The origin of order in random matrices with symmetries
arXiv:1206.5748 · doi:10.1063/1.4759388
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.
5 figures; contribution to "Beauty in Physics" conference in honor of Francesco Iachello, May 2012, Cocoyoc, Mexico