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CATEGORIES:CQIF Seminar
SUMMARY:Bulk-edge correspondence of one-dimensional quantu
m walks - Reinhard Werner (Leibniz Universität Han
nover)
DTSTART;TZID=Europe/London:20150319T141500
DTEND;TZID=Europe/London:20150319T151500
UID:TALK58449AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/58449
DESCRIPTION:We provide a classification of one-dimensional qua
ntum walks which satisfy a symmetry condition with
respect to some sitewise unitary or antiunitary r
eflections\, and also have a spectral gap up to ei
genvalues of finite multiplicity. No translation i
nvariance whatsoever is assumed. The classificati
on is stable under arbitrary local perturbations a
nd 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 th
e behavior of the walk far to the right and far to
the left\, respectively. Their sum is a lower bou
nd to the combined multiplicities of the eigenspac
es at 1 and -1 respectively. For translation invar
iant walks this classification is the same as the
K-theoretic classification of band projections ove
r the quasi-momentum torus. Therefore we confirm t
he predictions in the heuristic literature that wh
en joining two walks in different topological phas
es (here: with different index) a bound state at +
-1 will necessarily appear.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge
CONTACT:William Matthews
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