Related papers: Bulk-edge correspondence of classical diffusion ph…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one of the quintessential ideas in the physics of topological quantum matter. Nevertheless, it has not been proven in all generality and has…
Bound states in the continuum (BIC) have been studied mainly in optics. Recently, electronic BIC have been proposed. They appear as points in the momentum space and are protected topologically by the Chern number. In this study, we propose…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
The bulk-edge correspondence characterizes topological insulators and superconductors. We generalize this concept to the bulk-corner correspondence and the edge-corner correspondence in two dimensions. In the bulk-corner (edge-corner)…
Non-Hermitian topological systems show quite different properties as their Hermitian counterparts. An important, puzzled issue on non-Hermitian topological systems is the existence of defective edge states beyond usual bulk-boundary…
The bulk-boundary correspondence plays a crucial role in topological quantum systems, however,this principle is broken in non-Hermitian systems. The breakdown of the bulk-boundary correspondence indicates that the global phase diagrams…
In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in the…
This paper concerns the topological classification of continuous Hamiltonians that find applications in biased cold plasmas and photonics. Besides a magnetic bias, the Hamiltonians are parametrized by a plasma frequency and a fixed vertical…
The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a…
We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature)…
Topological physics opens up a plethora of exciting phenomena allowing to engineer disorder-robust unidirectional flows of light. Recent advances in topological protection of electromagnetic waves suggest that even richer functionalities…
Compared with conventional topological insulator that carries topological state at its boundaries, the higher-order topological insulator exhibits lower-dimensional gapless boundary states at its corners and hinges. Leveraging the form…
Topological photonic systems offer light transport that is robust against defects and disorder, promising a new generation of chip-scale photonic devices and facilitating energy-efficient on-chip information routing and processing. However,…
Topological phases and the associated multiple edge states are studied for parity and time-reversal $(\mathcal{PT})$ symmetric non-Hermitian open quantum systems by constructing a non-unitary three-step quantum walk retaining $\mathcal{PT}$…
Topological insulators are states of matter distinguished by the presence of symmetry protected metallic boundary states. These edge modes have been characterised in terms of transport and spectroscopic measurements, but a thermodynamic…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…