An example of dissipative quantum system: finite differences for complex Ginibre ensemble

الأصل · EN

The Ginibre ensemble of complex random Hamiltonian matrices H is considered. Each quantum system described by H is a dissipative system and the eigenenergies Zᵢ of the Hamiltonian are complex-valued random variables. For generic N-dimensional Ginibre ensemble analytical formula for distribution of second difference Δ¹ Zᵢ of complex eigenenergies is presented. The distributions of real and imaginary parts of Δ¹ Zᵢ and also of its modulus and phase are provided for N=3. The results are considered in view of Wigner and Dyson's electrostatic analogy. General law of homogenization of eigenergies for different random matrix ensembles is formulated.