Roberto Roncaglia

Tunneling rate fluctuations induced by nonlinear resonances: A quantitative treatment based on semiclassical arguments

This article discusses tunneling rate fluctuations induced by nonlinear resonances. The authors investigate the tunneling process between two symmetric stable islands of a forced pendulum Hamiltonian in the weak chaos regime.

Fractal properties of ion channels and diffusion

We focus our attention on a fractal model recently proposed by Liebovitch to account for the lack of a time scale in ion channel kinetics. We establish a connection between the dwell-time distributions and the correlation time of the ion channel signal, thereby making it possible to derive analytical predictions on the diffusion properties of a random walk constructed from the sum of the current fluctuations of ion channels. With the help of a numerical simulation of the Liebovitch model, it is shown that the Hurst analysis can provide a reliable determination of the standard (or anomalous) diffusion properties. On the basis of results of computer simulation we argue that by applying the Hurst analysis to the experimental distribution of closed times it is possible, in principle, to establish whether the Liebovitch model is valid.

Chaos and quantum irreversibility

We study the Hamiltonian of a two-level system interacting with a one-mode radiation field by means of the Wigner method and without using the rotating-wave approximation. We show that a phenomenon of collapses and revival, reminiscent of that exhibited by the Jaynes-Cummings model, takes place in the high-coupling limit. This process appears as irreversible or virtually reversible, according to whether the semiclassical regime is chaotic or not. Thus, we find a new mechanism for dissipation in the quantum domain.

IRREVERSIBILITY AND QUANTUM MACROSCOPIC EFFECTS IN CLASSICALLY CHAOTIC SYSTEMS

We show that in classically chaotic systems the quantum uncertainty, in spite of being assumed to be extremely small so as to make the classical approximation possible, increases very quickly thereby making these classical systems strongly quantum. It is argued that these systems also exhibit an irreversible-like behavior, albeit the phase correlations among different regions of the wavefunction make them reversible. From a statistical point of view it is difficult to distinguish the quantum behavior of these systems from the predictions of the classical approximation, unless the resulting transport process does not essentially rest either on tunneling or on localization processes (or on both). The dinstinctively quantum mechanical features of the transport process might be destroyed by the interaction between the system and environment. This possible role of environmental fluctuations, dealt within a fully quantum formalism, is discussed.