Related papers: Autocorrelation function of eigenstates in chaotic…
We evaluate the localization length of the wave solution of a random potential characterized by an arbitrary autocorrelation function. We go beyond the Born approximation to evaluate the localization length using a non-linear approximation…
The long time asymptotics of multi-time correlation functions of relaxing quantum mechanical systems can be conveniently studied by means of free-products of suitable C*-algebras and of states on these free products given by multiple…
We propose a new autocorrelation measure for functional time series that we term spherical autocorrelation. It is based on measuring the average angle between lagged pairs of series after having been projected onto the unit sphere. This new…
While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in…
We study chaotic eigenfunctions in wedge-shaped and rectangular regions using a generalization of Berry's conjecture. An expression for the two-point correlation function is derived and verified numerically.
Correlations of eigenfunctions, $\langle|\psi_k(r_1)|^2|\psi_l(r_2)|^2\rangle$, in a disordered system are investigated. We derive general formulae expressing these correlation functions in terms of the supermatrix sigma-model. In…
We discuss the dephasing induced by the internal classical chaotic motion in the absence of any external environment. To this end we consider a suitable extension of fidelity for mixed states which is measurable in a Ramsey interferometry…
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…
The grand potential $\Omega$ and the response $R = - \partial \Omega /\partial x$ of a phase-coherent confined noninteracting electron gas depend sensitively on chemical potential $\mu$ or external parameter $x$. We compute their…
It was recently shown (Keating & Prado, {\it Proc. R. Soc. Lond. A} {\bf 457}, 1855-1872 (2001)) that, in the semiclassical limit, the scarring of quantum eigenfunctions by classical periodic orbits in chaotic systems may be dramatically…
Using the random matrix description of open quantum chaotic systems we calculate in closed form the universal autocorrelation function and the probability distribution of the total photodissociation cross section in the regime of quantum…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
We investigate the short-time dynamic relaxation of the two-dimensional XY model in the high temperature phase. Starting from the ordered state, we measure the autocorrelation function and determine the autocorrelation time. It is shown…
The simplest examples of chaotic maps are linear, area-preserving maps on the circle, torus, or product of tori; respectively known as the Bernoulli map, the cat map, and the recently introduced "spatiotemporal" cat map. We study…
We propose the autocorrelator of conductance peak heights as a signature of the underlying chaotic dynamics in quantum dots in the Coulomb blockade regime. This correlation function is directly accessible to experiments and its decay width…
A linear oscillator very weakly coupled with the object quantum system is proposed as a detector measuring the lifetime of irreversibility exhibited by the system, and classically chaotic coupled kicked rotors are examined as ideal…
The classical regular and partial autocorrelation functions are powerful tools for stationary time series modelling and analysis. However, it is increasingly recognized that many time series are not stationary and the use of classical…
Temporal correlations in the time series observed in various systems have been characterized by the autocorrelation function. Such correlations can be explained by heavy-tailed interevent time distributions as well as by correlations…