Discrete Hessians in study of Quantum Statistical Systems: Complex Ginibre Ensemble
Abstract
Description
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.
6 pages; "QP-PQ: Quantum Probability and White Noise Analysis - Volume 13, Foundations of Probability and Physics, Proceedings of the Conference, Vaxjo, Sweden, 25 November - 1 December 2000"; A. Khrennikov, Ed.; World Scientific Publishers, Singapore, Vol. 13, 115-120 (2001)
6 pages; "QP-PQ: Quantum Probability and White Noise Analysis - Volume 13, Foundations of Probability and Physics, Proceedings of the Conference, Vaxjo, Sweden, 25 November - 1 December 2000"; A. Khrennikov, Ed.; World Scientific Publishers, Singapore, Vol. 13, 115-120 (2001)