Multiplying unitary random matrices - universality and spectral properties

Details Multiplying unitary random matrices - universality and spectral properties Multiplying unitary random matrices - universality and spectral properties

2003-12-16

arxiv.org/abs/math-ph/0312043v1

Physics

Mathematical Physics

12 pages, 2 figures

Scientific paper

10.1088/0305-4470/37/25/007

In this paper we calculate, in the large N limit, the eigenvalue density of an infinite product of random unitary matrices, each of them generated by a random hermitian matrix. This is equivalent to solving unitary diffusion generated by a hamiltonian random in time. We find that the result is universal and depends only on the second moment of the generator of the stochastic evolution. We find indications of critical behavior (eigenvalue spacing scaling like $1/N^{3/4}$) close to $\theta=\pi$ for a specific critical evolution time $t_c$.

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