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Journal Article

Spectral statistics of the uni-modular ensemble


Weidenmüller,  Hans A.
Prof. Hans A. Weidenmüller, Emeriti, MPI for Nuclear Physics, Max Planck Society;

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Joyner, C. H., Smilansky, U., & Weidenmüller, H. A. (2017). Spectral statistics of the uni-modular ensemble. Journal of Physics A, 50(38): 385101. doi:10.1088/1751-8121/aa836a.

Cite as: https://hdl.handle.net/21.11116/0000-0000-FA5E-E
We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U(1), called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a supersymmetric integration method, a combinatorial graph-theoretical analysis and a Brownian motion approach, we are able to derive expressions for 1/N corrections to the mean spectral moments and also analyse the fluctuations about this mean. By addressing the same ensemble from three different point of view, we can critically compare their relative advantages and derive some new results.