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CATEGORIES:Theory of Condensed Matter
SUMMARY:Spectral statistics of chaotic many-body systems -
Sebastian MÃ¼ller\, University of Bristol
DTSTART;TZID=Europe/London:20160121T153000
DTEND;TZID=Europe/London:20160121T163000
UID:TALK61747AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61747
DESCRIPTION:We derive a trace formula that expresses the level
density of chaotic\nmany-body systems as a smooth
term plus a sum over contributions\nassociated to
solutions of the nonlinear Schroedinger equation.
Our\nformula applies to bosonic systems with disc
retised positions\, such as\nthe Bose-Hubbard mode
l\, in the semiclassical limit as well as in the\n
limit where the number of particles is taken to in
finity. We use the\ntrace formula to investigate t
he spectral statistics of these systems\,\nby stud
ying interference between solutions of the nonline
ar\nSchroedinger equation. We show that in the lim
its taken the statistics\nof fully chaotic many-pa
rticle systems becomes universal and agrees\nwith
predictions from the Wigner-Dyson ensembles of ran
dom matrix\ntheory. The conditions for Wigner-Dyso
n statistics involve a gap in\nthe spectrum of the
Frobenius-Perron operator\, leaving the possibili
ty\nof different statistics for systems with weake
r chaotic properties.\nThis is joint work with Rem
y Dubertrand.
LOCATION:TCM Seminar Room\, Cavendish Laboratory
CONTACT:Dr G Moller
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