相关论文: Percolation model for nodal domains of chaotic wav…

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…

In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…

We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in arbitrary dimension. We give an explicit expression for the limiting distribution of normalised nodal counts and…

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…

The statistics of the nodal lines and nodal domains of the eigenfunctions of quantum billiards have recently been observed to be fingerprints of the chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett., Vol. 88…

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…

Recently it was conjectured that nodal domains of random wave functions are adequately described by critical percolation theory. In this paper we strengthen this conjecture in two respects. First, we show that, though wave function…

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…

We consider the nodal domains of Gaussian random waves in two dimensions. We present a method to calculate the distribution of the number of nodal domains and the average connectivity with the help of auxiliary Potts-spins. An analytical…

The nodal lines of random wave functions are investigated. We demonstrate numerically that they are well approximated by the so-called SLE_6 curves which describe the continuum limit of the percolation cluster boundaries. This result gives…

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…

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 purpose of this Note is to provide a deterministic implementation of the random wave model for the number of nodal domains in the context of the two-dimensional torus. The approach is based on recent work due to Nazarov and Sodin and…

Bogomolny and Schmit proposed that the critical edge percolation on the square lattice is a good model for the nodal domains of a random plane wave. Based on this they made a conjecture about the number of nodal domains. Recent computer…

We are concerned with the analysis of a mean field type equation and its linearization, which is a nonlocal operator, for which we estimate the number of nodal domains for the radial eigenfunctions and the related uniqueness properties.

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 discuss the statistical properties of the volume of the nodal set of wave function for two paradigmatic model systems which we consider in arbitrary dimension $s\ge 2$: the cuboid as a paradigm for a regular shape with separable wave…

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…

In this paper we investigate the properties of nodal structures in random wave fields, and in particular we scrutinize their recently proposed connection with short-range percolation models. We propose a measure which shows the difference…

Sequences of nodal counts store information on the geometry (metric) of the domain where the wave equation is considered. To demonstrate this statement, we consider the eigenfunctions of the Laplace-Beltrami operator on surfaces of…