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SUMMARY:Bulk-edge correspondence of one-dimensional quantum walks - Reinha
 rd Werner (Leibniz Universität Hannover)
DTSTART:20150319T141500Z
DTEND:20150319T151500Z
UID:TALK58449@talks.cam.ac.uk
CONTACT:William Matthews
DESCRIPTION:We provide a classification of one-dimensional quantum walks w
 hich satisfy a symmetry condition with respect to some sitewise unitary or
  antiunitary reflections\, and also have a spectral gap up to eigenvalues 
 of finite multiplicity. No translation invariance whatsoever is assumed.  
 The classification is stable under arbitrary local perturbations and is in
  terms of two indices whose range (either the integers or the integers mod
  2) depend on the symmetry type. The indices can be computed from the beha
 vior of the walk far to the right and far to the left\, respectively. Thei
 r sum is a lower bound to the combined multiplicities of the eigenspaces a
 t 1 and -1 respectively. For translation invariant walks this classificati
 on is the same as the K-theoretic classification of band projections over 
 the quasi-momentum torus. Therefore we confirm the predictions in the heur
 istic literature that when joining two walks in different topological phas
 es (here: with different index) a bound state at +-1 will necessarily appe
 ar.
LOCATION:MR4\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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