Ordering of Energy Levels in Heisenberg Models and Applications

Details Ordering of Energy Levels in Heisenberg Models and Applications Ordering of Energy Levels in Heisenberg Models and Applications

2005-03-23

arxiv.org/abs/math-ph/0503056v1

in J. Ash and A. Joye (Eds), Mathematical Physics of Quantum Mechanics, Selected and Refereed Lectures from QMath9, Lecture No

Physics

Mathematical Physics

20 pages, contribution for the proceedings of QMATH9, Giens, September 2004

Scientific paper

In a recent paper we conjectured that for ferromagnetic Heisenberg models the smallest eigenvalues in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin and called this property ferromagnetic ordering of energy levels (FOEL). We have proved this conjecture for the Heisenberg model with arbitrary spins and coupling constants on a chain. In this paper we give a pedagogical introduction to this result and also discuss some extensions and implications. The latter include the property that the relaxation time of symmetric simple exclusion processes on a graph for which FOEL can be proved, equals the relaxation time of a random walk on the same graph. This equality of relaxation times is known as Aldous' Conjecture.

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