Speaker
Description
Phenomena of Brownian particle transport and diffusion in tilted periodic potentials are realized in many diverse systems. Superionic conductors, magnetic ratchets, optical lattices, charge-density waves, granular gases, Josephson junctions, automatic phase-lock frequency control systems are some prominent examples. These phenomena have been studied meticulously in recent decades [1]. These investigations produced a host of intriguing discoveries, including dispersionless transport. Such a coherent motion of the packet of particles formed after them leaving the initial potential well under the action of the constant bias force was reported in [2].
We reassess the “dispersionless transport regime” of Brownian particles in tilted periodic potentials. We show that the particles exhibit normal diffusive motion right after transitioning into the running state dragged by the constant bias force. No special transient dynamics appears, contrary to conjectures in the previous studies. The observed flat segment in the dispersion evolution curve is solely due to the broad spatial distribution of particles formed in the early superdiffusion stage. We quantitatively describe the whole evolution of the distribution function during superdiffusion and the transition to the normal diffusion that follows, in the framework of the 2-well potential in the velocity space model. We show that the superdiffusion exponent is α = 3. Estimate of the duration of the ostensible “dispersionless regime” is provided. It is shown to diverge exponentially as the temperature decreases to zero.
[1] P. Hanggi, F. Marchesoni, Rev. of Mod. Phys. 81 (2009) 387.
[2] K. Lindenberg, J.M. Sancho, A.M. Lacasta, I. M. Sokolov, Phys. Rev. Let. 98 (2007) 020602.
