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SUMMARY:Stable and unstable equilibrium points in the quantum Gaudin model
  - Dr Benoit Doucot\, CNRS / LPTHE Jussieu\, France
DTSTART:20130530T131500Z
DTEND:20130530T141500Z
UID:TALK44374@talks.cam.ac.uk
CONTACT:Dr G Moller
DESCRIPTION:The Gaudin model consists of a collection of spins interacting
  with a single oscillator. It is of physical interest in many fields such 
 as quantum optics or cold atomic gases. Besides\, it is known to be integr
 able in both its classical and quantum-mechanical versions.\nWe will focus
 s on the behavior of this model system in the vicinity of stable and unsta
 ble equilibrium points. We show that\nthe latter present a topological obs
 truction (called monodromy)\nto the existence of action-angle coordinates\
 nin any phase-space neighbourhood containing them. At the quantum level\,\
 nthis phenomenon is reflected by the presence of a dislocation in the\nlat
 tice of joint eigenvalues of the mutually commuting Hamiltonians.\nIt also
  induces a non-trivial braiding of the roots of the Bethe-Ansatz equations
  in the complex plane\, if these joint eigenvalues are varied along a clos
 ed path encircling the critical value.\nThis shows that\, even in an integ
 rable system\, the notion of a global "quantum number" can be problematic.
LOCATION:TCM Seminar Room\, Cavendish Laboratory
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