Mathematics – Differential Geometry
Scientific paper
Apr 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007aipc..899...69p&link_type=abstract
SIXTH INTERNATIONAL CONFERENCE OF THE BALKAN PHYSICAL UNION. AIP Conference Proceedings, Volume 899, pp. 69-72 (2007).
Mathematics
Differential Geometry
Geometry, Differential Geometry, And Topology, Broken Symmetry Phases, Potential Energy Surfaces
Scientific paper
The important differences between the behavior of bulk matter and small systems with respect to their phases and phase changes keep the interest in the subject vivid. On the other hand, small systems display forms that have properties very similar to those we associate with specific phases of bulk matter. Thus various theoretical approaches are needed to understand both similarities and differences. One way is to study the topology of the configuration space of a small system, like atomic clusters, through the critical points of the multidimensional potential energy surface generated by bound model potentials. The dynamics of the system can be linked to the topology by master equations: a phase transition occurs if the topology of the configuration space of a cluster changes. The effective order of phase changes of small systems can be related directly to what kind of symmetry change occurs at the phase change.
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