Study On The Transport Phenomena Of Two Coupled Particles In Asymmetric Systems

Transport phenomena exists widely in nature, and the study of them has important significance in both theories and practices. As a unique classification, transport in periodic asymmetric systems does not require the existence of net force or the gradient of corresponding physical quantity. The breaking of spatial symmetry combined with an unbiased external disturbance with certain self-correlation time is enough to make the system generate directional transport. This kind of transport is called ratchet effect or Brownian motor. Normally in macroscale system, the particle is treated as a single mass point, thus the impact of its structure on its movement behavior is ignored. However, sometimes such neglects are not appropriate, especially when the size of the particle is comparable to the spatial structure of the system. At this time, the internal interactions and the asymmetry of the particle’s structure will have great impacts on the transport properties of the system, even cause the reversals of the transport currents.To study the influence of the interactions inner particles on the transport properties of the system, we consider two elastic coupling identical particles, which are placed in the same thermal environment and asymmetric saw-tooth potential, and are subject to external stochastic colored perturbations. We focus on the relationship between the transport property and the elastic coupling interaction, and find that the current of the system depends on the coupling parameters, especially when the equilibrium distance of the coupled particles is between the two slopes of the saw-tooth potential, the transport direction of the coupled particles will reverse with a certain harmonic coupling strength. In order to explain the phenomenon of current reversal, we compare two limit situations of no coupling and rigid coupling. In the situation of no coupling, two particles move independently in the original saw-tooth potential, while in the situation of rigid coupling, the two particles can be regarded as an equivalent single particle in an effective potential. By comparing the equivalent potential with the original potential, we find that when the equilibrium distance is between the two slopes of the original potential, the asymmetry of the effective potential could be reversed, which results in the current reversal.In macroscale situation, thermal noises are always treated as Gaussian white noises. However, many researches show that the correlation time of the thermal noises can’t be neglected in molecular scale systems, therefore it is not suitable to treat them as white noises in molecular scale systems. Due to the molecules’ structure, it is also not suitable to treat them as single mass points. The directions of the molecules would also have impacts on their motion behaviors. In order to study the influence of the thermal noises and the asymmetries of the molecules on the transport behaviors of the systems, we consider a simple asymmetric molecule model which is made up of two different parts, and maintain its direction. We treat the motions of the molecule in different directions with different damping coefficients, and select appropriate model to simulate the thermal noise. By numerical calculation we find that the asymmetric molecule shows directed motion towards the smaller damping direction, which shows that the asymmetries of molecules combined with the colored thermal noises are enable to generate the directional movements of the molecules. However, if the directions of the molecules are not maintained, this kind of directional movements will soon disappear, therefore this phenomenon does not violate the second law of thermodynamics.