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SUMMARY:Stability of local quantum dissipative systems - Angelo Lucia (Uni
 versidad Complutense de Madrid)
DTSTART:20130510T110000Z
DTEND:20130510T120000Z
UID:TALK45179@talks.cam.ac.uk
CONTACT:William Matthews
DESCRIPTION:Open quantum systems weakly coupled to the environment are mod
 elled by completely positive\, trace preserving semigroups of linear maps.
  The generators of such evolutions are called Liouvillians\, and similarly
  to the Hamiltonian in the case of coherent evolution\, they encode the ph
 ysical properties of the system. In the setting of quantum many-body syste
 ms on a lattice it is natural to consider local or exponentially decaying 
 interactions.\n\nFor theoretical and experimental reasons\, it is importan
 t to estimate the sensitivity of the system agains small perturbations\, c
 oming from numerical errors or physical noise.\nWe prove that local observ
 ables and correlation functions are stable under local and quasi- local pe
 rturbations if the Liouvillian is frustration free\, translational invaria
 nt (uniformly)\, has a unique fix point (with no restriction on its rank) 
 and has a mixing time which scales logarithmically with the system size. T
 hese conditions can be relaxed to the non-translational invariant case\, a
 t the cost of requiring Local Topological Quantum Order.\n\nAs a main exam
 ple we prove that classical Glauber dynamics is stable under local perturb
 ations\, including perturbations in the transition rates which do not pres
 erve detailed balance. To our knowledge\, this result is new even classica
 lly.
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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