Article

# Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: application to the time-delay problem.

Fachbereich Physik, Universität-GH Essen, 45117 Essen, Germany.

Physical Review E (Impact Factor: 2.31). 04/2001; 63(3 Pt 2):035202. DOI: 10.1103/PhysRevE.63.035202 Source: arXiv

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**ABSTRACT:**The influence of direct processes on the cross-correlation function c12(ν) and the elastic enhancement factor WS, β was studied experimentally using microwave networks in the presence of absorption. Microwave networks simulate quantum graphs with and without time-reversal symmetry. Direct processes exist because, for example, of non-perfect coupling between a studied system and a measuring device. We show that direct processes strongly influence the cross-correlation function c12(ν) in contrast to the enhancement factor WS, β, which is not sensitive to these processes. It makes the enhancement factor WS, β an important measure of the chaoticity of a quantum system.Physica Scripta - PHYS SCR. 01/2012; 2012. - [Show abstract] [Hide abstract]

**ABSTRACT:**We study the statistical properties of the impedance matrix (related to the scattering matrix) describing the input-output properties of waves in cavities in which ray trajectories that are regular and chaotic coexist (i.e., "mixed" systems). The impedance can be written as a summation over eigenmodes where the eigenmodes can typically be classified as either regular or chaotic. By appropriate characterizations of regular and chaotic contributions, we obtain statistical predictions for the impedance. We then test these predictions by comparison with numerical calculations for a specific cavity shape, obtaining good agreement.Physical Review E 06/2013; 87(6-1):062906. · 2.31 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We study the cumulants and their generating functions of the probability distributions of the conductance, shot noise and Wigner delay time in ballistic quantum dots. Our approach is based on the integrable theory of certain matrix integrals and applies to all the symmetry classes ${\beta \in \{1, 2, 4\}}$ of Random Matrix Theory. We compute the weak localization corrections to the mixed cumulants of the conductance and shot noise for β = 1, 4, thus proving a number of conjectures of Khoruzhenko et al. (in Phys Rev B 80:(12)125301, 2009). We derive differential equations that characterize the cumulant generating functions for all ${\beta \in \{1, 2, 4 \} }$ . Furthermore, when β = 2 we show that the cumulant generating function of the Wigner delay time can be expressed in terms of the Painlevé III′ transcendant. This allows us to study properties of the cumulants of the Wigner delay time in the asymptotic limit ${n \to \infty}$ . Finally, for all the symmetry classes and for any number of open channels, we derive a set of recurrence relations that are very efficient for computing cumulants at all orders.Communications in Mathematical Physics 12/2013; 324(2). · 1.97 Impact Factor

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