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CATEGORIES:Wednesday HEP-GR Colloquium
SUMMARY:From AdS to BEC (dynamics in spatially confined Ha
miltonian systems) - Piotr Bizon\, Jagiellonian Un
iversity
DTSTART;TZID=Europe/London:20180307T141500
DTEND;TZID=Europe/London:20180307T151500
UID:TALK97261AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/97261
DESCRIPTION: The long-time behavior of nonlinear dispersive wa
ves subject to spatial confinement can be very ric
h and complex because\, in contrast to unbounded d
omains\, waves cannot escape to infinity and keep
self-interacting for all times. If\, in addition\,
the linear spectrum around the ground state is fu
lly resonant\, then the nonlinearity can produce s
ignificant effects for arbitrarily small perturbat
ions. The weak field dynamics of such systems can
be approximated by solutions of the corresponding
infinite-dimensional time-averaged Hamiltonian sys
tems which govern resonant interactions between th
e modes. A major mathematical challenge in this co
ntext is to describe the energy transfer between t
he modes. I will discuss this problem for several
spatially confined systems: a cubic wave equation
on the 3-sphere\, the Einstein-scalar system with
negative cosmological constant (modeling the weak
ly turbulent behavior of small perturbations of th
e anti-de Sitter spacetime)\, the nonlinear Schroe
dinger equation with a trapping potential (modelin
g the dynamics of a Bose-Einstein condensate)\, a
nd the Schroedinger-Newton-Hooke system describing
a harmonically trapped self-gravitating condensat
e. Some intriguing parallels between these system
s will be emphasized.
LOCATION:MR2\, Centre for Mathematical Sciences
CONTACT:David Marsh
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