![]() We have used the 2D ESTER code to compute and evolve isolated rapidly rotating early-type stellar models along the MS, with and without anisotropic mass loss. In this paper, we aim to clarify the rotational evolution of rapidly rotating early-type stars along the main sequence (MS). The understanding of the rotational evolution of early-type stars is deeply related to that of anisotropic mass and angular momentum loss. IRAP, Université de Toulouse, CNRS, UPS, CNES, 14, Avenue Édouard Belin, 31400 Toulouse, FranceĮ-mail: of Astronomy, University of Geneva, Chemin des MailletVersoix, SwitzerlandĮ-mail: Research Group, University of Alcalá, 28871 Alcalá de Henares, Spain Astronomical objects: linking to databasesĭ.Including author names using non-Roman alphabets.Suggested resources for more tips on language editing in the sciences Punctuation and style concerns regarding equations, figures, tables, and footnotes The code used to compute the phase spectra and the topological invariants is available at Ref. . Bulk states are represented in green, the fast boundary state in red, and the slow boundary state in blue. (b) Eigenvalues of the corresponding Ho-Chalker evolution operator with θ ≈ 0 and ≈ π / 2 for clarity. At the two interfaces, edge states with different velocity, in sign and amplitude, arise. The system in periodic in both direction and finite in the x direction. (a) Interfaces between two networks with respectively θ = 0 and π / 2. Remarkably, the two chiral edge states (one at each interface) are found to have different group velocities, which is consistent with the simple intuitive sketch in (a) where one of the two channels (in red) can flow easily rather than the other one (in blue) is forced to propagate in pilgrimage, resulting in a decreasing of its velocity along the y axis compared to that of the other boundary state. This allows one to (i) avoid potential ambiguities due to the relative character of the invariant and (ii) confirm that the existence of chiral edge states is indeed due to the bulk topology, and not merely from the oriented nature of the links. We consider interfaces between the two phases of the L-lattice in a cylinder geometry (the system has periodic boundary conditions in the x direction and is infinite in the y direction). ![]() We finally show that the two invariants coincide, again through a phase rotation symmetry arising from the particular structure of the network model. Equipped with this new tool, we explore a possible explanation of the pervasiveness of anomalous phases in scattering network models, and we define bulk topological invariants suited to both equivalent descriptions of the network model, which fully capture the topology of the system. To investigate the origin of such anomalous phases, we introduce the phase rotation symmetry, a generalization of usual symmetries which only occurs in unitary systems (as opposed to Hamiltonian systems). Such systems may present anomalous topological phases where all the first Chern numbers are vanishing, but where protected edge states appear in a finite geometry. ![]() When the successive scattering events follow a cyclic sequence, the corresponding scattering network can be equivalently described by a discrete time-periodic unitary evolution, in line with Floquet systems. ![]() This evolution, which encodes the scattering processes occurring at the nodes of the graph, is described by a single-step global operator, in the spirit of the Ho-Chalker model. We investigate the topological properties of dynamical states evolving on periodic oriented graphs. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |