Related papers: Long-range correlations in the wave functions of c…
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…
Using the supersymmetry technique, we calculate the joint distribution of local densities of electron wavefunctions in two coupled disordered or chaotic quantum billiards. We find novel spatial correlations that are absent in a single…
The standard semiclassical calculation of transmission correlation functions for chaotic systems is severely influenced by unitarity problems. We show that unitarity alone imposes a set of relationships between cross sections correlation…
An energy eigenfunction in a classically chaotic system is known to have spatial correlations which (in the limit of small $\hbar$) are governed by a microcanonical distribution in the classical phase space. This result is valid, however,…
We consider the fluctuations of electromagnetic fields in chaotic microwave cavities. We calculate the transversal and longitudinal correlation function based on a random wave assumption and compare the predictions with measurements on two-…
At short distances, energy eigenfunctions of chaotic systems have spatial correlations that are well described by assuming a microcanonical density in phase space for the corresponding Wigner function. However, this is not correct on large…
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…
The wavefunctions in phase-space representation can be expressed as entire functions of their zeros if the phase space is compact. These zeros seem to hide a lot of relevant and explicit information about the underlying classical dynamics.…
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local…
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 arbitrary number of open channels and arbitrary coupling strength between…
We derive analytical expressions for the correlation functions of the electronic conductance fluctuations of an open quantum dot under several conditions. Both the variation of energy and that of an external parameter such as an applied…
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…
Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…
In the present work we study the two-point correlation function $R(\epsilon)$ of the quantum mechanical spectrum of a classically chaotic system. Recently this quantity has been computed for chaotic and for disordered systems using periodic…
We investigate the synchronization phenomenon in coupled chaotic map lattices where the couplings decay with distance following a power-law. Depending on the lattice size, the coupling strength and the range of the interactions, complete…
A form of "remote synchronization" was recently described wherein amplitude fluctuations across a ring of non-identical, non-linear electronic oscillators become entrained into spatially-structured patterns. According to linear models and…
We study the $n$-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit's universality conjecture, it is expected that the correlation functions…
Wavefunctions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wavefunctions display universal density distributions and density auto-correlations in agreement with…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry and generalized by…
We present a semiclassical approach to n-point spectral correlation functions of quantum systems whose classical dynamics is chaotic, for arbitrary n. The basic ingredients are sets of periodic orbits that have nearly the same action and…