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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Some Spectral Properties of Massless Dirac Operato
rs - Schmidt\, KM (Cardiff University)
DTSTART;TZID=Europe/London:20120803T094500
DTEND;TZID=Europe/London:20120803T103000
UID:TALK39165AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39165
DESCRIPTION:The one-dimensional massless Dirac operator not on
ly does not have a central gap in its spectrum\, b
ut it is even unitarily equivalent to the free mas
sless operator and hence has purely absolutely con
tinuous spectrum covering the whole real line. \n\
nThe talk reports on work regarding the question t
o what extent similar general statements about the
essential spectrum and the absolutely continuous
spectrum are possible in the higher-dimensional ca
se. Under the assumption of spherical symmetry\, i
t can be shown that the spectrum is purely absolut
ely continuous outside the limit range of the pote
ntial\, thus giving an a priori set containing all
eigenvalues. This can be partly extended to a far
more general situation by a virial technique. Mor
eover\, the essential spectrum is the whole real l
ine for a large class of potentials satisfying a l
ocal separability condition. This is joint work wi
th T. Umeda.\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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