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VOLUME 80 (2004) | ISSUE 12 | PAGE 855
Statistics of impedance, local density of states, and reflection in quantum chaotic systems with absorption
PACS: 05.45.Mt, 42.25.Bs, 73.23.-b
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 β2 and β4 symmetry class. In the case of β1 we provide an interpolation formula which incorporates all known limiting cases and fits excellently available experimental data as well as diverse numeric tests.