Unveiling the significance of eigenvectors in diffusing non-Hermitian matrices by identifying the underlying Burgers dynamics

@article{Burda2015UnveilingTS,
  title={Unveiling the significance of eigenvectors in diffusing non-Hermitian matrices by identifying the underlying Burgers dynamics},
  author={Z. Burda and J. Grela and M. Nowak and W. Tarnowski and Piotr Warchol},
  journal={Nuclear Physics},
  year={2015},
  volume={897},
  pages={421-447}
}
  • Z. Burda, J. Grela, +2 authors Piotr Warchol
  • Published 2015
  • Physics, Mathematics
  • Nuclear Physics
  • Abstract Following our recent letter [1] , we study in detail an entry-wise diffusion of non-hermitian complex matrices. We obtain an exact partial differential equation (valid for any matrix size N and arbitrary initial conditions) for evolution of the averaged extended characteristic polynomial. The logarithm of this polynomial has an interpretation of a potential which generates a Burgers dynamics in quaternionic space. The dynamics of the ensemble in the large N limit is completely… CONTINUE READING
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