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SUMMARY:A system equilibrates if diagonalizing its hamiltonian is difficul
 t - Lluis Masanes (ICFO)
DTSTART:20110609T131500Z
DTEND:20110609T141500Z
UID:TALK31358@talks.cam.ac.uk
CONTACT:Ashley Montanaro
DESCRIPTION:In classical mechanics there is a relation between\nintegrabil
 ity and equilibration\, but this is not well understood in the quantum cas
 e. Closed quantum systems never equilibrate to a stationary state. However
 \, in some circumstances\, the system equilibrates locally (the reduced de
 nsity matrix of a subsystem evolves to a stationary state). All finite-dim
 ensional quantum systems are integrable\, in the sense that solving its dy
 namics 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 quantified b
 y the computational complexity of diagonalizing its hamiltonian. We show t
 hat\, if this complexity is at least quadratic with the size of the system
  then local equilibration holds (for almost all hamiltonians)\; and if thi
 s complexity is sub-quadratic then local equilibration does not hold.
LOCATION:MR2\, Centre for Mathematical Sciences
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