Quantum symmetrical statistical system: Ginibre-Girko ensemble

Details Quantum symmetrical statistical system: Ginibre-Girko ensemble Quantum symmetrical statistical system: Ginibre-Girko ensemble

2003-01-30

arxiv.org/abs/cond-mat/0301605v2

Physics

Condensed Matter

Statistical Mechanics

4 pages; presented at poster session of the conference "The 32nd Symposium on Mathematical Physics (SMP 32)"; June 6th, 2000 t

Scientific paper

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 $\Delta^{1} Z_{i}$ of complex eigenenergies is presented. The distributions of real and imaginary parts of $\Delta^{1} Z_{i}$ 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.

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