Dresden 2000 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 4: Statistische Mechanik 1

MP 4.3: Talk

Monday, March 20, 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 J_ij. 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