Riemann meets Goldstone: magnon scattering off quantum Hall skyrmion crystals probes interplay of symmetry breaking and topology

We introduce a model to study magnon scattering in skyrmion crystals, sandwiched between ferromagnets which act as the source of magnons. Skyrmions are topological objects while skyrmion crystals break internal and translational symmetries, thus our setup allows us to study the interplay of topology and symmetry breaking. Starting from a basis of holomorphic theta functions, we construct an analytical ansatz for such a junction with finite spatially modulating topological charge density in the central region and vanishing in the leads. We then construct a suitably defined energy functional for the junction and derive the resulting equations of motion, which resemble a Bogoliubov-de Gennes-like equation. Using analytical techniques, field theory, heuristic models and microscopic recursive transfer-matrix numerics, we calculate the spectra and magnon transmission properties of the skyrmion crystal. We find that magnon transmission can be understood via a combination of low-energy Goldstone modes and effective emergent Landau levels at higher energies. The former manifests in discrete low-energy peaks in the transmission spectrum which reflect the nature of the Goldstone modes arising from symmetry breaking. The latter, which reflect the topology, lead to band-like transmission features, from the structure of which further details of the excitation spectrum of the skyrmion crystal can be inferred. Such characteristic transmission features are absent in competing phases of the quantum Hall phase diagram, and hence provide direct signatures of skyrmion crystal phases and their spectra. Our results directly apply to quantum Hall heterojunction experiments in monolayer graphene with the central region doped slightly away from unit filling, a $\nu = 1:1 \pm \delta \nu: 1$ junction and are also relevant to junctions formed by metallic magnets or in junctions with artificial gauge fields.Comment: 20+6 pages, 9+2 figures, comments welcom

ANALYSIS OF TIME-DELAYED NON-LINEAR EQUATIONS USING HF FUNCTIONS

The paper deals with the analysis of non-linear time delayed differential equations solved using HF functions. The analysis is first performed on Mackey-Glass Equation, which is a standard model for quantitative characterization of chaotic dynamics. The procedure is then performed on a generalized Human respiratory control model, where for different simulation parameters the analysis of Cheyne-Stokes Breathing is done. Both models are simulated in MATLAB. The graphs thus generated are used to provide suitable conclusions

Solution of Fractional Order Differential Equation Problems by Triangular Functions for Biomedical Applications

Abstract—Fractional Order Differential equations are used for modelling of a wide variety of biological systems but the solution process of such equations are quite complex. In this paper Orthogonal Triangular functions and their operational matrices have been used for finding an approximate solution of Fractional Order Differential Equations. This technique has been found to be more powerful in solving Fractional Order Differential Equations owing to the fact that the differential equations are reduced to systems of algebraic equations which are easy to solve numerically and the percentage error is lower compared to other methods of solutions (like: Laplace Transform Method). Also due to the recursive nature of this method, it can also be concluded that this method is less complex and more efficient in solving varieties of the Fractional Order Differential Equations

Disorder-free localization transition in a two-dimensional lattice gauge theory

Disorder-free localization is a novel mechanism for ergodicity breaking which can occur in interacting quantum many-body systems such as lattice gauge theories (LGTs). While the nature of the quantum localization transition (QLT) is still debated for conventional many-body localization, here we provide the first comprehensive characterization of the QLT in two dimensions (2D) for a disorder-free case. Disorder-free localization can appear in homogeneous 2D LGTs such as the U(1) quantum link model (QLM) due to an underlying classical percolation transition fragmenting the system into disconnected real-space clusters. Building on the percolation model, we characterize the QLT in the U(1) QLM through a detailed study of the ergodicity properties of finite-size real-space clusters via level-spacing statistics and localization in configuration space. We argue for the presence of two regimes - one in which large finite-size clusters effectively behave non-ergodically, a result naturally accounted for as an interference phenomenon in configuration space and the other in which all large clusters behave ergodically. As one central result, in the latter regime we claim that the QLT is equivalent to the classical percolation transition and is hence continuous. Utilizing this equivalence we determine the universality class and critical behaviour of the QLT from a finite-size scaling analysis of the percolation problem.Comment: 4.5 pages, 4 figures; comments welcome. V2 resembles published versio