Enhanced fluctuations of interacting particles confined in a box
Laboratoire MSC. UMR CNRS 7057, Université Paris Diderot, 75205 Paris Cedex 13, France.Physical Review E (Impact Factor: 2.29). 04/2012; 85(4 Pt 1):041137. DOI: 10.1103/PhysRevE.85.041137
We study the position fluctuations of interacting particles aligned in a finite cell that avoid any crossing in equilibrium with a thermal bath. The focus is put on the influence of the confining force directed along the cell length. We show that the system may be modeled as a 1D chain of particles with identical masses, linked with linear springs of varying spring constants. The confining force may be accounted for by linear springs linked to the walls. When the confining force range is increased toward the inside of the chain, a paradoxical behavior is exhibited. The outermost particles fluctuations are enhanced, whereas those of the inner particles are reduced. A minimum of fluctuations is observed at a distance of the cell extremities that scales linearly with the confining force range. Those features are in very good agreement with the model. Moreover, the simulations exhibit an asymmetry in their fluctuations which is an anharmonic effect. It is characterized by the measurement of the skewness, which is found to be strictly positive for the outer particles when the confining force is short ranged.
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ABSTRACT: We study with numerical simulations the transverse fluctuations in quasi-one-dimensional systems of particles in a thermal bath, near the zigzag transition. We show that close to the zigzag threshold, the transverse fluctuations exhibit an anormal diffusion, characterized by a mean square displacement that increases as the square root of time. In contrast with the longitudinal fluctuations, this behavior of the transverse fluctuations cannot be explained by the single-file ordering. We provide an analytical modelization, and in the thermodynamic limit we demonstrate the existence of this subdiffusive regime near the zigzag transition, showing that it results from overdamped collective modes of the system. These calculations are extended to finite systems, in excellent agreement with the simulations data. We also exhibit some effects of the thermal fluctuations on the zigzag transition, and analyze them in the light of stochastic bifurcation theory.Physical Review E 03/2013; 87(3). DOI:10.1103/PhysRevE.87.032163 · 2.29 Impact Factor
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ABSTRACT: We study the zigzag transition in a system of particles with screened electrostatic interaction, submitted to a thermal noise. At finite temperature, this configurational phase transition is an example of noisy supercritical pitchfork bifurcation. The measurements of transverse fluctuations allow a complete description of the bifurcation region, which takes place between the deterministic threshold and a thermal threshold beyond which thermal fluctuations do not allow the system to flip between the symmetric zigzag configurations. We show that a divergence of the saturation time for the transverse fluctuations allows a precise and unambiguous definition of this thermal threshold. Its evolution with the temperature is shown to be in good agreement with theoretical predictions from noisy bifurcation theory.Physical Review E 06/2013; 87(6-1):062135. DOI:10.1103/PhysRevE.87.062135 · 2.29 Impact Factor
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