Related papers: Statistical description of eigenfunctions in chaot…
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…
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…
We present an improved version of Berry's ansatz able to incorporate exactly the existence of boundaries and the correct normalization of the eigenfunction into an ensemble of random waves. We then reformulate the Random Wave conjecture…
In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of…
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for…
In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry and generalized by…
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…
We study a new statistics of wave functions in several chaotic and disordered systems: the random matrix model, band random matrix model, the Lipkin model, chaotic quantum billiard and the 1D tight-binding model. Both numerical and…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
We study the statistical properties of the high-lying chaotic eigenstates (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 construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
The supersymmetry method has proven to be a very powerful tool of study of the statistical properties of energy levels and eigenfunctions in disordered and chaotic systems. The aim of these lectures is to present a tutorial introduction to…
Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this…
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…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
Wavefunctions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wavefunctions display universal density distributions and density auto-correlations in agreement with…
We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of…