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

explicitlydemonstratestheexistenceofsuchatransitioninaphysicallyrealisticsystemisnotyetavailable.Thus,the‘thermodynamicglasstransition’scenarioremainsessentiallyspeculative.Inthisapproach,thegrowthoftherelaxationtimeisattributedtoagrowingcorrelationlengthwhichwoulddivergeattheidealglasstransition.Tworecentnumericalstudies25,26whichlookedforsuchagrowingcorrelationlengthdidnot ndanyevidence

27foritsexistence.Arecentexperiment,ontheotherhand,haspresentedevidencefor

theexistenceofalengthscalethatgrowsasthetemperatureisloweredbelowthecrossovertemperatureTc.

Thestaticanddynamicpropertiesofdenseliquidshavealsobeenstudiedexten-sivelybymoleculardynamics(MD)simulations28 32.Theverynatureofthesimulationmethodrestrictssuchstudiestosimplemodelsystemsandtotimescaleswhicharerathershort(oftheorderof10 9sec).Inspiteoftheselimitations,MDsimulationshavepro-ducedanumberofinterestingresultswhichareinqualitativeagreementwithpredictionsofMCtheoriesandresultsofexperiments(suchasthoseusingtheneutronspin-echotech-nique33)whichhavetimescalescomparabletothoseofthesimulations.Thisobservationleadstotheinterestingandusefulconclusionthatastudyofsimplemodelsystemsmaybesu cientforunderstandingthebasicphysicsoftheglasstransition.

Itisevidentfromthisbriefsurveyofthecurrentstatusoftheglasstransitionproblemthatanobviousneedexistsforthedevelopmentofnewanalyticandnumericalmethodswhichmayaddresssomeoftheoutstandingissuesrelatedtothisproblem.Inthispaper,wedescribetheresultsobtainedfromtheapplicationofanewnumericalmethodtoastudyofthedynamicbehaviorofadensehard-sphereliquidneartheglasstransition.ThemethodweuseconsistsofdirectnumericalintegrationofasetofLangevinequationswhichdescribethenonlinear uctuatinghydrodynamics(NFH)

rmation