Related papers: Topological classification of driven-dissipative n…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
Mechanical topological insulators are well understood for linear and weakly nonlinear systems, however traditional analysis methods break down for strongly nonlinear systems since linear methods can not be applied in that case. We study one…
The St\v{r}eda formula establishes a fundamental connection between the topological invariants characterizing the bulk of topological matter and the presence of gapless edge modes. In this work, we extend the St\v{r}eda formula to…
We introduce a driven-dissipative Bose-Hubbard chain describing coupled lossy photonic modes, in which time-reversal symmetry is broken by a coherent drive with a uniform phase gradient. We investigate this model by means of a Gaussian…
Topological phase of matter is now a mainstream of research in condensed matter physics, of which the classification, synthesis, and detection of topological states have brought excitements over the recent decade while remain incomplete…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an…
While periodically-driven phases offer a unique insight into non-equilibrium topology that is richer than its static counterpart, their experimental realization is often hindered by ubiquitous decoherence effects. Recently, we have proposed…
For spinful systems with spin 1/2, it is generally believed that P and T invariant strong and second-order topologies exist in four band and eight band system, respectively. Here, by using periodic driving, we find it is possible to have…
Non-Hermiticity enriches the contents of topological classification of matter including exceptional points, bulk-edge correspondence and skin effect. Gain and loss can be described by imaginary diagonal elements in Hamiltonians and the…
Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band…
The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory…
We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven…
Topologically protected edge states exactly at topological phase boundaries challenge the conventional belief that topological states must be associated with a bulk energy gap. Because periodically driven (Floquet) systems host unusually…
Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (i) A systematic formulation of topological…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
Recently, many novel and exotic phases have been proposed by considering the role of topology in non-Hermitian systems, and their emergent properties are of wide current interest. In this work we propose the non-Hermitian generalization of…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
Topological states of matter in non-Hermitian systems have attracted a lot of attention due to their intriguing dynamical and transport properties. In this study, we propose a periodically driven non-Hermitian lattice model in…
Over the past few years, topological insulators have taken center stage in solid state physics. The desire to tune the topological invariants of the bulk and thus control the number of edge states has steered theorists and experimentalists…