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1

Fluctuations and Correlations in Scattering on a Resonance Coupled to a Chaotic Background

100%

Savin D.

Acta Physica Polonica A

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2017

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vol. 132

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issue 6

1688-1694

EN

We discuss and briefly overview recent progress with studying fluctuations in scattering on a resonance state coupled to the background of many chaotic states. Such a problem arises naturally, e.g., when dealing with wave propagation in the presence of a complex environment. Using a statistical model based on random matrix theory, we obtain a number of nonperturbative results for various statistics of scattering characteristics. This includes the joint and marginal distributions of the reflection and transmission intensities and phases, which are derived exactly at arbitrary coupling to the background with finite absorption. The intensities and phases are found to exhibit highly non-trivial statistical correlations, which remain essential even in the limit of strong absorption. In the latter case, we also consider the relevant approximations and their accuracy. As an application, we briefly discuss the statistics of the phase rigidity (or mode complexness) in such a scattering situation.

2

Probing Eigenfunction Nonorthogonality by Parametric Shifts of Resonance Widths

63%

Savin D., De Vaulx J.

Acta Physica Polonica A

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2013

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vol. 124

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issue 6

1074-1077

EN

Recently, it has been shown that the change of resonance widths in an open system under a perturbation of its interior is a sensitive indicator of the nonorthogonality of resonance states. We apply this measure to quantify parametric motion of the resonances. In particular, a strong redistribution of the widths is linked with the maximal degree of nonorthogonality. Then for weakly open chaotic systems we discuss the effect of spectral rigidity on the statistical properties of the parametric width shifts, and derive the distribution of the latter in a picket-fence model with equidistant spectrum.

3

Correlation Functions of Impedance and Scattering Matrix Elements in Chaotic Absorbing Cavities

51%

Savin D., Fyodorov Y., Sommers H.

Acta Physica Polonica A

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2006

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vol. 109

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issue 1

53-64

EN

Wave scattering in chaotic systems with a uniform energy loss (absorption) is considered. Within the random matrix approach we calculate exactly the energy correlation functions of different matrix elements of impedance or scattering matrices for systems with preserved or broken time-reversal symmetry. The obtained results are valid at any number of arbitrary open scattering channels and arbitrary absorption. Elastic enhancement factors (defined through the ratio of the corresponding variance in reflection to that in transmission) are also discussed.

4

Statistics of Conductance and Shot-Noise Power for Chaotic Cavities

51%

Sommers H., Wieczorek W., Savin D.

Acta Physica Polonica A

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2007

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vol. 112

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issue 4

691-697

EN

We report on an analytical study of the statistics of conductance, g, and shot-noise power, p, for a chaotic cavity with arbitrary numbers N_{1,2} of channels in two leads and symmetry parameterβ = 1, 2, 4. With the theory of Selberg's integral the first four cumulants of g and first two cumulants of p are calculated explicitly. We give analytical expressions for the conductance and shot-noise distributions and determine their exact asymptotics near the edges up to linear order in distances from the edges. For 0 < g < 1 a power law for the conductance distribution is exact. All results are also consistent with numerical simulations.

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4 Acta Physica Polonica A

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4 Savin D.

2 Sommers H.

1 De Vaulx J.

1 Fyodorov Y.

1 Wieczorek W.

Fluctuations and Correlations in Scattering on a Resonance Coupled to a Chaotic Background

Probing Eigenfunction Nonorthogonality by Parametric Shifts of Resonance Widths

Correlation Functions of Impedance and Scattering Matrix Elements in Chaotic Absorbing Cavities

Statistics of Conductance and Shot-Noise Power for Chaotic Cavities