Discrete Hessians in study of Quantum Statistical Systems: Complex Ginibre Ensemble

Details Discrete Hessians in study of Quantum Statistical Systems: Complex Ginibre Ensemble Discrete Hessians in study of Quantum Statistical Systems: Complex Ginibre Ensemble

2002-12-18

arxiv.org/abs/cond-mat/0212453v2

Physics

Condensed Matter

Statistical Mechanics

6 pages; "QP-PQ: Quantum Probability and White Noise Analysis - Volume 13, Foundations of Probability and Physics, Proceedings

Scientific paper

The Ginibre ensemble of nonhermitean random Hamiltonian matrices $K$ is considered. Each quantum system described by $K$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. The second difference of complex eigenenergies is viewed as discrete analog of Hessian with respect to labelling index. The results are considered in view of Wigner and Dyson's electrostatic analogy. An extension of space of dynamics of random magnitudes is performed by introduction of discrete space of labeling indices.

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