相关论文: Spatial Correlations in Chaotic Eigenfunctions
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,…
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…
The expected root-mean-square value of a matrix element $A_{\alpha\beta}$ in a classically chaotic system, where $A$ is a smooth, $\hbar$-independent function of the coordinates and momenta, and $\alpha$ and $\beta$ label different energy…
In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation…
By using the supersymmetry method we derive an explicit expression for the parametric correlation function of densities of eigenphases $\theta_a$ of the S-matrix in a chaotic quantum system with broken time-reversal symmetry coupled to…
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…
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…
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-…
We study the spatial autocorrelation of energy eigenfunctions $\psi_n({\bf q})$ corresponding to classically chaotic systems in the semiclassical regime. Our analysis is based on the Weyl-Wigner formalism for the spectral average…
The fluctuations and correlations of matrix elements of cross sections are investigated in open systems that are chaotic in the classical limit. The form of the correlation functions is discussed within a statistical analysis and tested in…
We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the…
New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point…
Exact analytical expressions for the cross-section correlation functions of chaotic scattering sys- tems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are…
It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in…
We consider the properties of an observable (such as a single spin component that squares to the identity) when expressed as a matrix in the basis of energy eigenstates, and then truncated to a microcanonical slice of energies of varying…
The correlation between level velocities and eigenfunction intensities provides a new way of exploring phase space localization in quantized non-integrable systems. It can also serve as a measure of deviations from ergodicity due to quantum…
This paper establishes the universality of parametric correlations of eigenfunctions in chaotic and weakly disordered systems. We demonstrate this universality in the framework of the gaussian random matrix process and obtain predictions…
We derive a semiclassical expression for an energy smoothed autocorrelation function defined on a group of eigenstates of the Schr\"odinger equation. The system we considered is an energy-conserved Hamiltonian system possessing…
We study correlations of the amplitudes of wave functions of a chaotic system at large distances. For this purpose, a joint distribution function of the amplitudes at two distant points in a sample is calculated analytically using the…
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.…