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Abstract: We consider a class of graphs describing a system of N particles with r prescribed energy levels that interact through pair "collisions" in which they exchange energies. In the mathemtical physics problem associated to this model, the spectral gap of the graph Laplacian on the connected components is of interest. We present a simple method for determining the exact spectral gaps in all cases, and all of the gap eigenfunctions. The method also yields some additional information on the spectrum. We discuss some conjectures supported by Maple computations. This is joint work with Michael Loss.

Zoom link: https://rutgers.zoom.us/j/94346444480
password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420