Are citations of scientific papers a case of nonextensivity?

The distribution N(x) of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner (Eur. Phys. J. B 4, 131 (1998)). To fit the data, a stretched exponential () has been used with only partial success. The success is not complete because the data exhibit, for large citation count x, a power law (roughly for the ISI data), which, clearly, the stretched exponential does not reproduce. This fact is then attributed to a possibly different nature of rarely cited and largely cited papers. We show here that, within a nonextensive thermostatistical formalism, the same data can be quite satisfactorily fitted with a single curve (namely, [0pt] for the available values of x. This is consistent with the connection recently established by Denisov (Phys. Lett. A 235, 447 (1997)) between this nonextensive formalism and the Zipf-Mandelbrot law. What the present analysis ultimately suggests is that, in contrast to Redner's conclusion, the phenomenon might essentially be one and the same along the entire range of the citation number x. Received 13 April 1999     

The individual success of musicians, like that of physicists, follows a stretched exponential distribution

Over the last five years or so, a number of studies have focussed on the distribution of `success' in physics and other sciences; in these studies, `success' is measured by the number of times a paper, or an author, is cited. The distribution of citations of individual papers approximates to a power-law [S. Redner, Eur. Phys. J. B 4, 131 (1998)], while lifetime total citations of the 1120 most-cited physicists follows a stretched exponential [J. Laherrère, D. Sornette, Eur. Phys. J. B 2, 525 (1998)]. Here, I examine the distribution of success in popular music, a field of creativity that has social structures very different from those of physics, and which is generally held to be controlled primarily by fashion. For this study, the lifetime total success of bands was measured by the total number of weeks they were in the weekly `top 75' list of best-selling recordings. Like the lifetime success of physicists reported by Laherrere and Sornette, the success of the 6107 bands that appeared in the UK `top 75' from 1950 until 2000 follows a stretched exponential of the form P(x)dx = c(x ^{c - 1}/x ₀ ^c)exp[- (x/x ₀)^c]dx; for the music data, c = 0.5 and x ₀ = 9.37. Received 23 October 2001 Published online 25 June 2002     

On charged mesoscopic metallic bubbles

We investigate the existence of stable charged metallic bubbles using the shell correction method. We find that for a given mesoscopic system of n atoms of a given metal and (positive) elementary charges, a metallic bubble turns out to have a lower total energy than a compact spherical cluster, whenever the charge number q is larger than a critical charge number q_c. For a magic number (n-q) of free electrons, the spherical metallic bubble may become stable against fission. Received: 17 November 1997 / Revised: 28 May 1998 / Accepted: 20 July 1998     

Effect of topological thresholds on thermal behaviour of germanium telluride glasses containing metallic additive

Differential Scanning Calorimetric (DSC) studies on Ag_xGe₁₅Te_85-x glasses have been undertaken over a wide range of compositions, to understand the effect of topological thresholds on thermal properties. It is found that the compositional dependence of glass transition temperature (T _g ), crystallization temperature (T _c ), activation energy for crystallization and thermal stability show anomalies at the rigidity percolation threshold. Unusual variations also observed in different thermal properties at the composition x = 20, clearly establishes the occurrence of chemical threshold in these glasses. Received: 27 January 1998 / Revised: 12 June 1998 / Accepted: 3 July 1998     

How to get access to long range states of highly excited molecules

Due to competition between ionic and covalent dissociation, the excited potential curves of the alkali dimers display long range structures, leading in some cases to secondary wells. We discuss the possibility of populating the well (with a depth of 1614.8 cm^-1, located at R _e = 30.5a ₀ ) that is present in the Na₂ potential curve and propose detection schemes. Received: 28 May 1998 / Revised: 5 August 1998 / Accepted: 24 September 1998     

Reaction kinetics in polymer melts

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi [#!doi:inter2!#], de Gennes [#!gennes:polreactionsiandii!#], and Friedman and O'Shaughnessy [#!ben:interdil_all_aip!#], to arbitrary initial reactive group density n₀ and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, .For high Q, a transition occurs to diffusion-controlled (DC) kinetics with (where x_t is rms monomer displacement in time t) leading to a density decay . If n₀ exceeds the chain overlap threshold, this behavior is followed by a regime where during which k has the same power law dependence in time, , but possibly different numerical coefficient. For unentangled melts this gives while for entangled cases one or more of the successive regimes ,t ^-3/8 and t ^-3/4 may be realized depending on the magnitudes of Q and n₀. Kinetics at times longer than the longest polymer relaxation time are always MF. If a DC regime has developed before then the long time rate constant is where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis. Received: 2 June 1998 / Revised: 9 July 1998 / Accepted: 10 July 1998     

Configuration space for random walk dynamics

Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a configuration to be sampled depends on a number of unusual quantities, which are explained in this paper. This has been overlooked in recent literature, where the method is advertised for the calculation of canonical expectation values. We illustrate these points for the 2d Ising model. In addition, we prove a previously conjectured equation which relates microcanonical expectation values to the spectral density. Received: 13 May 1998 / Received in final form and Accepted: 26 May 1998     

Pressure effects in ferromagnetic manganites and carrier scattering by disordered magnetic rare earths

The influence of hydrostatic pressure on the transport properties of (La_1-xR_x)_0.67Ca_0.33MnO₃ (,Tb) ferromagnetic manganites is investigated. The enhancement of the Curie temperature T_C under pressure agrees with previous data. In the paramagnetic range, the resistivity can be represented by a Mott localisation law, with a characteristic temperature T₀ decreasing with pressure. The variation of T_C with pressure is compared to the effect induced by replacing La by a magnetic rare earth in (La_1-xR_x)_0.67Sr_0.33MnO₃ manganites (, ..., Tm). The main effect is not related to the decrease of the mean radius of the cation, but to an additional scattering by the magnetic moment of the rare earth. Received: 15 May 1998 / Revised: 6 July 1998 / Accepted: 16 July 1998     

Twin-correlations in atoms

We discuss the possibility of preparing an atomic sample of atoms with minimum fluctuations in the difference between populations of two levels. A first scheme involves absorption of twin beams of light, and it presents a variant of a recent proposal for atomic spin squeezing within an excited state manifold [Kuzmich et al., Phys. Rev. Lett. 79, 4782 (1997)]. A second scheme involves atoms with two stable states, and we suggest that by use of quantum non-demolition detection and feed-back optical pumping, we may ensure a perfect agreement between the number of atoms in these two states. Received: 14 May 1998 / Revised: 10 August 1998 / Accepted: 8 October 1998     

Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

For two particles in a disordered chain of length L with on-site interaction U, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics. Received: 22 May 1998 / Received in final form: 24 August 1998 / Accepted: 4 September 1998