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CATEGORIES:CQIF Seminar
SUMMARY:A system equilibrates if diagonalizing its hamilto
nian is difficult - Lluis Masanes (ICFO)
DTSTART;TZID=Europe/London:20110609T141500
DTEND;TZID=Europe/London:20110609T151500
UID:TALK31358AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/31358
DESCRIPTION:In classical mechanics there is a relation between
\nintegrability and equilibration\, but this is no
t well understood in the quantum case. Closed quan
tum systems never equilibrate to a stationary stat
e. However\, in some circumstances\, the system eq
uilibrates locally (the reduced density matrix of
a subsystem evolves to a stationary state). All fi
nite-dimensional quantum systems are integrable\,
in the sense that solving its dynamics reduces to
diagonalizing its hamiltonian. This procedure may
need a large computational effort\, which differs
from system to system. In some sense\, the lack of
integrability of a quantum system can be quantifi
ed by the computational complexity of diagonalizin
g its hamiltonian. We show that\, if this complexi
ty is at least quadratic with the size of the syst
em then local equilibration holds (for almost all
hamiltonians)\; and if this complexity is sub-quad
ratic then local equilibration does not hold.
LOCATION:MR2\, Centre for Mathematical Sciences
CONTACT:Ashley Montanaro
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