Physics 7 019, (2019).

[5] MS, and E. J. Bergholtz, Classification of exceptional nodal topologies protected by PT symmetry, Phys. Rev. B 104, L201104 (2021).

[6] MS, J. Laraña Aragón, L. Rødland, and F. K. Kusnt, PT symmetry-protected exceptional cones and analogue Hawking radiation, New Journal of Physics 25, 043012 (2023).

[7] S. Sayyad, MS, L. Rødland, and F. K. Kunst, Symmetry-protected exceptional and nodal points in non-Hermitian systems, SciPost Physics 15, 200 (2023).

[8] MS, C. Morais Smith, Fractal nodal band structures, Phys. Rev. Research 5, 043043 (2023).

[9] K. Yang, Z. Li, J. L. K. König, L. Rødland, MS, and E. J. Bergholtz, Homotopy, symmetry, and non-Hermitian band topology, Reports on Progress in Physics 87, 078002 (2024).

Welcome!