Symmetry Decomposition of Potentials with Channels

Details Symmetry Decomposition of Potentials with Channels Symmetry Decomposition of Potentials with Channels

1996-09-10

arxiv.org/abs/chao-dyn/9609004v1

J.Phys.A vol.30, 533 (1997).

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1088/0305-4470/30/2/018

We discuss the symmetry decomposition of the average density of states for the two dimensional potential $V=x^2y^2$ and its three dimensional generalisation $V=x^2y^2+y^2z^2+z^2x^2$. In both problems, the energetically accessible phase space is non-compact due to the existence of infinite channels along the axes. It is known that in two dimensions the phase space volume is infinite in these channels thus yielding non-standard forms for the average density of states. Here we show that the channels also result in the symmetry decomposition having a much stronger effect than in potentials without channels, leading to terms which are essentially leading order. We verify these results numerically and also observe a peculiar numerical effect which we associate with the channels. In three dimensions, the volume of phase space is finite and the symmetry decomposition follows more closely that for generic potentials --- however there are still non-generic effects related to some of the group elements.

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