Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glas(4)

We conduct a numerical study of the dynamic behavior of a dense hard sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free energy functional of the Ramakrishnan-Yussouff form. We find that th

uncoveredacuto mechanismwhichissupposedtoroundo thepredicteddivergenceandtorestoreergodicityoveramuchlongertimescale.MostoftheexistingMCstudiesoftheglasstransitiondonottakeintoaccounttheequilibriumshort-rangestructureofthedenseliquid.Asaresult,thesetheoriesdonotleadtoanypredictionforthewavenumberdependenceoftherelaxation.SomeattemptstowardstheincorporationofinformationaboutliquidstructureintheMCformalismhavebeenmaderecently8,10.MCtheories3,7andexperimentalinformationcanbecombinedinaconsistentdescriptionofthedecayofS(q,t),thespatialFouriertransformofthedynamicdensitycorrelationfunction,atsuf- cientlylowtemperaturesorhighdensities,whenthedecaytimeshavegrownverylarge.Thedecayaccordingtothisschemetakesplaceinasuccessionofseveralregimes:afterafastdecayintimesoforderoftheinversephononfrequency,a rstslowdecayoccurswhichMCtheoriespredicttobeaninversepowerlawintime.Thisiscalledtheβ-relaxationregime.Evidenceforpower-lawdecayofcorrelationsintheβregimeisprovidedbylight11andneutronscatteringexperiments12.Thisdecayistoanonzerovalue(anapparentnonergodicphase)fromwhichthesystemeventuallymovesawayleadingtotheprimaryorα-relaxationregime.Therelaxationintheαregimeisfoundtofollowtheso-calledKohlrausch-Williams-Watts‘stretchedexponential’form13.Boththedurationoftheβrelaxationandthetimescaleofthestretchedexponentialdecayintheαregimearefoundtoincreasesharplyasthe‘glasstransition’isapproached.Insomecases,theβandtheαregimesareseparatedbyaregionofso-calledvonSchweidlerrelaxationwhichhasapowerlawform.ThestretchedexponentialbehaviorintheαregimeandthevonSchweidlerrelaxationareseenindielectricmeasurements

scattering1614andinlight15andneutronexperiments.TheparameterswhichdescribethedecayofS(q,t)areknowntobeq-dependent,butthenatureofthisdependencehasnotbeenstudiedindetail.Thus,