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CATEGORIES:CQIF Seminar
SUMMARY:Stability of local quantum dissipative systems - A
ngelo Lucia (Universidad Complutense de Madrid)
DTSTART;TZID=Europe/London:20130510T120000
DTEND;TZID=Europe/London:20130510T130000
UID:TALK45179AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/45179
DESCRIPTION:Open quantum systems weakly coupled to the environ
ment are modelled by completely positive\, trace p
reserving semigroups of linear maps. The generator
s of such evolutions are called Liouvillians\, and
similarly to the Hamiltonian in the case of coher
ent evolution\, they encode the physical propertie
s of the system. In the setting of quantum many-bo
dy systems on a lattice it is natural to consider
local or exponentially decaying interactions.\n\nF
or theoretical and experimental reasons\, it is im
portant to estimate the sensitivity of the system
agains small perturbations\, coming from numerical
errors or physical noise.\nWe prove that local ob
servables and correlation functions are stable und
er local and quasi- local perturbations if the Lio
uvillian is frustration free\, translational invar
iant (uniformly)\, has a unique fix point (with no
restriction on its rank) and has a mixing time wh
ich scales logarithmically with the system size. T
hese conditions can be relaxed to the non-translat
ional invariant case\, at the cost of requiring Lo
cal Topological Quantum Order.\n\nAs a main exampl
e we prove that classical Glauber dynamics is stab
le under local perturbations\, including perturbat
ions in the transition rates which do not preserve
detailed balance. To our knowledge\, this result
is new even classically.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:William Matthews
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