Related papers: Phase-space correlations of chaotic eigenstates
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…
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 study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann-Husimi representations for quantum states, as well as…
We investigate the relation between the chaotic dynamics and the hierarchical phase-space structure of generic Hamiltonian systems. We demonstrate that even in ideal situations when the phase space is dominated by an exactly self-similar…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
Local parametric statistics of zeros of Husimi representations of quantum eigenstates are introduced. It is conjectured that for a classically fully chaotic systems one should use the model of parametric statistics of complex roots of…
The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The…
The statistical properties of random analytic functions psi(z) are investigated as a phase-space model for eigenfunctions of fully chaotic systems. We generalize to the plane and to the hyperbolic plane a theorem concerning the…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
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…
Gaussian wavepackets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an…
As examples of quantum-"classical" coupling systems, multi-component systems are studied by semiclassical evaluations of the Feynman kernels in the coherent-state representation. From the observation of the phase space caustics due to the…
In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced that sensitively probes phase space localization properties of eigenstates. It is based on a system's response to varying an external…
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the…
The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for 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,…
Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase space distribution functions. The similarities and differences between quantum and…
We study correlations of observables in energy eigenstates of chaotic systems of a large size $N$. We show that the bipartite entanglement of two subsystems is quite strong, whereas macroscopic entanglement of the total system is absent. It…
Using Husimi function approach, we study the ``quantum phase space'' of a harmonic oscillator interacting with a plane monochromatic wave. We show that in the regime of weak chaos, the quantum system has the same symmetry as the classical…
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…