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Keywords
(6)
Dirac Operator
Eigenvalues
Magnetic Field
Phase Shift
3 dimensional
Spectral Shift Function
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Asymptotics near +m of the spectral shift function for Dirac operators with nonconstant magnetic fields
Asymptotics near +m of the spectral shift function for Dirac operators with nonconstant magnetic fields,Rafael Tiedra De Aldecoa
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Asymptotics near +m of the spectral shift function for Dirac operators with nonconstant magnetic fields
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Rafael Tiedra De Aldecoa
We consider a 3dimensional
Dirac operator
H_0 with nonconstant
magnetic field
of constant direction, perturbed by a signdefinite matrixvalued potential V decaying fast enough at infinity. Then we determine asymptotics, as the energy goes to +m and m, of the
spectral shift function
for the pair (H_0,H_0+V). We obtain, as a byproduct, a generalised version of Levinson's Theorem relating the
eigenvalues
asymptotics of H_0+V near +m and m to the scattering
phase shift
for the pair (H_0,H_0+V).
Published in 2009.
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