Related papers: Universal Continuum Theory for Topological Edge So…
Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a new paradigm of synthetic matter, and their energy levels were characterized by a band structure in a four- (or higher-)dimensional momentum space.…
We study and classify the emergence of protected edge modes at the junction of one-dimensional materials. Using symmetries of Lagrangian planes in boundary symplectic spaces, we present a novel proof of the periodic table of topological…
Bulk-edge correspondence is a wide-ranging principle that applies to topological matter, as well as a precise result established in a large and growing number of cases. According to the principle, the distinctive topological properties of…
We present a general analysis of two-dimensional optical lattice models that give rise to topologically non-trivial insulating states. We identify the main ingredients of the lattice models that are responsible for the non-trivial…
The 4D Maxwell theory with single-sided planar boundary is considered. As a consequence of the presence of the boundary, two broken Ward identities are recovered, which, on-shell, give rise to two conserved currents living on the edge. A…
The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the last decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces…
Candidates for random network media include, e.g., systems consisting of long, flexible macromolecules cross-linked (i.e., permanently bonded) together at random to form the network. Owing to the random architecture, the characteristics of…
Unlike the edge state of a topological insulator where its energy level lives in the bulk energy gap, the edge state of a topological semimetal hides in the bulk spectrum and is difficult to be identified by the energy. We investigate the…
Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological…
Topological insulators feature a number of topologically protected boundary modes linked to the value of their bulk invariant. While in one-dimensional systems the boundary modes are zero dimensional and localized, in two-dimensional…
We propose a method to address the existence of topological edge modes in one-dimensional (1D) nonlinearlattices, by deforming the edge modes of linearized models into solutions of the fully nonlinear system. Forlarge enough nonlinearites,…
This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the…
Consider a sequence of Gibbsian line ensembles, whose lowest labeled curves (i.e., the edge) have tight one-point marginals. Then, given certain technical assumptions on the nature of the Gibbs property and underlying random walk measure,…
In this paper we evaluate the dynamic effects of the fluid viscosity for fluid filled elastic tubes in the framework of a linear uni-axial theory. Because of the linear approximation, the effects on the fluid inside the elastic tube are…
A systematic approach for deriving tight-binding approximations in general longitudinally driven lattices is presented. As prototypes, honeycomb and staggered square lattices are considered. Time-reversal symmetry is broken by…
Recent studies have extended the notion of band topology to nonlinear systems by defining nonlinear counterparts of eigenvalue problems. They have found the nonlinearity-induced topological transition, while it has required complicated…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
By using a limit analysis for the motion equations of viscous fluid endowed with internal capillarity, we are able to propose a dynamical expression for the surface tension of moving liquid-vapour interfaces without any phenomenological…
We predict that spatial self-trapping of light can occur in soft matter encompassing a wide class of new materials such as colloids, foams, gels, fractal aggregates etc. We develop a general nonlocal theory that allows to relate the…
In these lecture notes we will try to give an introduction to the use of the mathematics of fibre bundles in the understanding of some global aspects of gauge theories, such as monopoles and instantons. They are primarily aimed at beginning…