Application of hermitean and nonhermitean random matrices to quantum statistical systems

Abstract

The Ginibre ensemble of nonhermitean random Hamiltonian matrices $K$ is considered. Each quantum system described by $K$ is a dissipative system and the eigenenergies $Z_i$ of the Hamiltonian are complex-valued random variables. The second difference of complex eigenenergies is viewed as discrete analog of Hessian with respect to labelling index. The results are considered in view of Wigner and Dyson's electrostatic analogy. An extension of space of dynamics of random magnitudes is performed by introduction of discrete space of labeling indices. The comparison with the Gaussian ensembles of random hermitean Hamiltonian matrices $H$ is performed.

arXiv comment5 pages; presented as a poster at "Coherent Evolution in Noisy Environments"; Workshop: May 21th, 2001- May 25th, 2001; Seminar: April 2nd, 2001 - May 30th, 2001; Max Planck Institute for the Physics of Complex Systems, Dresden, Germany