Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption

2004/09/05 by Yan V. Fyodorov, Dmitry V. Savin · 2 citations
Physics and Astronomy · #cond-mat.mes-hall

paper · pdf · doi:10.1134/1.1868794

published as JETP Letters 80, 725 (2004) [Pis'ma v ZhETP 80, 855 (2004)] · 4 pages, 1 figure

arxiv created 2004/09/05 · arxiv updated 2009/12/01

Abstract

We are interested in finding the joint distribution function of the real and imaginary parts of the local Green function for a system with chaotic internal wave scattering and a uniform energy loss (absorption). For a microwave cavity attached to a single-mode antenna the same quantity has a meaning of the complex cavity impedance. Using the random matrix approach, we relate its statistics to that of the reflection coefficient and scattering phase and provide exact distributions for systems with beta=2 and beta=4 symmetry class. In the case of beta=1 we provide an interpolation formula which incorporates all known limiting cases and fits excellently available experimental data as well as diverse numeric tests.

Cited by

• Universal Frequency Correlations and Recurrence Statistics of Complex Impedance Matrices
• Superuniversal Statistics with Topological Origins for non-Hermitian Scattering Singularities

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