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Documents  Weinstein, Michael | enregistrements trouvés : 4

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Research talks;Partial Differential Equations

We discuss the 2D Schrödinger equation for periodic potentials with the symmetry of a hexagonal tiling of the plane. We first review joint work with CL Fefferman on the existence of Dirac points, conical singularities in the band structure, and the resulting effective 2D Dirac dynamics of wave-packets. We then focus on periodic potentials which are superpositions of localized potential wells, centered on the vertices of a regular honeycomb structure, corresponding to the single electron model of graphene and its artificial analogues. We prove that for sufficiently deep potentials (strong binding) the lowest two Floquet-Bloch dispersion surfaces, when appropriately rescaled, are uniformly close to those of the celebrated two-band tight-binding model, introduced by PR Wallace (1947) in his pioneering study of graphite. We then discuss corollaries, in the strong binding regime, on (a) spectral gaps for honeycomb potentials with PT symmetry-breaking perturbations, and (b) topologically protected edge states for honeycomb structures with "rational edges. This is joint work with CL Fefferman and JP Lee-Thorp. Extensions to Maxwell equations (with Y Zhu and JP Lee-Thorp) will also be discussed. We discuss the 2D Schrödinger equation for periodic potentials with the symmetry of a hexagonal tiling of the plane. We first review joint work with CL Fefferman on the existence of Dirac points, conical singularities in the band structure, and the resulting effective 2D Dirac dynamics of wave-packets. We then focus on periodic potentials which are superpositions of localized potential wells, centered on the vertices of a regular honeycomb ...

35J10 ; 35B32 ; 35Q41 ; 37G40

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Research talks;Partial Differential Equations;Mathematical Physics

74J30 ; 74N15 ; 35B27

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- 231 p.
ISBN 978-0-936428-06-2

Localisation : Ouvrage RdC (Betw)

20D10 ; 20D15 ; 20D20 ; 20D25

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- 307 p.

Localisation : Ouvrage RdC (WEIN)

axiome du choix et lemme de Zorn # groupe fini # groupe hypercyclique # groupe infini abélien ou nonabélien # groupe libre et présentation # groupe nilpotent # groupe résoluble # matrice # série centrale ascendante # série dérivée # treillis de sousgroupes

20-01

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