Thermalization of a Brownian particle via coupling to low-dimensional chaos

It is shown that a paradigm of classical statistical mechanics --- the thermalization of a Brownian particle --- has a low-dimensional, deterministic analogue: when a heavy, slow system is coupled to fast deterministic chaos, the resultant forces drive the slow degrees of freedom toward a state of statistical equilibrium with the fast degrees. This illustrates how concepts useful in statistical mechanics may apply in situations where low-dimensional chaos exists.Comment: Revtex, 11 pages, no figures

On the Bergman representative coordinates

We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric, contained in this set. By concrete examples we show that these estimates are the best possible.Comment: 20 page

Extension of holomorphic functions and cohomology classes from non reduced analytic subvarieties

The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are generalized versions of the Ohsawa-Takegoshi extension theorem, and borrow many techniques from the long series of papers by T. Ohsawa. The recent achievement that we want to point out is that the surjectivity property holds true for restriction morphisms to non necessarily reduced subvarieties, provided these are defined as zero varieties of multiplier ideal sheaves. The new idea involved to approach the existence problem is to make use of L 2 approximation in the Bochner-Kodaira technique. The extension results hold under curvature conditions that look pretty optimal. However, a major unsolved problem is to obtain natural (and hopefully best possible) L 2 estimates for the extension in the case of non reduced subvarieties -- the case when Y has singularities or several irreducible components is also a substantial issue.Comment: arXiv admin note: text overlap with arXiv:1703.00292, arXiv:1510.0523

Dynamics of "binary" 197Au+197 Au collisions as a test of energy dissipation mechanism

197Au+197Au collisions at 15 MeV/nucleon were studied using the multidetector array CHIMERA and heavy ion beams from the superconducting cyclotron of LNS Catania. The experiment was aimed at studying the mechanism of energy dissipation in collisions of very heavy systems. In the present contribution we report on a part of our study concentrated on a subject of basically binary damped collisions, in which only two main fragments are formed prior to secondary deexcitation processes. Such “binary” events were selected by using complete information from the exclusive-type data (including all Z 3 fragments) obtained with the CHIMERA multidetector. Results are compared with predictions of a classical dynamical model of Błocki et al., in which both scenarios of energy dissipation, one-body or two-body dissipation mechanisms, are assumed