Related papers: Probing topology in nonlinear topological material…
We study the logarithmic topological Hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory. Our results apply, for example, to connective covers of periodic ring spectra like…
Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase…
Topological materials have potential applications for quantum technologies. Non-interacting topological materials, such as e.g., topological insulators and superconductors, are classified by means of fundamental symmetry classes. It is…
In this work we provide a classification scheme for topological phases of certain systems whose observable algebra is described by a trivial $C^*$-bundles. The classification is based on the study of the homotopy classes of…
Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use. Many different identification approaches were developed over the years to estimate the…
The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…
One of the main goals and challenges of materials discovery is to find the best candidates for each interest property or application. Machine learning rises in this context to efficiently optimize this search, exploring the immense…
Searching for topological insulators/superconductors is a central subject in recent condensed matter physics. As a theoretical aspect, various classification methods of symmetry-protected topological phases have been developed, where the…
The field of optimal design of linear elastic structures has seen many exciting successes that resulted in new architected materials and structural designs. With the availability of cloud computing, including high-performance computing,…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
The nontrivial topology of spin systems such as skyrmions in real space can promote complex electronic states. Here, we provide a general viewpoint at the emergence of topological electronic states in spin systems based on the methods of…
Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium. Recent experimental progress is much from optical, cold-atomic, and classical platforms due to the vast tunability and clear identification…
Topological insulators are newly discovered materials with the defining property that any boundary cut into such crystal supports spectrum which is immune to the Anderson localization. The present paper summarizes our efforts on the…
Qualitative methods such as the linear sampling method and the factorization method reconstruct acoustic scatterers through sampling indicators. In practice, these indicators are gray-scale fields on a prescribed sampling window and a…
Nonlinear phenomena are inherent in most systems in nature. Second or higher-order harmonic generations, three-wave and four-wave mixing are typical phenomena in nonlinear optics. To obtain a nonzero signal for second-harmonic generation in…
While topology can impose obstructions to exponentially localized Wannier functions, certain topological insulators are exempt from such Wannier obstructions. The absence of the Wannier obstructions can further accompany topological…
Topological insulators are new quantum states with helical gapless edge or surface states inside the bulk band gap.These topological surface states are robust against the weak time-reversal invariant perturbations, such as lattice…
We propose a unified framework, dubbed topological word, for the complete non-Abelian bulk-boundary correspondence in multigap non-Abelian topological insulators. Composed by an ordered sequence of letters, each a non-Abelian charge…
The null space of the $k$-th order Laplacian $\mathbf{\mathcal L}_k$, known as the {\em $k$-th homology vector space}, encodes the non-trivial topology of a manifold or a network. Understanding the structure of the homology embedding can…
The introduction of structural defects in otherwise periodic media is well known to grant exceptional space control and localization of waves in various physical fields, including elasticity. Despite the variety of designs proposed so far,…