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SUMMARY:Some Spectral Properties of Massless Dirac Operators - Schmidt\, K
 M (Cardiff University)
DTSTART:20120803T084500Z
DTEND:20120803T093000Z
UID:TALK39165@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The one-dimensional massless Dirac operator not only does not 
 have a central gap in its spectrum\, but it is even unitarily equivalent t
 o the free massless operator and hence has purely absolutely continuous sp
 ectrum covering the whole real line. \n\nThe talk reports on work regardin
 g the question to what extent similar general statements about the essenti
 al spectrum and the absolutely continuous spectrum are possible in the hig
 her-dimensional case. Under the assumption of spherical symmetry\, it can 
 be shown that the spectrum is purely absolutely continuous outside the lim
 it range of the potential\, thus giving an a priori set containing all eig
 envalues. This can be partly extended to a far more general situation by a
  virial technique. Moreover\, the essential spectrum is the whole real lin
 e for a large class of potentials satisfying a local separability conditio
 n. This is joint work with T. Umeda.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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