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STATISTICS OF COMPLEX DISSIPATIVE SYSTEMS ”Space Time Chaos: Characterization, Control and

A quantum statistical random system with energy dissipation is studied. Its statistics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble of random matrices. The eigenenergies of Hamiltoni-ans are shown to form stable structure. Analogy of Wigner and Dyson with system of electrical charges is drawn. A complex quantum system with energy dissipation is considered. The quantum Hamiltonians H belong the complex Ginibre ensemble. The complex-valued eigenenergies Z i are random variables. The second differences ∆ 1 Z i are also complex-valued random variables. The second differences have their real and imaginary parts and also radii (moduli) and main arguments (angles). For N =3 dimensional Ginibre ensemble the distributions of above random variables are provided whereas for generic N-dimensional Ginibre ensemble second difference's, radius's and angle's distributions are analytically calculated. The law of homogenization of eigenergies is formulated. The analogy of Wigner and Dyson of Coulomb gas of electric charges is studied. The stabilisation of system of electric charges is dealt with.