The Experts below are selected from a list of 15306 Experts worldwide ranked by ideXlab platform
Micha Wasem - One of the best experts on this subject based on the ideXlab platform.
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Equilibria of plane convex bodies
arXiv: Differential Geometry, 2019Co-Authors: Jonas Allemann, Norbert Hungerbuhler, Micha WasemAbstract:We obtain a formula for the Number of horizontal equilibria of a planar convex body $K$ with respect to a center of mass $O$ in terms of the Winding Number of the evolute of $\partial K$ with respect to $O$. The formula extends to the case where $O$ lies on the evolute of $\partial K$ and a suitably modified version holds true for non-horizontal equilibria.
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non integer valued Winding Numbers and a generalized residue theorem
Journal of Mathematics, 2019Co-Authors: Norbert Hungerbuhler, Micha WasemAbstract:We define a generalization of the Winding Number of a piecewise cycle in the complex plane which has a geometric meaning also for points which lie on the cycle. The computation of this Winding Number relies on the Cauchy principal value but is also possible in a real version via an integral with bounded integrand. The new Winding Number allows to establish a generalized residue theorem which covers also the situation where singularities lie on the cycle. This residue theorem can be used to calculate the value of improper integrals for which the standard technique with the classical residue theorem does not apply.
P J Morrison - One of the best experts on this subject based on the ideXlab platform.
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breakup of shearless meanders and outer tori in the standard nontwist map
Chaos, 2006Co-Authors: K Fuchss, Alexander Wurm, Amit Apte, P J MorrisonAbstract:The breakup of shearless invariant tori with Winding Number ω=(11+γ)∕(12+γ) (in continued fraction representation) of the standard nontwist map is studied numerically using Greene’s residue criterion. Tori of this Winding Number can assume the shape of meanders [folded-over invariant tori which are not graphs over the x axis in (x,y) phase space], whose breakup is the first point of focus here. Secondly, multiple shearless orbits of this Winding Number can exist, leading to a new type of breakup scenario. Results are discussed within the framework of the renormalization group for area-preserving maps. Regularity of the critical tori is also investigated.
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breakup of shearless meanders and outer tori in the standard nontwist map
arXiv: Chaotic Dynamics, 2006Co-Authors: K Fuchss, Alexander Wurm, Amit Apte, P J MorrisonAbstract:The breakup of shearless invariant tori with Winding Number $\omega=[0,1,11,1,1,...]$ (in continued fraction representation) of the standard nontwist map is studied numerically using Greene's residue criterion. Tori of this Winding Number can assume the shape of meanders (folded-over invariant tori which are not graphs over the x-axis in $(x,y)$ phase space), whose breakup is the first point of focus here. Secondly, multiple shearless orbits of this Winding Number can exist, leading to a new type of breakup scenario. Results are discussed within the framework of the renormalization group for area-preserving maps. Regularity of the critical tori is also investigated.
Juntao Song - One of the best experts on this subject based on the ideXlab platform.
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effect of strong disorder on three dimensional chiral topological insulators phase diagrams maps of the bulk invariant and existence of topological extended bulk states
Physical Review B, 2014Co-Authors: Juntao Song, Carolyn Fine, Emil ProdanAbstract:The effect of strong disorder on chiral-symmetric three-dimensional lattice models is investigated via analytical and numerical methods. The phase diagrams of the models are computed using the noncommutative Winding Number, as functions of disorder strength and model's parameters. The localized/delocalized characteristic of the quantum states is probed with level statistics analysis. Our study reconfirms the accurate quantization of the noncommutative Winding Number in the presence of strong disorder, and its effectiveness as a numerical tool. Extended bulk states are detected above and below the Fermi level, which are observed to undergo the so-called ``levitation and pair annihilation'' process when the system is driven through a topological transition. This suggests that the bulk invariant is carried by these extended states, in stark contrast with the one-dimensional case where the extended states are completely absent and the bulk invariant is carried by the localized states.
Steven G Louie - One of the best experts on this subject based on the ideXlab platform.
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unifying optical selection rules for excitons in two dimensions band topology and Winding Numbers
Physical Review Letters, 2018Co-Authors: Ting Cao, Steven G LouieAbstract:We show that band topology can dramatically change the photophysics of two-dimensional semiconductors. For systems in which states near the band extrema are of multicomponent character, the spinors describing these components (pseudospins) can pick up nonzero Winding Numbers around the extremal k point. In these systems, we find that the strength and required light polarization of an excitonic optical transition are dictated by the optical matrix element Winding Number, a unique and heretofore unrecognized topological characteristic. We illustrate these findings in three gapped graphene systems-monolayer graphene with inequivalent sublattices and biased bi- and trilayer graphene, where the pseudospin textures manifest into nontrivial optical matrix element Winding Numbers associated with different valley and photon circular polarization. This Winding-Number physics leads to novel exciton series and optical selection rules, with each valley hosting multiple bright excitons coupled to light of different circular polarization. This valley-exciton selective circular dichroism can be unambiguously detected using optical spectroscopy.
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nonanalyticity valley quantum phases and lightlike exciton dispersion in monolayer transition metal dichalcogenides theory and first principles calculations
Physical Review Letters, 2015Co-Authors: Ting Cao, Steven G Louie, Diana Y QiuAbstract:Exciton dispersion as a function of center-of-mass momentum Q is essential to the understanding of exciton dynamics. We use the ab initio GW-Bethe-Salpeter equation method to calculate the dispersion of excitons in monolayer MoS(2) and find a nonanalytic lightlike dispersion. This behavior arises from an unusual |Q|-term in both the intra- and intervalley exchange of the electron-hole interaction, which concurrently gives rise to a valley quantum phase of Winding Number two. A simple effective Hamiltonian to Q(2) order with analytic solutions is derived to describe quantitatively these behaviors.
L S Levitov - One of the best experts on this subject based on the ideXlab platform.
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topological transition in a non hermitian quantum walk
Physical Review Letters, 2009Co-Authors: Mark S Rudner, L S LevitovAbstract:We analyze a quantum walk on a bipartite one-dimensional lattice, in which the particle can decay whenever it visits one of the two sublattices. The corresponding non-Hermitian tight-binding problem with a complex potential for the decaying sites exhibits two different phases, distinguished by a Winding Number defined in terms of the Bloch eigenstates in the Brillouin zone. We find that the mean displacement of a particle initially localized on one of the nondecaying sites can be expressed in terms of the Winding Number, and is therefore quantized as an integer, changing from zero to one at the critical point. We show that the topological transition is relevant for a variety of experimental settings. The quantized behavior can be used to distinguish coherent from incoherent dynamics.
