Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering

Details Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering

1999-03-02

arxiv.org/abs/cond-mat/9903043v2

Phys.Rev.Lett. v.83 (1999) p.65

Physics

Condensed Matter

4 pages, no figures. Misprints corrected, some details on single-channel and many-channel cases are added

Scientific paper

10.1103/PhysRevLett.83.65

We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all n-point correlation functions in the complex plane. As a by-product, we establish the Ginibre-like statistics of resonances for many open channels. Our method is a combination of Itzykson-Zuber integration and a variant of nonlinear $\sigma-$model and can be applied when the use of orthogonal polynomials is problematic.

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