Diffusion Of Active Brownian Particles Far From Equilibrium

The nonequlibrium Brownian motion has attracted considerable interests since almost twenty years. In particularly, the nonlinear active brownian particles (ABP) have many applications in studying self-propelled motion of biological system. For ABP subjected both to additive and multiplicative noises, we investigate the diffusion of system. Four aspects are included in this paper.First, We introduce the motion of the ABP and analytical formula of effective diffusion coefficient.Second, We investigate the diffusion of ABP with internal energy depot. By reasonably assuming that the internal energy depot of the particle is affected by environmental fluctuations, we derive a Langevin equation which contains a multiplicative as well as an additive noise term. We study the dependences of the effective diffusion coefficient ( De ff) on both the additive and multiplicative noises. It is found that for fixed small additive noise intensity De ff varies nonmonotonously with multiplicative noise intensity, with a minimum at a finite multiplicative noise intensity, and De ff increases monotonously, however, with the multiplicative noise intensity for relatively strong additive noise; for fixed multiplicative noise intensity De ff decreases with growing additive noise intensity until it approaches a constant. An explanation is also given of the different behavior of De ff as additive and multiplicative noises approach infinity, respectively.Third, We investigate the active Brownian motion in which both the friction and noise function depend on the particle's velocity in a nonlinear way. An important subclass of such functions is given by power laws, i.e., instead of the friction constantγ0and noise function g ( v ) one include functionsγ( v )^v2α and g 2 ( v ) D ( v ^2β +κ)+ Q, respectively. The dependence of De ff on the multiplicative noise intensity D is discussed for two different cases: (i)κ= 0, (ii)κ> 0. For the limit of strong noise, we show that the diffusion coefficient is proportional to a simple power of the noise intensity and power exponent is determined by the parameterαandβ.Fourth, We investigate the diffusion of ABP which exist an bias F . We show the diffusion coefficient as a function of the bias F and obtain the giant diffusion phenomenon.