The path integral gives us the time evolution operator, which in principle contains all the information about the dynamics of the system. However, in order to use the path integral to do physics we need to find a way to describe initial and final particle states in path integral language. The way to do this is to couple the fields to spacetimedependent background fields (“sources”) that can cre...

We review the most striking experimental results on aging in a variety of disordered systems, which reveal similar features but also important differences. We argue that a generic model that reproduce many of these features is that of pinned defects in a disordered environment, hoping between different metastable states. The fact that energy barriers grow with the size of the reconforming regio...

We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and nd results which are compatible with an exponential mixing hypothesis, rst put forward by Friedman and Martin, FM]: they do not seem compatible with the stretched exponentials believed, in spite of FM] and more recently of Chernov, C], to describe the mixing. The a...

We apply Bayesian statistics to the estimation of correlation functions. give probability distributions auto- and cross-correlations as functions data. Our procedure uses measured data optimally informs about certainty level estimation. results general stationary processes their essence is a nonparametric spectra. It allows one better understand statistical noise fluctuations, assess correlatio...

This paper studies one application of mutual information to symbolic sequence: the mutual information function M(d). This function is compared with the more frequently used correlation function (d). An exact relation between M(d) and (d) is derived for binary sequences. For sequences with more than two symbols, no such general relation exists; in particular, (d) = 0 may or may not lead to M(d) ...