Performance characteristics of Brownian motors

Abstract

Brownian motors are nonequilibrium systems that rectify thermal fluctuations to achieve directed motion, using spatial or temporal asymmetry. We provide a tutorial introduction to this basic concept using the well-known example of a flashing ratchet, discussing the micro- to nanoscopic scale on which such motors can operate. Because of the crucial role of thermal noise, the characterization of the performance of Brownian motors must include their fluctuations, and we review suitable performance measures for motor coherency and efficiency. Specifically, we highlight that it is possible to determine the energy efficiency of Brownian motors by measuring their velocity fluctuations, without detailed knowledge of the motor function and its energy input. Finally, we exemplify these concepts using a model for an artificial single-molecule motor with internal degrees of freedom.

Scaling of characteristic frequencies of organic electronic ratchets

“…11 Apart from these two single-particle timescales, a third timescale related to the collective response can be identified, namely the time the charge carrier distribution needs to globally equilibrate, i.e. to redistribute itself over the entire device after a perturbation.…”

Quantum ratchet transport with minimal dispersion rate

“…The diffusion is naturally quantified by using the dispersion of the wave packet σ 2 (t) = x(t) 2 − x(t) 2 . In the case of normal diffusion, dispersion scales like σ 2 (t) ∝ t, and in the classical limit it perfectly describes the kinetics of over- [23,25,26] and underdamped [27] ratchets. Yet the situation with normal diffusion is rarely the case even in the classical, dissipation-free limit, where ac-driven Hamiltonian systems demonstrate typically superdiffusive kinetics σ 2 (t) ∝ t γ with a parameter-sensitive exponent 1 < γ < 2 [30,31].…”

“…Yet the coherent quantum transport in ac-driven periodic potentials is severely hampered by diffusion, additionally enhanced by tunneling effects [20]. The issue of the transport efficiency [21][22][23] now becomes of importance, meaning that one should search for a set of optimal parameters in order to maximize the correspondingly chosen efficiency measure. It is intuitive that the ratchet transport with large transport velocity and minimal dispersion rate would be preferable in the context of the delivery problem.…”

Diffusion enhancement in on/off ratchets

“…The shape of the curve only depends on a, all other parameters are contained in the scaled axis variables which include the temperature, viscosity, and particle radius. The scaling can be explained by describing the diffusion with an expression for the fraction of particles that is displaced to the spatially nearest trap, for t off ( (1 À a) 2 L 2 /2 D ES , 11,29 as…”