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SUMMARY:Schrodinger or Pauli operators with self-generated magnetic fields
  - Solovej\, J P (University of Copenhagen)
DTSTART:20150211T140000Z
DTEND:20150211T150000Z
UID:TALK57849@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:There is a huge literature on Schrodinger or Pauli operators w
 ith fixed exterior magnetic fields. If however the magnetic field is not g
 iven a-priori but is the field generated by the charged particles themselv
 es we get the coupled Shrodinger-Maxwell or Pauli-Maxwell systems. I will 
 discuss the spectral theory and what is known\, but in particular what is 
 not known for these systems. It is known that there is stability of matter
  for both the Schrodinger and Pauli systems. It is however an open problem
  if there is existence of the thermodynamic limit. Depending on the coupli
 ng strength to the magnetic field it is also known that the semiclassical 
 Weyl law sometimes holds and sometimes does not. A \nsemiclassical eigenva
 lue estimate that holds generally in all regimes is not known.\n\nThe work
  on stablity of matter is joint work with Lieb and Loss from 1995. The wor
 k on semiclassics is more recent work with Erdos and Fournais.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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