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On the ground states of vector nonlinear Schrödinger equations

Thierry Colin; Michael I. Weinstein — 1996

Annales de l'I.H.P. Physique théorique

Waves in Honeycomb Structures

Charles L. Fefferman; Michael I. Weinstein — 2012

Journées Équations aux dérivées partielles

We review recent work of the authors on the non-relativistic Schrödinger equation with a honeycomb lattice potential, $V$ . In particular, we summarize results on (i) the existence of Dirac points, conical singularities in dispersion surfaces of $H_{V} = - Δ + V$ and (ii) the two-dimensional Dirac equations, as the large (but finite) time effective system of equations governing the evolution $e^{- i H_{V} t} ψ_{0}$ , for data $ψ_{0}$ , which is spectrally localized near a Dirac point. We conclude with a formal derivation and discussion of the...

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