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SUMMARY:Michael Weinstein
DTSTART:20210614T150000Z
DTEND:20210614T160000Z
DTSTAMP:20260423T022811Z
UID:MCQM21/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MCQM21/2/">T
 ight binding approximation of continuum 2D quantum materials</a>\nby Micha
 el Weinstein as part of Mathematical Challenges in Quantum Mechanics 2021 
 Workshop\n\n\nAbstract\nWe consider 2D quantum materials\, modeled by a co
 ntinuum Schroedinger operator whose potential\nis composed of an array of 
 identical potential wells centered on the vertices of a discrete subset\, 
 \\Omega\, of the plane. \nWe study the low-lying spectrum in the regime of
  very deep potential wells.\n\nWe present results on scaled resolvent norm
  convergence to a discrete (tight-binding) operator and\, \nin the transla
 tion invariant case\, corresponding results on the scaled convergence of l
 ow-lying dispersion surfaces.\nExamples include the single electron model 
 for bulk graphene ($\\Omega$=honeycomb lattice)\, and \na sharply terminat
 ed graphene half-space\, interfaced with the vacuum along an arbitrary lin
 e-cut. \nWe also apply our methods to the case of strong constant perpendi
 cular magnetic fields. \nThis is joint work with CL Fefferman and J Shapir
 o.\n\nA detailed analysis of the spectrum of the limiting tight binding mo
 del on a honeycomb lattice\, which is terminated along an arbitrary ration
 al line-cut (joint work with CL Fefferman and S Fliss)\, will be presented
  in the upcoming lecture of CL Fefferman.\n
LOCATION:https://researchseminars.org/talk/MCQM21/2/
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