Glass transition and glassy dynamics

(i) Microscopic theories for the glass transition

We have extended mode coupling theory for supercooled simple liquids to molecular ones. This allows to study the interplay between translational and orientational degrees of freedom. This extended theory has already been applied to a liquid of diatomic molecules, dipolar hard spheres and hard ellipsoids. The results demonstrate that both types of degrees of freedom can undergo a glass transition at, e.g. different densities , and that the glass transition by itself can be driven (e.g. for hard ellipsoids) by a precursor of an orientational order (e.g. nematic order for hard ellipsoids). Furthermore, we have found that the orientational-translation coupling can introduce in the dynamical structure factor an extra peak about a decade below a high-frequency peak. The features of this additional peak resemble some of these of the boson peak .

Our present activity in this field is two-fold. First, we apply mode coupling theory to hard ellipsoids on a simple cubic lattice. This type of system allows to model plastic crystals and to investigate their orientational glass transition. Second, if the diameter of the hard ellipsoids converges to zero, the static orientational correlators become trivial, i.e. they do not depend on the length of the rods. Since mode coupling theory needs as an input the static correlators, which drive the glass transition after an increase of density or decrease of temperature, this theory can not yield a glass transition for infinitely thin or even sufficiently thin hard rods on a lattice, although simulations have demonstrated the existence of such a transition. Recently, we have developed a microscopic theory which is based on a Smoluchowski-equation . Although this approach leads to an orientational glass transition, it has several drawbacks . To mention one: The glass transition turns out to be a continuous one, in contrast to the simulation result. The elimination of these drawbacks and the extension of present mode coupling theory to systems with no or weak static correlations is one of the great challenges for our future work.
 

2. Quantum Physics: Reduced Density Matrix Functional Theory

Reduced density matrix functional theory (an extension of density functional theory) uses that the ground state properties of a N particle quantum system can be obtained from minimizing a functional of the reduced one-particle density matrix.