Related papers: Bulk-edge correspondence of classical diffusion ph…
A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to…
We study a class of periodic Schr\"odinger operators, which in distinguished cases can be proved to have linear band-crossings or "Dirac points". We then show that the introduction of an "edge", via adiabatic modulation of these periodic…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
Understanding the rich spatial and temporal structures in nonequilibrium thermal environments is a major subject of statistical mechanics. Because universal laws, based on an ensemble of systems, are mute on an individual system, exploring…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
We study diffusion of (fluorescently) tagged hard-core interacting particles of finite size in a finite one-dimensional system. We find an exact analytical expression for the tagged particle probability density using a coordinate…
This paper reports on the experimental observation of topologically protected edge state and exceptional point in an open and Non-Hermitian system. While the theoretical underpinning is generic to wave physics, the simulations and…
The breathing honeycomb lattice hosts a topologically non-trivial bulk phase due to the crystalline-symmetry of the system. Pseudospin-dependent edge states which emerge at the interface between trivial and non-trivial regions can be used…
Photonic crystal topological insulators host protected states at their edges. In the band structure these edge states appear as continuous bands crossing the photonic band gap. They allow light to propagate unidirectionally and without…
Capital to topological insulators, the bulk-boundary correspondence ties a topological invariant computed from the bulk (extended) states with those at the boundary, which are hence robust to disorder. Here we put forward an ordering unique…
In these decades, it has been gradually established that edge modes of a wide class of topologically ordered systems are governed by the bulk-edge correspondence and anyon condensation. The former has been studied many times because it can…
In a finite one-dimensional non-Hermitian system, the number of zero modes does not necessarily reflect the topology of the system. This is known as the breakdown of the bulk-boundary correspondence and has led to misconceptions about the…
We present a multiple scattering analysis of robust interface states for flexural waves in thin elastic plates. We show that finite clusters of linear arrays of scatterers built on a quasi-periodic arrangement support bounded modes in the…
The bulk-edge correspondence (BEC) is the hallmark of topological systems. In continuous (nonlattice) Hermitian systems with an unbounded wave vector, it was recently shown that the BEC of Chern insulators is modified. How would it be…
Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the bulk-boundary correspondence is broken down in general non-Hermitian systems. In this paper,…
Symmetry-protected topological phases cannot be described by any local order parameter and are beyond the conventional symmetry-breaking paradigm for understanding quantum matter. They are characterized by topological boundary states robust…
We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…
A topological measure characterizing symmetry-protected topological phases in one-dimensional open fermionic systems is proposed. It is built upon the kinematic approach to the geometric phase of mixed states and facilitates the extension…
The Toda lattice is a model of nonlinear wave equations allowing exact soliton solutions. It is realized by an electric circuit made of a transmission line with variable capacitance diodes and inductors. It has been generalized to the…
We describe the formation of bulk and edge arcs in the dispersion relation of two-dimensional coupled-resonator arrays that are topologically trivial in the hermitian limit. Each resonator provides two asymmetrically coupled internal modes,…