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SUMMARY:Computational and theoretical tools for the magnetic Schrödinger 
 eigenvalue problem - Jeffrey Ovall (Portland State University)
DTSTART:20260414T143000Z
DTEND:20260414T153000Z
UID:TALK244006@talks.cam.ac.uk
DESCRIPTION:The magnetic Schr&ouml\;dinger equation provides a probabilist
 ic model of the motion of a charged particle in an electromagnetic field. 
 The associated eigenvalue problem provides probability densities\, via nor
 malized eigenvectors\, of the location of the charged particle at certain 
 energies associated with the eigenvalues. &nbsp\;Properties of the magneti
 c and electric potentials can cause eigenvectors to be strongly spatially 
 localized. &nbsp\;This phenomenon has been extensively studied in the case
  where the magnetic potential is absent\, and a we will briefly illustrate
  some known results about localization and its driving mechanisms in that 
 context. &nbsp\;Much less is known in the case where the behavior is domin
 ated by the magnetic field. &nbsp\;Our talk will focus on that case\, prov
 iding computational tools that exploit the notion of gauge invariance to d
 ramatically reduce the cost of eigenvector computations\, and providing pr
 actical predictors of where eigenvectors lower in the spectrum are likely 
 to localize.&nbsp\; &nbsp\;\nThis is joint work with Hadrian Quan\, Robin 
 Reid\, Stefan Steinerberger and Julie Zhu.
LOCATION:Seminar Room 1\, Newton Institute
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