Related papers: Topological Euler class as a dynamical observable …
We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the…
Topological materials exhibit properties dictated by quantised invariants that make them robust against perturbations. This topological protection is a universal wave phenomenon that applies not only in the context of electrons in…
Establishing the fundamental relation between the homotopy invariants and the band topology of Hamiltonians has played a critical role in the recent development of topological phase research. In this work, we establish the homotopy…
There is a remarkable and canonical problem in 3D geometry and topology: To understand existing models of 3D fluid motion or to create new ones that may be useful. We discuss from an algebraic viewpoint the PDE called Euler's equation for…
A recent prominent result asserts that steady incompressible Euler flows strictly away from stagnation in a two-dimensional infinitely long strip must be shear flows. On the other hand, flows with stagnation points, very challenging in…
In this article, we construct infinitely many (small Seifert fibred, hyperbolic and toroidal) rational homology $3$-spheres that admit co-orientable taut foliations, but none with vanishing Euler class. In the context of the $L$-space…
We study the Euler equations on a rotating unit sphere, focusing on the dynamics of vortex caps. Leveraging the $L^1$-stability of monotone, longitude-independent profiles, we demonstrate that certain ill-prepared initial data within the…
In the first part of the paper we provide a new classification of incompressible fluids characterized by a continuous monotone relation between the velocity gradient and the Cauchy stress. The considered class includes Euler fluids,…
The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures. However, when nonlinearity is introduced, many intriguing questions arise. For example, are there…
Topological insulators are typically characterized by particularly stable properties, such as global invariants, and can be identified by probing their robust surface states. A recently discovered novel form of band topology, delicate…
We study continuations of topological edge states in the Su-Schrieffer-Heeger model with on-site cubic (Kerr) nonlinearity, which is a 1D nonlinear photonic topological insulator (TI). Based on the topology of the underlying spatial…
We study the band topology and the associated linking structure of topological semimetals with nodal lines carrying $Z_{2}$ monopole charges, which can be realized in three-dimensional systems invariant under the combination of inversion…
Topological insulators are insulating in the bulk but feature conducting states on their surfaces. Standard methods for probing their topological properties largely involve probing the surface, even though topological invariants are defined…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
We classify in terms of Hopf-type properties mapping tori of residually finite Poincar\'e Duality groups with non-zero Euler characteristic. This generalises and gives a new proof of the analogous classification for fibered 3-manifolds.…
Hopf insulators are exotic topological states of matter outside the standard ten-fold way classification based on discrete symmetries. Its topology is captured by an integer invariant that describes the linking structures of the Hamiltonian…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…
Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field defined on two and three dimensional manifolds. While the…
Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, non-reciprocal chiral edge states and cavity-like confined states that have applications in both linear and…