AJM-2021-0025-0002-a005.pdf (389.78 kB)
Poisson wave trace formula for Dirac resonances at spectrum edges and applications
Version 2 2023-06-07, 08:57
Version 1 2023-06-07, 07:50
journal contribution
posted on 2023-06-07, 08:57 authored by Bobby Cheng, Michael MelgaardMichael MelgaardWe study the self-adjoint Dirac operators D = D0 + V (x), where D0 is the free three-dimensional Dirac operator and V (x) is a smooth compactly supported Hermitian matrix potential. We define resonances of D as poles of the meromorphic continuation of its cut-off resolvent. By analyzing the resolvent behaviour at the spectrum edges ±m, we establish a generalized Birman-Krein formula, taking into account possible resonances at ±m. As an application of the new Birman-Krein formula we establish the Poisson wave trace formula in its full generality. The Poisson wave trace formula links the resonances with the trace of the difference of the wave groups. The Poisson wave trace formula, in conjunction with asymptotics of the scattering phase, allows us to prove that, under certain natural assumptions on V , the perturbed Dirac operator has infinitely many resonances; a result similar in nature to Melrose’s classic 1995 result for Schr¨odinger operators.
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Publication status
- Published
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- Published version
Journal
Asian Journal of MathematicsISSN
1093-6106Publisher
International PressExternal DOI
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2Volume
25Page range
243-276Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2020-09-01First Open Access (FOA) Date
2021-11-02First Compliant Deposit (FCD) Date
2020-08-30Usage metrics
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