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arXiv · 1206.5748

The origin of order in random matrices with symmetries

Calvin W. Johnson
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Abstract

From Noether's theorem we know symmetries lead to conservation laws. What is left to nature is the ordering of conserved quantities; for example, the quantum numbers of the ground state. In physical systems the ground state is generally associated with `low' quantum numbers and symmetric, low-dimensional irreps, but there is no \textit{a priori} reason to expect this. By constructing random matrices with nontrivial point-group symmetries, I find the ground state is always dominated by extremal low-dimensional irreps. Going further, I suggest this explains the dominance of J=0 g.s. even for random two-body interactions.

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Calvin W. Johnson. 2012-06-25. The origin of order in random matrices with symmetries. https://doi.org/10.1063/1.4759388

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