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CATEGORIES:Theory of Condensed Matter
SUMMARY:Delocalised atoms and electrons in quasi-periodic
lattices\, their edge modes and interactions with
heavy impurities - Dr Manuel Valiente\, Heriot-Wat
t University
DTSTART;TZID=Europe/London:20180301T141500
DTEND;TZID=Europe/London:20180301T151500
UID:TALK101911AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/101911
DESCRIPTION:The problem of quantum particles in periodic poten
tials is one of the pillars of modern condensed ma
tter physics. For some years now\, atoms can be pr
epared in optical lattices\, and even light in pho
tonic lattices can emulate quantum physics in peri
odic media under certain conditions. In this case\
, the single particle problem in the infinite size
limit is solved by Bloch's theorem as a consequen
ce of discrete\, rather than continuous translatio
n symmetry. Even for finite and semi-infinite latt
ices\, Bloch's theorem is easily adapted for bulk
states\, while its extension to complex quasi-mome
nta may be utilised to extract topological edge mo
des when the system has non-trivial topology -- an
d these states have very unique properties. \nThe
situation drastically changes if the particles mov
e in a superposition of periodic potentials whose
periods are incommensurate with each other\, i.e.
when their ratio is an irrational number: (i) Sinc
e periodicity is lost\, Bloch's theorem does not a
pply\; (ii) energy bands cannot be defined\, so on
e cannot in principle decide whether states with e
nergies lying within spectral gaps (in the semi-in
finite limit) are topological edge modes\; (iii) t
he system is inhomogeneous and therefore it is unc
lear whether particle-particle or even potential s
cattering can happen at all\; (iv) there are gener
ally localised and delocalised phases and regions
of the spectrum depending. In this talk\, I will c
onsider and give a solution to points (i) to (iii)
above in the tight-binding approximation and in t
he delocalised phase. The results I will present a
re fully general\, but will use as an illustration
Harper's or Hofstadter's model.
LOCATION:TCM Seminar Room\, Cavendish Laboratory
CONTACT:
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