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SUMMARY:Topology in shallow-water waves: A violation of bulk-edge correspo
 ndence
DTSTART:20211119T141500
DTSTAMP:20260502T044722Z
UID:38b48d47cf2cbb8d33ac98a0109d58a2873a9f0724c786ae93d0594f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof.  Gian Michele  GRAF  (ETH - CH)\nAbstract:\n\nTopolog
 ical matter in seen to enjoy a remarkable duality\, no matter the specific
  instance or model being considered\, namely bulk-edge correspondence: The
  homotopy class characterizing the extended material is reflected in a mat
 ching property of the excitations running along its boundary. After review
 ing the correspondence\, we will address a counterexample. A two-dimension
 al rotating shallow-water model describes a layer of water\, in guise of o
 ceans covering the Earth. Its mathematical description parallels that of a
  band insulator\, except for the energy range of a band being unbounded. O
 nce regularized at small scale by an odd-viscous term\, such a model has a
  well-defined bulk topological index. However\, in presence of a sharp bou
 ndary\, the number of edge modes depends on the boundary condition\, showi
 ng an explicit violation of the bulk-edg correspondence. We study a contin
 uous family of boundary conditions with a varied phase diagram\, and expla
 in the origin of this mismatch. Our approach relies on scattering theory a
 nd Levinson’s theorem. The latter does not apply at infinite momentum be
 cause of the analytic structure of the scattering amplitude there\, which 
 is ultimately the reason for the violation.\n(Joint work with H. Jud and C
 . Tauber.)\n 
LOCATION:MA B1 11 https://plan.epfl.ch/?room==MA%20B1%2011
STATUS:CONFIRMED
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