Dynamics of complex quantum systems with energy dissipation

2003/01/30 by M. M. Duras, Maciej M. Duras, Duras, Maciej M.
Physics and Astronomy · #FOS: Physical sciences #Quantum chaos and dynamical systems #Scientific Research and Discoveries #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0301600

4 pages; presented at poster session of the conference "Dynamics and Statistics of Complex Systems"; May 17th, 2000 to May 18th, 2000; Max Planck Institute for the Physics of Complex Systems; Dresden, Germany (2000)

openalex publication_date 2003/01/30 · arxiv created 2003/07/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A complex quantum system with energy dissipation is considered. The quantum Hamiltonians H belong the complex Ginibre ensemble. The complex-valued eigenenergies Z_i are random variables. The second differences Δ¹ Z_i are also complex-valued random variables. The second differences have their real and imaginary parts and also radii (moduli) and main arguments (angles). For N=3 dimensional Ginibre ensemble the distributions of above random variables are provided whereas for generic N- dimensional Ginibre ensemble second difference distribution is analytically calculated. The law of homogenization of eigenergies is formulated. The analogy of Wigner and Dyson of Coulomb gas of electric charges is studied.

Related

• An example of dissipative quantum system: finite differences for complex Ginibre ensemble
• Quantum symmetrical statistical system: Ginibre-Girko ensemble
• Complex-valued second difference as a measure of stabilization of complex dissipative statistical systems: Girko ensemble
• Statistics of complex dissipative systems
• Extension of the Ginibre Ensembles of Random Matrices