Dmitry V. Savin

Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption

We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric σ-model, we are able to derive closed-form analytic expressions for the distribution of reflection probability in a generic disordered system. One of the most important properties resulting from such an analysis is statistical independence between the phase and the modulus of the reflection amplitude in every perfectly open channel. The developed theory has far-reaching consequences for many quantities of interest, including local Green functions and time delays. In particular, we point out the role played by absorption as a sensitive indicator of mechanisms behind the Anderson localization transition. We also provide a random-matrix-based analysis of S-matrix and impedance correlations for various symmetry classes as well as the distribution of transmitted power for systems with broken time-reversal invariance, completing previous works on the subject. The results can be applied, in particular, to the experimentally accessible impedance and reflection in a microwave or an ultrasonic cavity attached to a system of antennas.

Statistics of resonance width shifts as a signature of eigenfunction nonorthogonality.

We consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the nonorthogonality of resonance wave functions, being zero only if those were orthogonal. Focusing further on chaotic systems, we employ random matrix theory to introduce a new type of parametric statistics in open systems and derive the distribution of the resonance width shifts in the regime of weak coupling to the continuum.

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

We write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with M statistically equivalent channels at nonideal coupling to that for ideal coupling. Unfolding the phases by their local density leads to universality of their local fluctuations for large M. A relation between the partial time delays and diagonal matrix elements of the Wigner-Smith matrix is revealed for ideal coupling. This helped us in deriving the joint probability distribution of partial time delays and the distribution of the Wigner time delay.

Shot noise in chaotic cavities with an arbitrary number of open channels

Using the random matrix approach, we calculate analytically the average shot-noise power in a chaotic cavity at an arbitrary number of propagating modes (channels) in each of the two attached leads. A simple relationship between this quantity, the average conductance and the conductance variance is found. The dependence of the Fano factor on the channel number is considered in detail.

Time delay correlations in chaotic scattering: random matrix approach

Abstract We study the correlations of time delays in a model of chaotic resonance scattering based on the random matrix approach. Analytical formulae which are valid for an arbitrary number of open channels and arbitrary coupling strength between resonances and channels are obtained by the supersymmetry method. We demonstrate that in the limit of a large number of open channels the time delay correlation function, though being not a Lorentzian, is characterized, similar to that of the scattering matrix, by the gap between the cloud of complex poles of the S -matrix and the real energy axis.

Nonlinear statistics of quantum transport in chaotic cavities

In the framework of the random matrix approach, we apply the theory of Selbergs integral to problems of quantum transport in chaotic cavities. All the moments of transmission eigenvalues are calculated analytically up to the fourth order. As a result, we derive exact explicit expressions for the skewness and kurtosis of the conductance and transmitted charge as well as for the variance of the shot-noise power in chaotic cavities. The obtained results are generally valid at arbitrary numbers of propagating channels in the two attached leads. In the particular limit of large (and equal) channel numbers, the shot-noise variance attends the universal value

QUANTUM VERSUS CLASSICAL DECAY LAWS IN OPEN CHAOTIC SYSTEMS

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Systematic approach to statistics of conductance and shot-noise in chaotic cavities

that determines a universal Gaussian statistics of shot-noise fluctuations in this case.

Distribution of Proper Delay Times in Quantum Chaotic Scattering: A Crossover from Ideal to Weak Coupling

We study analytically the time evolution in decaying chaotic systems and discuss in detail the hierarchy of characteristic time scales that appeared in the quasiclassical region. There exist two quantum time scales: the Heisenberg time

Statistics of impedance, local density of states, and reflection in quantum chaotic systems with absorption

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