Enhancement of mobilities in a pinned multidomain crystal

Mobility properties inside and around degenerate domains of an elastic lattice partially pinned on a square array of traps are explored by means of a fully controllable model system of macroscopic particles. We focus on the different configurations obtained for filling ratios equal to 1 or 2 when the pinning strength is lowered. These theoretically expected but never observed configurations are degenerated, which implies the existence of a multidomain crystal. We show that the distinction between trapped and untrapped particles that is made in the case of strong pinning is not relevant for such a weaker pinning. Indeed, one ought to distinguish between particles inside or around the domains associated to positional degeneracies. The possible consequences on the depinning dynamics of the lattice are discussed.Comment: 7 pages, 10 figures Version 2 : longer versio

Local Symmetries and Order-Disorder Transitions in Small Macroscopic Wigner Islands

The influence of local order on the disordering scenario of small Wigner islands is discussed. A first disordering step is put in evidence by the time correlation functions and is linked to individual excitations resulting in configuration transitions, which are very sensitive to the local symmetries. This is followed by two other transitions, corresponding to orthoradial and radial diffusion, for which both individual and collective excitations play a significant role. Finally, we show that, contrary to large systems, the focus that is commonly made on collective excitations for such small systems through the Lindemann criterion has to be made carefully in order to clearly identify the relative contributions in the whole disordering process.Comment: 14 pages, 10 figure

Comment on ''Elastic constants from microscopic strain fluctuations''

International audienceSengupta [Phys. Rev. E 61, 1072 (2000)] presented an elegant and simple finite-size scaling method for the calculation of elastic constants and their corresponding correlation lengths, which is suitable for many finite discrete systems considered through simulations or experiments. We take into account a mathematical finite-size effect that was neglected by the authors in order to propose a more accurate method. Consequences on the authors' results are also discussed

Local symmetries and order-disorder transitions in small macroscopic Wigner islands

International audienceThe influence of local order on the disordering scenario of small Wigner islands is discussed. A first disordering step is put in evidence by the time correlation functions and is linked to individual excitations resulting in configuration transitions, which are very sensitive to the local symmetries. This is followed by two other transitions, corresponding to orthoradial and radial diffusion, for which both individual and collective excitations play a significant role. Finally, we show that, contrary to large systems, the focus that is commonly made on collective excitations for such small systems through the Lindemann criterion has to be made carefully in order to clearly identify the relative contributions in the whole disordering process

On the physical importance of the "logarithmic transformation" in statistical mechanics

The basic functions of statistical mechanics (number of accessible states, or partition function, or grand partition function,..., according to the statistical ensemble considered) are most often replaced by their logarithms (entropy, or free energy, or grand potential,...). This "logarithmic transformation" is systematically used, in particular, to approximate probability distributions. Its essential virtue is then to enlarge considerably the validity domain of the approximation. The origin of such an interesting property lies in the extensive nature of the "logarithmic quantities". However, the traditional proof of the canonical distribution is shown by the foregoing general argument to have limited validity, excluding the physically most important values of the energy. This unexpected though unavoidable problem can be overcome in practice, because the "logarithmic transform" of the probability of the various microstates, not the probability itself, plays the crucial role in the physical predictions. Now this logarithm of the canonical probability is given, to an excellent approximation, by the usual proof