Contents - Max-Planck-Institut für Physik komplexer Systeme
Contents - Max-Planck-Institut für Physik komplexer Systeme
Contents - Max-Planck-Institut für Physik komplexer Systeme
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architectures.TogetherwithdevelopersfromtheMPGcomputingcenterinGarchingweareworkingon<br />
thischallengingproject,withtheaimtopushthelimitsofaccessiblesystemsizefromcurrently42spins<br />
topossibly48or50quantumspinsinthefuture.<br />
Cooperations<br />
• Theorygroups<br />
– Lausanne,ÉcolePolytechniqueFédéraledeLausanne,collaborationwiththegroupofF.Mila<br />
ontopicsinfrustratedquantummagnetism.<br />
– Palaiseau,ÉcolePolytechnique,collaborationwithC.Kollathonnonequilibriumpropertiesof<br />
stronglycorrelatedsystems.<br />
– Zürich,ETHZürich,collaborationwithP.WerneronalgorithmicaspectsofDMFTsolvers.<br />
– Toulouse,LaboratoiredePhysiqueThéorique,collaborationwithS.CapponiandM.Mambrini<br />
ontopicsinfrustratedquantummagnetism.<br />
– Dortmund,TUDortmund,collaborationwiththegroupofK.P.Schmidtonmagneticsystems<br />
closetotheMotttransition.<br />
– Dresden, MPI-CPfS,collaborationwiththegroupofH.Rosneronab-initiomodelingof<br />
magneticinsulators.<br />
• Experimentalgroups<br />
– CollaborationswithneutronscatteringgroupattheUniversityCollegeLondon(Ch.Rüegg)<br />
onthemodelingandinterpretationofinelasticneutronscatteringexperimentsperformedon<br />
low-dimensionalquantummagnets.<br />
– Dresden,MPI-CPfS,collaborationwiththegroupofH.Rosnerontheexperimentalcharacterizationofmagneticinsulators.<br />
ResearchGroup:NonlinearTimeSeriesAnalysis<br />
(Head:Prof.Dr.H.Kantz)<br />
Thisgroupwasestablishedin1995witharesearchprogrammeinnonlineardynamicsandtimeseries<br />
analysis.Overtheyearsthefocushasshifted.Timeseriesanalysisisnowadaysonlypartofouractivities,<br />
withparticularemphasisonpredictions.Themainguidelineforusistheaimtounderstand,model,and<br />
predictfluctuationsinopen,i.e.,drivensystems. Thiscomprisesresearchinnon-equilibriumstatistical<br />
physics,low-andhigh-dimensionaldynamicalsystems,nonlinearstochasticprocesses,andinmodels<br />
oftheatmosphere. Moreprecisely,inthesesettingsweaimforanunderstandingofthemagnitude<br />
distributionsandtemporal(andspatial,whereapplicable)correlationsoffluctuations,andofthedetails<br />
ofthemechanismsbehind. Particularmotivationarisesfromthestudyofextremeevents,whichoften<br />
occurasnaturaldisastersandthenhavelargeimpactonhumancivilization. Extremeeventsindriven<br />
systemsareverylargebutrarefluctuations,wherefirstofalldynamicalmechanisms(feedbackloops)<br />
existwhichdrivethesystemsofaroffitsnormalstate,butwheresecondlythefrequencyandmagnitude<br />
ofsuchexcursionsinphasespaceareconstrainedbyphysicalconservationlaws.<br />
Non-equilibriumfluctuationtheorems. Forthermodynamicsystemsoutofequilibrium,anumberof<br />
strictrelationsforratiosofprobabilitiesoffluctuationsareknownasfluctuationtheorems. Onemodel<br />
wherewestudytheseisthefluctuatinglatticeBoltzmannmodel,akinematicmodelforaviscousgas<br />
incontactwithaheatbath. Inthethermodynamiclimit, itsdynamicsisequivalenttotheoneof<br />
theNavier-Stokesequations. Forsmallsystemsize,onecanstudynon-equilibriumfluctuationsand<br />
verifiesthevalidityoftheoremssuchasCrooksorJarzynski. Throughthetheoremsonecanprobe<br />
whichsystemparameterscorrespondtothethermodynamictemperature. Anotherinterestingfeature<br />
isthatnon-equilibrium-fluctuationsinthismodelareequivalenttoequilibriumfluctuations,i.e.,they<br />
arethermalfluctuationsduetoexchangeofenergywiththeheatbath. Thisisnotageneralfeature,<br />
sincemacroscopicdynamicalinstabilitieswouldcreateverydifferentfluctuations. Itisthereforean<br />
interestingissuetounderstandunderwhichconditionsnon-equilibriumfluctuationsareexclusivelyheat<br />
bathfluctuations.<br />
1.8. DepartmentsandResearchGroups 21