Related papers: Statistical properties of high-lying chaotic eigen…
In this work we study the geometrical properties of the high-lying eigenfunctions (200,000 and above) which are deep in the semiclassical regime. The system we are analyzing is the billiard system inside the region defined by the quadratic…
We study the quantum mechanics of a billiard (Robnik 1983) in the regime of mixed-type classical phase space (the shape parameter \lambda=0.15) at very high-lying eigenstates, starting at about 1.000.000th eigenstate and including the…
In this work we semiclassically analyzed the high lying eigenstates of a mixed type Hamiltonian system. For the regular states we employ the Einstein-Brillouin-Keller quantization, while for the chaotic states, following the principle of…
We study the quantum localization in the chaotic eigenstates of a billiard with mixed-type phase space, after separating the regular and chaotic eigenstates, in the regime of slightly distorted circle billiard where the classical transport…
We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on…
We study the fluctuations that are predicted in the autocorrelation function of an energy eigenstate of a chaotic, two-dimensional billiard by the conjecture (due to Berry) that the eigenfunction is a gaussian random variable. We find an…
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 boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance 2B between their centers, as introduced by Heller and Tomsovic in Phys. Today 46 38 (1993). We study two classical and…
We study numerically the scaling properties of scars in stadium billiard. Using the semiclassical criterion, we have searched systematically the scars of the same type through a very wide range, from ground state to as high as the 1…
We demonstrate that the energy or quasienergy level spacing distribution in dynamically localized chaotic eigenstates is excellently described by the Brody distribution, displaying the fractional power law level repulsion. This we show in…
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 develop a statistical description of chaotic wavefunctions in closed systems obeying arbitrary boundary conditions by combining a semiclassical expression for the spatial two-point correlation function with a treatment of eigenfunctions…
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…
The localization measures $A$ (based on the information entropy) of localized chaotic eigenstates in the Poincar\'e-Husimi representation have a distribution on a compact interval $[0,A_0]$, which is well approximated by the {\em beta…
The phenomenon of quantum localization in classically chaotic eigenstates is one of the main issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or even in general wave mechanics. In this…
In mixed systems, besides regular and chaotic states, there are states supported by the chaotic region mainly living in the vicinity of the hierarchy of regular islands. We show that the fraction of these hierarchical states scales as…
In this paper we study in detail the localized wave functions defined in Phys. Rev. Lett. {\bf 76}, 1613 (1994), in connection with the scarring effect of unstable periodic orbits in highly chaotic Hamiltonian system. These functions appear…
We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational C3 symmetry. Its band…
In this paper, by using our improved plane wave decomposition method, we study the scars in the eigenfunctions of the stadium billiard from very low state to as high as about the one millionth state. In the systematic searching for scars of…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…