Quantum symmetrical statistical system: Ginibre-Girko ensemble
Abstract
Description
The Ginibre ensemble of complex random Hamiltonian matrices $H$ is considered. Each quantum system described by $H$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. For generic $N$-dimensional Ginibre ensemble analytical formula for distribution of second difference $Δ^{1} Z_{i}$ of complex eigenenergies is presented. The distributions of real and imaginary parts of $Δ^{1} Z_{i}$ 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.
4 pages; presented at poster session of the conference "The 32nd Symposium on Mathematical Physics (SMP 32)"; June 6th, 2000 to June 10th, 2000; Institute of Physics, Nicholas Copernicus University; Torun, Poland (2000)
4 pages; presented at poster session of the conference "The 32nd Symposium on Mathematical Physics (SMP 32)"; June 6th, 2000 to June 10th, 2000; Institute of Physics, Nicholas Copernicus University; Torun, Poland (2000)