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We studied the transport process of overdamped Brownian particles, in a chain of asymmetric cavities, interacting through a hard-core potential. When a force is applied in opposite directions a difference in the drift velocity of the particles inside the cavity can be observed. Previous works on similar systems deal with the low-concentration regime, in which the interaction is irrelevant. In this case it was found that large particles show a stronger asymmetry in the drift velocity when a small force is applied, allowing for the separation of different size particles [Reguera et al., Phys. Rev. Lett. 108, 020604 (2012)]. We found that when the interaction between particles is considered, the behavior of the system is substantially different. For example, as concentration is increased, the small particles are the ones that show a stronger asymmetry. For the case where all the particles in the system are of the same size we took advantage of the particle-vacancy analogy to predict that the left and right currents are almost equal in a region around the concentration 0.5 despite the asymmetry of the cavity.
RESUMO
We derive and study a theoretical description for single-file diffusion, i.e., diffusion in a one-dimensional lattice of particles with hard core interaction. It is well known that for this system a tagged particle has anomalous diffusion for long times. The novelty of the present approach is that it allows for the derivation of correlations between a tagged particle and other particles of the system at a given distance with empty sites in between. The behavior of the correlation gives deeper insights into the processes involved. The numerical integration of differential equations are in good agreement with Monte Carlo simulations.
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The Boltzmann's entropy of a continuous Markov process, in local thermal equilibrium, in contact with a reservoir at temperature T , is analyzed. Assuming that the corresponding Fokker-Planck equation has constant coefficients and satisfies detailed balance, an equation for the entropy density is derived, from which it is possible to obtain expressions for the transport coefficients as functions of the diffusion matrix. Expressions for the entropy production terms of the system and of the combination of system plus reservoir are obtained. Known relations among transport coefficients are derived. The multicomponent case is also analyzed and the Prigogine theorem of minimum entropy production is derived in the context of reaction diffusion systems. The derivations presented in this paper are proposed as a framework for a deeper understanding of concepts used in nonequilibrium diffusion systems.
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We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative-refraction-index material with third-order effective electric and magnetic nonlinearities. Two coupled nonlinear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato-Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.
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The vector complex Ginzburg-Landau equation is an amplitude equation appropriate for describing instabilities in oscillatory media when the order parameter is a vector field (for example, laser light or two-component Bose condensate). It is known that this equation presents a variety of phase singularities or topological defects. We study the parameters that characterize the different kinds of defects and show that the results are useful for a better understanding of the system dynamics.
RESUMO
The consequences of introducing the polarization degree of freedom of the light are studied for the transverse patterns of a laser with detuning equal to zero. We deduce the vectorial Swift-Hohenberg amplitude equation from the corresponding Maxwell-Bloch equations. The vectorial character of the equation introduces modifications in the stability of traveling waves and new types of localized structures.