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SUMMARY:Spectrum and propagation in electric quantum walks. - Werner\, R (
 Leibniz University Hannover)
DTSTART:20131107T140000Z
DTEND:20131107T150000Z
UID:TALK48735@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:(joint work with A.H. Werner\, C. Cedzich\, D. Meschede\, A. A
 lberti\, T. Rybar. \nSee arXiv:1302.2094 and  arXiv:1302.2081\, resp. PRL 
 111\, 160601 and  110\, 190601)\n\nI present a very simple quantum system\
 , whose long time behavior depends extremely sensitively on a parameter E.
  \n(1) For rational E one sees some revivals (exponentially sharp in the d
 enominator of E) followed ultimately by ballistic expansion. (2) For typic
 al E (Lebesgue- almost all) one has localization with exponentially locali
 zed eigenfunctions\, but there is also (3) a dense set of E for which one 
 has hierarchical motion: An infinite hierarchy of time scales on each of w
 hich one has sharper and sharper revivals (with a repetition of everything
  before that)  followed by larger and larger recursions. The spectrum of t
 he walk operator is absolutely continuous\, pure point\, and singular cont
 inuous in these three cases. We also explain how on a fixed finite time sc
 ale these distinctions become irrelevant and it is enough to know an appro
 priate initial segment of the continued fraction expansion of E. \n\n
LOCATION:Seminar Room 1\, Newton Institute
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