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

aboutthestaticstructureoftheliquidisincorporatedintheLangevinequationsthroughafree-energyfunctionalwhichhasaformsuggestedbyRamakrishnanandYussou (RY).35Recently,ithasbeenshown36thattheRYfreeenergyfunctionalprovidesacorrectmean- elddescriptionofthestaticsoftheglasstransitioninthissystem.Inthatwork,anumericalprocedurewasusedtolocatelocalminimaofadiscretizedversionoftheRYfreeenergyappropriateforthehardspheresystem.Alargenumberofglassylocalminimawithinhomogeneousbutaperiodicdensitydistributionwerefoundtoappearastheaveragedensitywasincreasedabovethevalueatwhichequilibriumcrystallizationtakesplace.Athigherdensities,thefreeenergiesoftheseminimawerefoundtodropbelowthatoftheminimumrepresentingtheuniformliquidsignalingamean- eldglasstransition.ThesuccessoftheRYfreeenergyfunctionalinprovidingacorrectdescriptionofthestaticsoftheglasstransitionofthehardspheresystemsuggeststhatagoodstartingpointforastudyofthedynamicsofthissystemwouldbeobtainedbyincorporatingthisfreeenergyintheappropriateNFHequations.

Anumberofimportantissuesareaddressedinourstudyofthedynamics.BycomparingtheresultsofourcalculationswithexistingMDresults28onthesamesystem,weareabletotestthevalidityoftheNFHdescriptionwhichiscastintermsofcoarse-grainednumberandcurrentdensityvariablesinsteadofthecoordinatesandmomentaofindividualparticles.ThecorrectnessoftheNFHequationsweuse,althoughusuallytakenforgranted,isnotobviousinviewofthefactthatthehydrodynamictermsintheseequationsdescribethephysicsatrelativelylonglengthscales,whereasthetermsarisingfromthefreeenergyfunctionalinvolvelengthscalesoftheorderof(orsmallerthan)theinterparticlespacing.IntheRYfreeenergyfunctional,informationaboutthemicroscopicinteractionsisincorporatedintheformoftheOrnstein-Zernikedirectpaircorrelation