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Integer and fractional Chern insulators exhibit a nonzero quantized anomalous Hall conductivity due to a spontaneous breaking of time reversal symmetry. To identify nontrivial topology in their time-reversal symmetric many-body spectra, we…

Strongly Correlated Electrons · Physics 2026-01-21 Axel Fünfhaus , Titus Neupert , Thilo Kopp , Roser Valentí

We propose a novel and systematic recurrence method for the energy spectra of non-Hermitian systems under open boundary conditions based on the recurrence relations of their characteristic polynomials. Our formalism exhibits better accuracy…

Mesoscale and Nanoscale Physics · Physics 2025-04-16 Haoyan Chen , Yi Zhang

The non-Hermitian skin effect dramatically reshapes the energy bands of non-Hermitian systems, meaning that the usual Bloch band theory is fundamentally inadequate as their characterization. The non-Bloch band theory, in which the concept…

Mesoscale and Nanoscale Physics · Physics 2024-05-02 Hong-Yi Wang , Fei Song , Zhong Wang

The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…

Pattern Formation and Solitons · Physics 2022-07-20 S. J. Chapman , M. E. Kavousanakis , E. G. Charalampidis , I. G. Kevrekidis , P. G. Kevrekidis

We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at the boundary of the medium encoded in the Dirichlet-to-Neumann…

Analysis of PDEs · Mathematics 2022-03-08 Gunther Uhlmann , Yang Zhang

Nonlinear spectral graph theory is an extension of the traditional (linear) spectral graph theory and studies relationships between spectral properties of nonlinear operators defined on a graph and topological properties of the graph…

Spectral Theory · Mathematics 2025-04-07 Piero Deidda , Francesco Tudisco , Dong Zhang

The bulk-edge correspondence is a fundamental principle of topological wave physics, which states that the difference in gap Chern numbers between the interfaced materials is equal to the net number of topological edge modes. Although this…

Optics · Physics 2022-02-09 Samaneh Pakniyat , S. Ali Hassani Gangaraj , George W Hanson

This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…

Numerical Analysis · Mathematics 2016-11-03 Shanghui Jia , Hehu Xie , Manting Xie , Fei Xu

Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local-global correspondence between the…

Quantum Physics · Physics 2023-08-11 Annan Fan , Shi-Dong Liang

Here, we develop a gauge-independent Green function approach to characterize the Chern invariants of generic non-Hermitian systems. It is shown that analogous to the Hermitian case, the Chern number can be expressed as an integral of the…

Optics · Physics 2019-04-03 Mário G. Silveirinha

Topological Insulators are a novel state of matter where spectral bands are characterized by quantized topological invariants. This unique quantized non-local property commonly manifests through exotic bulk phenomena and corresponding…

Mesoscale and Nanoscale Physics · Physics 2018-05-15 Mark Kremer , Ioannis Petrides , Eric Meyer , Matthias Heinrich , Oded Zilberberg , Alexander Szameit

Theory of nonlinear resonance, including stochastic one, is developed on the basis of the statistical field theory and using variables action-angle. Explicit expressions of action, proper frequency and nonlinearity parameter as functions of…

Statistical Mechanics · Physics 2007-05-23 A. I. Olemskoi

Understanding how systems respond to external perturbations is fundamental to statistical physics. For systems far from equilibrium, a general framework for response remains elusive. While progress has been made on the linear response of…

Statistical Mechanics · Physics 2026-03-04 Ruicheng Bao , Shiling Liang

The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…

Classical Analysis and ODEs · Mathematics 2012-05-11 Yu. A. Konyaev

We introduce a novel gauge-invariant, quantized interband index in two-dimensional (2D) multiband systems. It provides a bulk topological classification of a submanifold of parameter space (e.g., an electron valley in a Brillouin zone), and…

Mesoscale and Nanoscale Physics · Physics 2023-08-17 Tharindu Fernando , Ting Cao

Topological invariants in the band structure, such as Chern numbers, are crucial for the classification of topological matters and dictate the occurrence of exotic properties, yet their direct spectroscopic determination has been largely…

The bulk-boundary correspondence predicts the existence of boundary modes localized at the edges of topologically nontrivial systems. The wavefunctions of hermitian boundary modes can be obtained as the eigenmodes of a modified Jackiw-Rebbi…

High Energy Physics - Theory · Physics 2026-02-16 Pasquale Marra , Angela Nigro

This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…

Functional Analysis · Mathematics 2022-01-10 Kamal N. Soltanov

In recent research, it has been shown that non-Hermitian systems exhibit sensitivity to boundaries, and it is caused by the non-Hermitian skin effect. In this work, we construct the non-Bloch band theory in bosonic Bogoliubov--de Gennes…

Mesoscale and Nanoscale Physics · Physics 2021-04-28 Kazuki Yokomizo , Shuichi Murakami

We study the influence of reflective boundaries on time-dependent responses of one-dimensional quantum fluids at zero temperature beyond the low-energy approximation. Our analysis is based on an extension of effective mobile impurity models…

Strongly Correlated Electrons · Physics 2016-06-01 I. S. Eliëns , F. B. Ramos , J. C. Xavier , R. G. Pereira