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

Maciej M. Duras
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Abstract

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.

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Maciej M. Duras. 2003-07-02. An example of dissipative quantum system: finite differences for complex Ginibre ensemble. https://arxiv.org/abs/cond-mat/0301603

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