Anomalous Transports Of Particle In Periodic Potential Systems

Anomalous transports of particle,which include absolute negative mobility(ANM)and current reversal(CR),usually exist in periodic systems,and people have paid more and more attention to it.Investigations in the transports not only help people understand transports of matter and energy in periodic systems,but also provide some guidance functions,in separation of long DNA molecules,protein separation,etc.By means of combination of theoretical analysis and numerical calculation-s,anomalous transports of particle in space-time separately periodic systems for stochastic and deterministic cases,and deterministic space-time inseparately peri-odic systems were investigated.Research results were summarized as follows:1.Anomalous transports of space-time separately periodic systems in the s-tochastic case were investigated in the respect of normal and anomalous diffusions.(1)spatially symmetric periodic system driven by correlated noises(correlation be-tween additive noise and multiplicative noise)and symmetric periodic driving were considered.Numerical results indicates that:the correlated noises can induce CR of the system,and the driving and the correlation between the noises are two im-portant ingredients for the CR in the system.(2)Symmetric periodic system and time-delayed ratchet system driven by the levy noise(anomalous diffusion)were in-vestigated,respectively.The former study indicates:the levy noise is able to cause ANM in the symmetric periodic system,moreover,the ANM occurs in the region of super diffusion while disappears in the region of normal diffusion,depending on stable index and symmetry parameter of the levy noise.The latter study indicates:in the time-delayed ratchet system,the time delay effect not only induces multiple CRs,but also brings about ANM.Furthermore,The CRs and ANM phenomena can take place in the region of superdiffusion,while disappear in the regions of normal diffusion.2.Anomalous transports of space-time separately periodic systems in the deter-ministic case were studied.(1)Considering transport of a particle in a gating ratchet potential without noise and chaos.In the system,adjusting system parameter(e.g.,mass of the particle,the frequency of the spatial potential,etc)can make ANM of the system emerge arbitrary segments,even up to more than thirty.According to time evolution of position of the particle and generalized potential at particular moments,the anomalous transports of the particle were analyzed via nonlinear dynamic theory.The analysis shows that occurrence of the ANM needs three necessary conditions:(?)Frequencies of multiplicative and additive periodic signals of the system must be unequal so that temporal symmetry of the system is broken;(?)An acceleration process to make the particle move against the external constant force;(?)Some pe-riodic potential wells to lock the particle as the generalized potential tiles to right.If there occurs noise or chaos,the particle can not be trapped in the wells,then it will obtain a greater positive acceleration and move along positive direction,which leads to normal transport of the system.(2)Transports of an inertial particle in a symmetric periodic potential subjected to an external driving force were considered,where mass of the particle is modulated sine-periodically.Numerical results shown that the mass modulation and the driving force can result in temporal symmetry breaking,and brings about multiple CRs and ANM.Furthermore,current of the system depends on amplitude and frequency of the mass modulation.3.Anomalous transports of particle in space-time inseparably periodic systems were investigated.(1)Considering transports of an inertial particle in a spatially symmetric periodic potential,where phase of the potential is controlled by two time periodic modulations.Research results indicates that as frequencies of the modula-tions are not equal,symmetry of the system will be broken.Further investigations shown that there exists phenomena of multiple CRs and ANM in the system.In addition,current of the system depends on amplitudes and frequencies of the phase modulation.In the presence of one time periodic modulation,the system is devoid of the anomalous transports.(2)Transports of a inertia particle in traveling wave system subjected to a periodic driving was studied.The results are as follows:on-ly with the help of the driving,can the particle move against motion direction of the traveling wave and form a counter motion.That is,the driving is a important ingredient for the anomalous transport of the traveling wave system.Furthermore,multiple CRs and ANM were found in the system.