相关论文: Nodal domain distributions for quantum maps

We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…

We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting…

We characterise the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns…

We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two--dimensional area--preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of…

We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2-$d$ quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic…

Nodal domains are regions where a function has definite sign. In recent paper [nlin.CD/0109029] it is conjectured that the distribution of nodal domains for quantum eigenfunctions of chaotic systems is universal. We propose a…

We study analytically and numerically the classical diffusive process which takes place in a chaotic billiard. This allows to estimate the conditions under which the statistical properties of eigenvalues and eigenfunctions can be described…

We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as useful measure to detect localization effects. For the momentum distribution, the radially integrated…

We consider the real eigenfunctions of the Schr\"odinger operator on graphs, and count their nodal domains. The number of nodal domains fluctuates within an interval whose size equals the number of bonds $B$. For well connected graphs, with…

Quantum walks are at present an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior.…

Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated…

We perform a detailed numerical study of energy-level and wavefunction statistics of a deformable quantum billiard focusing on properties relevant to semiconductor quantum dots. We consider the family of Robnik billiards generated by simple…

The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…

We construct an autonomous chaotic Hamiltonian ratchet as a channel billiard subdivided by equidistant walls attached perpendicularly to one side of the channel, leaving an opening on the opposite side. A static homogeneous magnetic field…

We investigate the transition from integrable to chaotic dynamics in the quantum mechanical wave functions from the point of view of the nodal structure by employing a two dimensional quartic oscillator. We find that the number of nodal…

Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained…

The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…

Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, $\nu$, of the eigenfunctions are considered. The billiards for which the time-independent Schr\"odinger equation (Helmholtz equation) is…

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…

We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of "quantum chaotic dynamics". It is shown that under quite general conditions their roots…