Dresden 2000 – wissenschaftliches Programm
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MP: Theoretische und Mathematische Grundlagen der Physik
MP 4: Statistische Mechanik 1
MP 4.3: Vortrag
Montag, 20. März 2000, 17:00–17:15, W A317
Isospektrale Spinsysteme — •H.-J. Schmidt1 and M. Luban2 — 1Fachbereich Physik, Universität Osnabrück — 2Ames Laboratory and Department of Physics and Astronomy, Iowa State University
Isospectral Hamilton operators do not only occur in the context of Schrödinger operators and supersymmetry but also for spin systems. We consider N spin sites with spin s and Heisenberg coupling with arbitrary coupling constants Jij. It has been observed [1] that for N=3, s=1/2 there exist one-parameter families of isospectral Hamilton operators. To date we have found only one other example of an isospectral spin system, the case N = 4, s = 1/2, whereas we can exclude the cases N=3, s>1/2. These examples will be presented and analyzed. There exist interesting connections to computational algebraic geometry.
[1] S. Jun, M. Sc. thesis, Iowa State University, 1999. einmal