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Related papers: Geometric Phase for Non-Hermitian Hamiltonians and…

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Exceptional points associated with non-hermitian operators, i.e. operators being non-hermitian for real parameter values, are investigated. The specific characteristics of the eigenfunctions at the exceptional point are worked out. Within…

Quantum Physics · Physics 2009-11-10 W. D. Heiss

The multipartite non-Hermitian Su-Schrieffer-Heeger model is explored as a prototypical example of one-dimensional systems with several sublattice sites for unveiling intriguing insulating and metallic phases with no Hermitian counterparts.…

Mesoscale and Nanoscale Physics · Physics 2022-05-10 Ritu Nehra , Dibyendu Roy

We present a non-trivial metric tensor field on the space of 2-by-2 real-valued, symmetric matrices whose Levi-Civita connection renders frames of eigenvectors parallel. This results in fundamental reimagining of the space of symmetric…

Differential Geometry · Mathematics 2024-11-25 Jakub Rondomanski , José D. Cojal González , Jürgen P. Rabe , Carlos-Andres Palma , Konrad Polthier

Appearance of adiabatic geometric phase shift in the context of noncommutative quantum mechanics is studied using an exactly solvable model of 2D simple harmonic oscilator in Moyal plane, where momentum non-commutativity are also considered…

High Energy Physics - Theory · Physics 2020-09-02 Saptarshi Biswas , Partha Nandi , Biswajit Chakraborty

The time-dependent pseudo-Hermitian formulation of quantum mechanics allows to study open system dynamics in analogy to Hermitian quantum systems. In this setting, we show that the notion of holonomic quantum computation can equally be…

Quantum Physics · Physics 2019-10-23 Julien Pinske , Lucas Teuber , Stefan Scheel

Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…

Quantum Physics · Physics 2024-04-02 Carl M. Bender , Daniel W. Hook

Square-root topological phases have been discussed mainly for systems with chiral symmetry. In this paper, we analyze the topology of the squared Hamiltonian for systems preserving the time-reversal and particle-hole symmetry. Our analysis…

Mesoscale and Nanoscale Physics · Physics 2021-06-23 Tsuneya Yoshida , Tomonari Mizoguchi , Yoshihito Kuno , Yasuhiro Hatsugai

Recently, there has been a lot of activity in the research field of topological non-Hermitian physics, partly driven by fundamental interests and partly driven by applications in photonics. However, despite these activities, a general…

Mesoscale and Nanoscale Physics · Physics 2019-06-26 W. B. Rui , Y. X. Zhao , Andreas P. Schnyder

In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…

Mathematical Physics · Physics 2025-10-10 C. Sardón , X. Zhao

Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…

Dynamical Systems · Mathematics 2022-06-24 Tomoo Yokoyama

The integration of artificial intelligence (AI) into fundamental science has opened new possibilities to address long-standing scientific challenges rooted in mathematical limitations. For example, topological invariants are used to…

Mesoscale and Nanoscale Physics · Physics 2025-11-18 Yang Long , Haoran Xue , Baile Zhang

We report an open three-state perturbed system with quasi-statically varying Hamiltonian depending on the topological parameters. The effective system hosts two second order exceptional points (EP2s). Here a third order exceptional point…

Optics · Physics 2018-09-19 Sayan Bhattacherjee , Arnab Laha , Somnath Ghosh

We classify gapped phases and characteristic nodal points of non-Hermitian band structures on two-dimensional nonorientable parameter spaces. Such spaces arise in a wide range of physical systems in the presence of nonsymmorphic parameter…

Mesoscale and Nanoscale Physics · Physics 2026-03-30 J. Lukas K. König , Kang Yang , André Grossi Fonseca , Sachin Vaidya , Marin Soljačić , Emil J. Bergholtz

The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…

Statistical Mechanics · Physics 2022-08-19 Matteo Gori , Roberto Franzosi , Giulio Pettini , Marco Pettini

The study of topological properties by machine learning approaches has attracted considerable interest recently. Here we propose machine learning the topological invariants that are unique in non-Hermitian systems. Specifically, we train…

Computational Physics · Physics 2021-01-27 Ling-Feng Zhang , Ling-Zhi Tang , Zhi-Hao Huang , Guo-Qing Zhang , Wei Huang , Dan-Wei Zhang

Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous…

Mesoscale and Nanoscale Physics · Physics 2021-08-10 Helene Spring , Anton R. Akhmerov , Daniel Varjas

We analyze chiral topological edge modes in a non-Hermitian variant of the 2D Dirac equation. Such modes appear at interfaces between media with different "masses" and/or signs of the "non-Hermitian charge". The existence of these edge…

Mesoscale and Nanoscale Physics · Physics 2017-01-25 Daniel Leykam , Konstantin Y. Bliokh , Chunli Huang , Y. D. Chong , Franco Nori

The canonical formalism of the (2+2) formulation of general relativity of 4 spacetime dimensions is studied under no symmetry assumptions, where the spacetime is viewed as a local product of a 2 dimensional base manifold of Lorentzian…

General Relativity and Quantum Cosmology · Physics 2024-06-03 J. H. Yoon

Parity-time (PT)-symmetric Hamiltonians have widespread significance in non-Hermitian physics. A PT-symmetric Hamiltonian can exhibit distinct phases with either real or complex eigenspectrum, while the transition points in between, the…

Quantum Physics · Physics 2021-07-13 Lei Xiao , Tianshu Deng , Kunkun Wang , Zhong Wang , Wei Yi , Peng Xue

We study a new class of non-Hermitian topological phases in three dimension in the absence of any symmetry, where the topological robust band degeneracies are Hopf-link exceptional lines. As a concrete example, we investigate the…

Mesoscale and Nanoscale Physics · Physics 2019-12-17 Zhesen Yang , Jiangping Hu