Universität Augsburg

Dr. Leonard Kreutz
Universität Wien
spricht am
Donnerstag, 13. Dezember 2018
um
17:30 Uhr
im
Raum 2004 (L1)
über das Thema:
Abstract: 
In this talk we will present some crystallization results of ionic dimers. In partic ular we consider nite discrete systems consisting of two dierent atomic types and investigate groundstate congurations for congurational energies featuring two body shortranged particle interactions. The atomic potentials favor some reference distance between dierent atomic types and include repulsive terms for atoms of the same type, which are typical assumptions in models for ionic dimers. Our goal is to show a twodimensional crystallization result. More precisely, we give conditions in order to prove that energy minimizers are connected subsets of the hexagonal lattice where the two atomic types are alternately arranged in the crystal lattice. We also provide explicit formulas for the groundstate energy. Finally, we charac terize the net charge, that means, the dierence of the number of the two atomic types. Analyzing the deviation of congurations from the hexagonal Wul shape, we prove that for ground states consisting of n particles the net charge is at most of order O(n ^{1/4}) where the scaling is sharp. 
Hierzu ergeht herzliche Einladung. 
Prof. Dr. Bernd Schmidt 
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2004 (L1).