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SUMMARY:Essential spectra and black hole modes for inhomogeneous\, anisotr
 opic dissipative Maxwell and Drude-Lorentz systems  - Marco Marletta (Ca
 rdiff University)
DTSTART:20230622T150000Z
DTEND:20230622T160000Z
UID:TALK202534@talks.cam.ac.uk
DESCRIPTION:The methods required to study spectral pollution for dissipati
 ve Maxwell and Drude-Lorentz systems turn out to be closely connected to t
 he methods required to study the essential spectrum for such systems and a
 re very different from the methods used for Schroedinger equations. The pr
 esence of dissipation\, &nbsp\;e.g. in the form of conductivity\, means th
 at the essential spectrum can be changed by changing the coefficients &nbs
 p\;in the system on any arbitrarily small\, non-empty open set. The proof 
 of this result consists of a reduction of &nbsp\;the system to a triangula
 r block operator matrix\, together with an analysis of quasi-modes associa
 ted with one of the diagonal blocks. In the case of conductivity discontin
 uous across an interface\, additional modes arise&nbsp\; whose rapid expon
 ential decay away from the interface makes them effectively invisible at a
  distance - hence the&nbsp\; name `black hole modes'. These modes have pre
 viously been observed by various authors for \\div(p \\grad) operators wit
 h sign-changing p\,&nbsp\;and may also occur in transmission eigenvalue pr
 oblems.\n&nbsp\;This talk describes joint work with various co-authors inc
 luding Giovanni Alberti\, Sabine Boegli\, &nbsp\;Francesco Ferraresso\, Ch
 ristiane Tretter\, Ian Wood and the late Malcolm Brown.
LOCATION:Seminar Room 1\, Newton Institute
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