Bayesian approach to superstatistics

The superstatistics approach recently introduced by Beck [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism that aims to deal in a unifying way with a large variety of complex nonequilibrium systems, for which spatio-temporal fluctuations of one intensive variable (the "temperature" 1/b) are supposed to exist. The intuitive explanation provided by Beck for superstatistics is based on the ansatz that the system under consideration, during its evolution, travels within its phase space which is partitioned into cells. Within each cell, the system is described by ordinary Maxwell-Boltzmann statistical mechanics, i.e., its statistical distribution is the canonical one, but b varies from cell to cell, with its own probability density f(b). In this work we first address that the explicit inclusion of the density of states in this description is essential for its correctness. The correction is not relevant for developments of the theory, but points to the fact that its correct starting point, as well its meaning, must be found at a more basic level: the pure probability product rule involving the intensive variable b and its conjugate extensive one. The question therefore arises how to assign a meaning to these probabilities for each specific problem. We will see that it is easily answered through Bayesian analysis. This way, we are able to provide an interpretation for f(b), that was not fully elucidated till now.Comment: 13 pages. To be published in The European Physics Journal

SWKB for the Angular Momentum

In this paper we solve the eigenvalue problem of the angular momentum operator by using the supersymmetric semiclassical quantum mechanics (SWKB), and show that it gives the correct quantization already at the leading order.Comment: latex, 9 pages, no figures, to be published in Modern Physics Letters

Further study of the Over-Barrier Model to compute charge exchange processes

In this paper we study theoretically the process of electron capture between one-optical-electron atoms (e.g. hydrogenlike or alkali atoms) and ions at low-to-medium impact velocities ($v/v_e \approx 1$) working on a modification of an already developed classical In this work we present an improvement over the Over Barrier Model (OBM) described in a recent paper [F. Sattin, Phys. Rev. A {\bf 62}, 042711 (2000)]. We show that: i) one of the two free parameters there introduced actually comes out consistently from the starting assumptions underlying the model; ii) the modified model thus obtained is as much accurate as the former one. Furthermore, we show that OBMs are able to accurately predict some recent results of state selective electron capture, at odds with what previously supposed.Comment: RevTeX, 7 pages, 4 eps figures. To appear in Physical Review A (2001-september issue

A classical Over Barrier Model to compute charge exchange between ions and one-optical-electron atoms

In this paper we study theoretically the process of electron capture between one-optical-electron atoms (e.g. hydrogenlike or alkali atoms) and ions at low-to-medium impact velocities (v/v_e <= 1) working on a modification of an already developed classical Over Barrier Model (OBM) [V. Ostrovsky, J. Phys. B: At. Mol. Opt. Phys. {\bf 28} 3901 (1995)], which allows to give a semianalytical formula for the cross sections. The model is discussed and then applied to a number of test cases including experimental data as well as data coming from other sophisticated numerical simulations. It is found that the accuracy of the model, with the suggested corrections and applied to quite different situations, is rather high.Comment: 12 pages REVTEX, 5 EPSF figures, submitted to Phys Rev

Chaotic features in classical scattering processes between ions and atoms

A numerical study has been done of collisions between protons and hydrogen atoms, treated as classical particles, at low impact velocities. The presence of chaos has been looked for by investigating the processes with standard techniques of the chaotic--scattering theory. The evidence of a sharp transition from nearly regular scattering to fully developed chaos has been found at the lower velocities.Comment: 10 pages, Latex, 3 figures (available upon request to the authors), submitted to Journal of Physics

A Self-Organized-Criticality model consistent with statistical properties of edge turbulence in a fusion plasma

The statistical properties of the intermittent signal generated by a recent model for self-organized-criticality (SOC) are examined. A successful comparison is made with previously published results of the equivalent quantities measured in the electrostatic turbulence at the edge of a fusion plasma. This result re-establishes SOC as a potential paradigm for transport in magnetic fusion devices, overriding shortcomings pointed out in earlier works [E. Spada, et al, Phys. Rev. Lett. 86, 3032 (2001); V. Antoni, et al, Phys. Rev. Lett. 87, 045001 (2001)].Comment: 4 pages, 4 figure

A semi-classical over-barrier model for charge exchange between highly charged ions and one-optical electron atoms

Absolute total cross sections for electron capture between slow, highly charged ions and alkali targets have been recently measured. It is found that these cross sections follow a scaling law with the projectile charge which is different from the one previously proposed basing on a classical over-barrier model (OBM) and verified using rare gases and molecules as targets. In this paper we develop a "semi-classical" (i.e. including some quantal features) OBM attempting to recover experimental results. The method is then applied to ion-hydrogen collisions and compared with the result of a sophisticated quantum-mechanical calculation. In the former case the accordance is very good, while in the latter one no so satisfactory results are found. A qualitative explanation for the discrepancies is attempted.Comment: RevTeX, uses epsf; 6 pages text + 3 EPS figures Journal of Physics B (scehduled March 2000). This revision corrects fig.

Multi-parameter generalization of nonextensive statistical mechanics

We show that the stochastic interpretation of Tsallis' thermostatistics given recently by Beck [Phys. Rev. Lett {\bf 87}, 180601 (2001)] leads naturally to a multi-parameter generalization. The resulting class of distributions is able to fit experimental results which cannot be reproduced within the Boltzmann's or Tsallis' formalism.Comment: ReVTex 4.0, 4 eps figure

On the Convergence of the WKB Series for the Angular Momentum Operator

In this paper we prove a recent conjecture [Robnik M and Salasnich L 1997 J. Phys. A: Math. Gen. 30 1719] about the convergence of the WKB series for the angular momentum operator. We demonstrate that the WKB algorithm for the angular momentum gives the exact quantization formula if all orders are summed.Comment: latex, 9 pages, no figures, to be published in Journal of Physics A: Math. and Ge