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Nuclear Physics B
We formulate and study a class of U(N)-invariant quantum mechanical models of large normal matrices with arbitrary rotation-invariant matrix potentials. We concentrate on the U(N) singlet sector of these models. In the particular case of quadratic matrix potential, the singlet sector can be mapped by a similarity transformation onto the two-dimensional Calogero-Marchioro-Sutherland model at specific couplings. For this quadratic case we were able to solve the $N-$body Schr\"odinger equation anddoi:10.1016/j.nuclphysb.2004.10.060 fatcat:wiaqbydnlrdbta5bxim73mb6r4