- Main
Quotient Maps and Configuration Spaces of Hard Disks
Abstract
Hard disks systems are often considered as prototypes for simple fluids. In a statistical mechanics context, the hard disk configuration space is generally quotiented by the action of various symmetry groups. The changes in the topological and geometric properties of the configuration spaces effected by such quotient maps are studied for small numbers of disks on a square and hexagonal torus. A metric is defined on the configuration space and the various quotient spaces that respects the desired symmetries. This is used to construct explicit triangulations of the configuration spaces as $\alpha$-complexes. Critical points in a configuration space are associated with changes in the topology as a function of disk radius, are conjectured to be related to the configurational entropy of glassy systems, and could reveal the origins of phase transitions in other systems. The number and topological and geometric properties of the critical points are found to depend on the symmetries by which the configuration space is quotiented.
Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.
Main Content
Enter the password to open this PDF file:
-
-
-
-
-
-
-
-
-
-
-
-
-
-