Numerical study of relaxation in electron glasses

We perform a numerical simulation of energy relaxation in three-dimensional electron glasses in the strongly localized regime at finite temperatures. We consider systems with no interactions, with long-range Coulomb interactions and with short-range interactions, obtaining a power law relaxation with an exponent of 0.15, which is independent of the parameters of the problem and of the type of interaction. At very long times, we always find an exponential regime whose characteristic time strongly depends on temperature, system size, interaction type and localization radius. We extrapolate the longest relaxation time to macroscopic sizes and, for interacting samples, obtain values much larger than the measuring time. We finally study the number of electrons participating in the relaxation processes of very low energy configurations.Comment: 6 eps figures. To be published in Phys. Rev.

Length Distributions in Loop Soups

Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show how to calculate moments of these distributions using $CP^{n-1}$ or $RP^{n-1}$ and O(n) $\sigma$ models together with replica techniques. The resulting joint length distribution for macroscopic loops is Poisson-Dirichlet with a parameter $\theta$ fixed by the loop fugacity and by symmetries of the ensemble. We also discuss features of the length distribution for shorter loops, and use numerical simulations to test and illustrate our conclusions.Comment: 4.5 page

Charging of highly resistive granular metal films

We have used the Scanning Kelvin probe microscopy technique to monitor the charging process of highly resistive granular thin films. The sample is connected to two leads and is separated by an insulator layer from a gate electrode. When a gate voltage is applied, charges enter from the leads and rearrange across the sample. We find very slow processes with characteristic charging times exponentially distributed over a wide range of values, resulting in a logarithmic relaxation to equilibrium. After the gate voltage has been switched off, the system again relaxes logarithmically slowly to the new equilibrium. The results cannot be explained with diffusion models, but most of them can be understood with a hopping percolation model, in which the localization length is shorter than the typical site separation. The technique is very promising for the study of slow phenomena in highly resistive systems and will be able to estimate the conductance of these systems when direct macroscopic measurement techniques are not sensitive enough.Comment: 8 pages, 7 figure

Search for charginos, neutralinos, and gravitinos at LEP

The hep-ex data base was decided not to be an appropriate place to make DELPHI notes public. Sorry for the inconvenience.Comment: the paper should not have been made publi

Platinum(0)-mediated C–O bond activation of ethers via an SN2 mechanism

A computational study of the C(methyl)–O bond activation of fluorinated aryl methyl ethers by a platinum(0) complex Pt(PCyp3)2 (Cyp = cyclopentyl) (N. A. Jasim, R. N. Perutz, B. Procacci and A. C. Whitwood, Chem. Commun., 2014, 50, 3914) demonstrates that the reaction proceeds via an SN2 mechanism. Nucleophilic attack of Pt(0) generates an ion pair consisting of a T-shaped platinum cation with an agostic interaction with a cyclopentyl group and a fluoroaryloxy anion. This ion-pair is converted to a 4-coordinate Pt(II) product trans-[PtMe(OArF)(PCyp3)2]. Structure-reactivity correlations are fully consistent with this mechanism. The Gibbs energy of activation is calculated to be substantially higher for aryl methyl ethers without fluorine substituents and higher still for alkyl methyl ethers. These conclusions are in accord with the experimental results. Further support was obtained in an experimental study of the reaction of Pt(PCy3)2 with 2,3,5,6-tetrafluoro-4-allyloxypyridine yielding the salt of the Pt(η3-allyl) cation and the tetrafluoropyridinolate anion [Pt(PCy3)2(η3-allyl)][OC5NF4]. The calculated activation energy for this reaction is significantly lower than that for fluorinated aryl methyl ethers