Dynamical van der Waals Model of Glassy Behavior

A model fluid system whose intermolecular forces consist of the short range part characterizing usual stable fluid and the long range part of Kac-type is considered. When the ratio of the force ranges is large enough, the system can be described by regarding the system having only short range interactions as a reference fluid treated as a continuum, on which long range forces acting among tiny fluid elements are superimposed. We discuss the glassy behavior of this model relating it to the mode coupling theory and using real replica theory. These theories lead to the two equations for non-ergodicity parameter which are totally different from each other. We argue that our model can be a basis for examining nature of the drastic approximations entering derivations of the mode coupling equations. We further explore the possibility of developing the dynamical real replica approach for our model system with the hope of providing a framework to cope with different time scales characterizing complex glassy behavior.