简介:WeconstructaclassofintegrablegeneralizationofTodamechanicswithlong-rangeinteractions.ThesesystemsareassociatedwiththeloopalgebrasL(Cr)andL(Dr)inthesensethattheirLaxmatricescanberealizedintermsofthec=0representationsoftheaffineLiealgebrasCr(1)andDr(1)andtheinteractionspatterninvolvedbearsthetypicalcharactersofthecorrespondingrootsystems.WepresenttheequationsofmotionandtheHamiltonianstructure.Thesegeneralizedsystemscanbeidentifiedunambiguouslybyspecifyingtheunderlyingloopalgebratogetherwithanorderedpairofintegers(n,m).Itturnsoutthatdifferentsystemsassociatedwiththesameunderlyingloopalgebrabutwithdifferentpairsofintegers(n1,m1)and(n2,m2)withn2<n1andm2<m1canberelatedbyanestedHamiltonianreductionprocedure.Forallnontrivialgeneralizations,theextracoordinatesbesidesthestandardTodavariablesarePoissonnon-commute,andwheneithernorm≥3,thePoissonstructurefortheextracoordinatevariablesbecomessomeLiealgebra(i.e.theextravariablesappearlinearlyontheright-handsideofthePoissonbrackets).Inthequantumcase,suchgeneralizationswillbecomesystemswithnoncommutativevariableswithoutspoilingtheintegrability.
简介:Anon-linearoptical(NLO)materialwassynthesizedbymeansofasimplemethod.Thismaterialcanbeappliedinelectro-optical(EO)devices,suchasEOswitchesandmodulators.TheDisperseRed1(DR1)wasdopedinpolymethyl-methacrylate-co-glycidylmethacrylate(PMMA-co-GMA)astheNLOactivechromophore.Thesynthesisprocessandmaterialstructurewereexpressed.Thethermalproperties,surfacemorphologyandopticalcharacteristicsofthematerialwereinvestigatedbymeansofdifferentialscanningcalorimetry(DSC),thermogravimetricanalysis(TGA),atomicforcemicroscopy(AFM),andm-linestechnique.Usingthereflectiontechnique,thevalueoftheelectro-opticalcoefficientγ33wasmeasuredas11pm/Vatawavelengthof1310nm.AnEOswitchwithnanosecondresponsebasedonthismaterialhasbeenfabricated.