Related papers: One-dimensional non-Hermitian band structures as R…

We consider a 3-dimensional (3D) non-Hermitian exceptional line semimetal model and take open boundary conditions in x, y, and z directions separately. In each case, we calculate the parameter regions where the bulk-boundary correspondence…

Braiding has attracted significant attention in physics because of its important role in describing the fundamental exchange of particles. Infusing the braiding with topological protection will make it robust against imperfections and…

We study bosons interacting with an abelian Chern-Simons field on Riemann surfaces of genus $g>0$. It is shown that a singular gauge transformation brings the hamiltonian to free form. The transformed wave functions furnish a…

It is well-known that any covering space of a Riemannian manifold has the natural structure of a Riemannian manifold. This article contains a noncommutative generalization of this fact. Since any Riemannian manifold with a Spin-structure…

We study isospectrality for manifolds with mixed Dirichlet-Neumann boundary conditions and express the well-known transplantation method in graph- and representation-theoretic terms. This leads to a characterization of transplantability in…

The Clifford spectrum is an elegant way to define the joint spectrum of several Hermitian operators. While it has been know that for examples as small as three $2$-by-$2$ matrices the Clifford spectrum can be a two-dimensional manifold, few…

Topological semimetals exhibit band crossings near the Fermi energy, which are protected by the nontrivial topological character of the wave functions. In many cases, these topological band degeneracies give rise to exotic surface states…

Any oriented Riemannian manifold with a Spin-structure defines a spectral triple, so the spectral triple can be regarded as a noncommutative Spin-manifold. Otherwise for any unoriented Riemannian manifold there is the two-fold covering by…

We consider a semi-periodic two-dimensional Schr\"odinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure. We prove that in the…

We establish exact relations between the winding of "energy" (eigenvalue of Hamiltonian) on the complex plane as momentum traverses the Brillouin zone with periodic boundary condition, and the presence of "skin modes" with open boundary…

As a promising approach for optical nonreciprocity without magnetic materials, optomechanically induced nonreciprocity has great potential for all-optical controllable isolators and circulators on chips. However, as a very important issue…

Energy bands of non-Hermitian crystalline systems are described in terms of the generalized Brillouin zone (GBZ) having unique features which are absent in Hermitian systems. In this paper, we show that in one-dimensional non-Hermitian…

The topological classification of energy bands has laid the groundwork for the discovery of various topological phases of matter in recent decades. While this classification has traditionally focused on real-energy bands, recent studies…

We examine the problem of determining which representations of the braid group on a Riemann surface are carried by the wave function of a quantized Abelian Chern-Simons theory interacting with non-dynamical matter. We generalize the…

A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral…

Combining several previously known arguments, we prove marked length spectrum rigidity for surfaces with nonpositively curved Riemannian metrics away from a finite set of cone-type singularities with cone angles $>2\pi$. With an additional…

We define the notion of a braided link cobordism in $S^3 \times [0,1]$, which generalizes Viro's closed surface braids in $\mathbb{R}^4$. We prove that any properly embedded oriented surface $W \subset S^3 \times [0,1]$ is isotopic to a…

We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.

In quantum mechanics, observables correspond to Hermitian operators, and the spectra are restricted to be real. However, the dynamics of the underlying fields may allow complex eigenvalues and therefore create the possibility of braiding…

We consider non-Hermitian energy band theory in two-dimensional systems, and study eigenenergy braids on slices in the two-dimensional Brillouin zone. We show the consequences of reciprocity and geometric symmetry on such eigenenergy…