Dynamics of complex quantum systems with energy dissipation
Duras, Maciej M.
Original · EN
A complex quantum system with energy dissipation is considered. The quantum Hamiltonians H belong the complex Ginibre ensemble. The complex-valued eigenenergies Zᵢ are random variables. The second differences Δ¹ Zᵢ 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 distribution is analytically calculated. The law of homogenization of eigenergies is formulated. The analogy of Wigner and Dyson of Coulomb gas of electric charges is studied.
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