Ratchet transport for a chain of interacting charged particles

Abstract

We study analytically and numerically the overdamped, deterministic dynamics of a chain of charged, interacting particles driven by a longitudinal alternating electric field and additionally interacting with a smooth ratchet potential. We derive the equations of motion, analyze the general properties of their solutions and find the drift criterion for chain motion. For ratchet potentials of the form of a double-sine and a phase-modulated sine it is demonstrated that both, a so-called integer and fractional transport of the chain can occur. Explicit results for the directed chain transport for these two classes of ratchet potentials are presented.

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

“…[1][2][3][4][5][6][7] Generally speaking, the appearance of ratchetlike behavior requires two ingredients, departure from thermal equilibrium, either by using correlated stochastic forces or deterministic forces, and breaking of spatial and/or temporal symmetries. 4,6,[8][9][10][11][12][13][14] Many applications of the ratchet theoretical framework deal with the scenario of spatial symmetry breaking, beginning with the proposal for nonequilibrium rectifiers in Ref. 1.…”

“…In this context, the ratio of the frequencies of a biharmonic force is related with the breaking of the temporal-shift symmetry ͓given by f͑t͒ =−f͑t + T /2͒ with T being the period͔ whereas suitable choices for the driving phases and damping 20 lead to timereversal symmetry breaking. 21 This mechanism to obtain directed motion from a zero-mean force has been first proposed for particle ͑zero-dimensional͒ systems, 4,8,9 and it has recently been extended to extended systems, both classical 12,13,22,23 and quantum ones. 24 A very relevant system, mostly because its character of paradigmatic of phenomena arising in connection with topological solitons and its many applications, is the damped and driven sine-Gordon ͑sG͒ model, where m is an integer number and ⑀ 1 ͑⑀ 2 ͒ is the amplitude of the harmonic component with frequency ␦ ͑m␦͒ and phase 1 ͑ 2 ͒.…”

Mechanical coupling in flashing ratchets

“…One reason is that such studies may provide a route to models of the linear transport of biological molecular motors. A number of studies have demonstrated behavior of mechanically coupled particles which is qualitatively different than that of a single particle [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], for example: In contrast to the behavior of an individual particle, two harmonically coupled particles in a flashing ratchet undergo directed motion in the absence of thermal fluctuations [12,13]. For a flashing ratchet, two harmonically coupled particles have a smaller velocity than a single particle, while for a rocking ratchet, the coupled particles have a greater velocity [14].…”

Interaction induced directed transport in ac-driven periodic potentials

“…Despite often considered as being of single particle character, ratchets can experience a profound impact by interactions [11][12][13][14][15][16][17][18][19][20]. Specifically, interactions can accelerate single particle transport [15][16][17][18][19]21], enhance their controllability [15][16][17][18][19] and lead to one or multiple reversals [21][22][23] of the transport direction which could be observed experimentally e.g.…”

“…While most of the above works explored the impact of either linear or short range interactions in a noisy environment, we focus here on a deterministic and dissipative setup [27][28][29] of power law interacting particles (see also [14]) in a laterally oscillating lattice. This is inspired by the exceptional progress of modern atomic cooling and trapping techniques [30,31] which have allowed for particularly clean and versatile realizations of ratchets with cold atoms in ac-driven optical lattices [9,[32][33][34][35][36].…”