Related papers: Statistics of time delay and scattering correlatio…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…
An $S$--matrix approach is developed for the chaotic dynamics of a nonlinear oscillator with dissipation. The quantum--classical crossover is studied in the framework of the semiclassical expansion for the $S$--matrix. Analytical…
We develop a semiclassical approach for the statistics of the time delay in quantum chaotic systems in the presence of a tunnel barrier, for broken time-reversal symmetry. Results are obtained as asymptotic series in powers of the…
The concept of fidelity decay is discussed from the point of view of the scattering matrix, and the scattering fidelity is introduced as the parametric cross-correlation of a given S-matrix element, taken in the time domain, normalized by…
Motivated by recent studies of the phenomenon of Coherent Perfect Absorption, we develop the random matrix theory framework for understanding statistics of the zeros of the (subunitary) scattering matrices in the complex energy plane, as…
We consider the statistics of the impedance of a chaotic microwave cavity coupled to a single port. We remove the non-universal effects of the coupling from the experimental data using the radiation impedance obtained directly from the…
We show that in clean chaotic cavities the power of shot noise takes a universal form. Our predictions go beyond previous results from random-matrix theory, in covering the experimentally relevant case of few channels. Following a…
The correlation between the values of wavefunctions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the…
We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
Networks of nonlinear units with time-delayed couplings can synchronize to a common chaotic trajectory. Although the delay time may be very large, the units can synchronize completely without time shift. For networks of coupled Bernoulli…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
For the theoretical prediction of cross-section fluctuations in chaotic scattering, the cross-section autocorrelation function is needed. That function is not known analytically. Using experimental data and numerical simulations, we show…
Lack of memory (locality in time) is a major limitation of almost all present time-dependent density functional approximations. By using semiclassical dynamics to compute correlation effects within a density-matrix functional approach, we…
A semiclassical diagrammatic approach is constructed for calculating correlation functions of observables in open chaotic systems with time reversal symmetry. The results are expressed in terms of classical correlation functions involving…
We point out that the transmission eigenvalue density and higher order correlation functions in chaotic cavities for an arbitrary number of incoming and outgoing leads $(N_1,N_2)$ are analytically known from the Jacobi ensemble of Random…
Transport properties of open chaotic ballistic systems and their statistics can be expressed in terms of the scattering matrix connecting incoming and outgoing wavefunctions. Here we calculate the dependence of correlation functions of…
When time-reversal symmetry is broken, the average conductance through a chaotic cavity, from an entrance lead with $N_1$ open channels to an exit lead with $N_2$ open channels, is given by $N_1N_2/M$, where $M=N_1+N_2$. We show that, when…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…