High-temperature ratchets with sawtooth potentials.

The concept of the effective potential is suggested as an efficient instrument to get a uniform analytical description of stochastic high-temperature on-off flashing and rocking ratchets. The analytical representation for the average particle velocity, obtained within this technique, allows description of ratchets with sharp potentials (and potentials with jumps in particular). For sawtooth potentials, the explicit analytical expressions for the average velocity of on-off flashing and rocking ratchets valid for arbitrary frequencies of potential energy fluctuations are derived; the difference in their high-frequency asymptotics is explored for the smooth and cusped profiles, and profiles with jumps. The origin of the difference as well as the appearance of the jump behavior in ratchet characteristics are interpreted in terms of self-similar universal solutions which give the continuous description of the effect. It is shown how the jump behavior in motor characteristics arises from the competition between the characteristic times of the system.

Diffusion of a massive particle in a periodic potential: Application to adiabatic ratchets.

We generalize a theory of diffusion of a massive particle by the way in which transport characteristics are described by analytical expressions that formally coincide with those for the overdamped massless case but contain a factor comprising the particle mass which can be calculated in terms of Risken's matrix continued fraction method (MCFM). Using this generalization, we aim to elucidate how large gradients of a periodic potential affect the current in a tilted periodic potential and the average current of adiabatically driven on-off flashing ratchets. For this reason, we perform calculations for a sawtooth potential of the period L with an arbitrary sawtooth length (l

Inertial effects in adiabatically driven flashing ratchets.

We study analytically the effect of a small inertial correction on the properties of adiabatically driven flashing ratchets. Parrondo's lemma [J. M. R. Parrondo, Phys. Rev. E 57, 7297 (1998)] is generalized to include the inertial term so as to establish the symmetry conditions allowing directed motion (other than in the overdamped massless case) and to obtain a high-temperature expansion of the motion velocity for arbitrary potential profiles. The inertial correction is thus shown to enhance the ratchet effect at all temperatures for sawtooth potentials and at high temperatures for simple potentials described by the first two harmonics. With the special choice of potentials represented by at least the first three harmonics, the correction gives rise to the motion reversal in the high-temperature region. In the low-temperature region, inertia weakens the ratchet effect, with the exception of the on-off model, where diffusion is important. The directed motion adiabatically driven by potential sign fluctuations, though forbidden in the overdamped limit, becomes possible due to purely inertial effects in neither symmetric nor antisymmetric potentials, i.e., not for commonly used sawtooth and two-sinusoid profiles.

Fluctuation-induced transport of two coupled particles: effect of the interparticle interaction.

We consider a system of two coupled particles fluctuating between two states, with different interparticle interaction potentials and particle friction coefficients. An external action drives the interstate transitions that induces reciprocating motion along the internal coordinate x (the interparticle distance). The system moves unidirectionally due to rectification of the internal motion by asymmetric friction fluctuations and thus operates as a dimeric motor that converts input energy into net movement. We focus on how the law of interaction between the particles affects the dimer transport and, in particular, the role of thermal noise in the motion inducing mechanism. It is argued that if the interaction potential behaves at large distances as x(α), depending on the value of the exponent α, the thermal noise plays a constructive (α > 2), neutral (α = 2), or destructive (α < 2) role. In the case of α = 1, corresponding piecewise linear potential profiles, an exact solution is obtained and discussed in detail.

Adiabatically driven Brownian pumps.

We investigate a Brownian pump which, being powered by a flashing ratchet mechanism, produces net particle transport through a membrane. The extension of the Parrondo's approach developed for reversible Brownian motors [Parrondo, Phys. Rev. E 57, 7297 (1998)] to adiabatically driven pumps is given. We demonstrate that the pumping mechanism becomes especially efficient when the time variation of the potential occurs adiabatically fast or adiabatically slow, in perfect analogy with adiabatically driven Brownian motors which exhibit high efficiency [Rozenbaum et al., Phys. Rev. E 85, 041116 (2012)]. At the same time, the efficiency of the pumping mechanism is shown to be less than that of Brownian motors due to fluctuations of the number of particles in the membrane.

Symmetry interplay in Brownian photomotors: From a single-molecule device to ensemble transport.

Unlike most of Brownian motor models in which the state of a point particle is described by a single scalar fluctuating parameter, we consider light-induced dichotomic fluctuations of electron density distributions in an extended molecule moving in the electrostatic periodic potential of a polar substrate. This model implies that the potential energy profiles of two motor states differ substantially and their symmetry is dictated by the interplay between the symmetries of the substrate potential and of molecular electronic states. As shown, a necessary condition for the occurrence of directed motion, the asymmetry of the potential energy profiles, is satisfied for (i) symmetric electron density distributions in molecules on asymmetric substrates and (ii) asymmetric electron density distributions in molecules on symmetric substrates. In the former case, the average velocity of directed motion is independent of molecular orientations and the ensemble of molecules moves as a whole, whereas in the latter case, oppositely oriented molecules move counterdirectionally thus causing the ensemble to diffuse. Using quantum chemical data for a specific organic-based photomotor as an example, we demonstrate that the behavior of molecular ensembles is controllable by switching on/off resonance laser radiation: they can be transported as a whole or separated into differently oriented molecules depending on the ratio of symmetric and antisymmetric contributions to the substrate electrostatic potential and to the molecular electron density distributions.

Nonequilibrium molecular transport photoinduced by potential energy fluctuations.

The mechanism of directed substrate-parallel motion of molecules caused by photoinduced potential energy fluctuations is investigated. Unlike simplistic models (e.g., an on-off ratchet), the approach suggested implies that the necessary asymmetry of the potential energy can arise not only from the asymmetry of the substrate potential but also from an asymmetric distribution of the fluctuating charge density in the molecule. The thus induced asymmetry of the potential energy governs the direction motion and enables, under certain conditions, its reversal at some frequencies of resonant laser pulses or temperature. These inferences are exemplified by the model charge distributions in the molecule and substrate, and the charge density fluctuations which are obtained by quantum chemical calculations for the realistic molecule of a substituted phenylpyrene compound on a model substrate.

Net transport due to noise-induced internal reciprocating motion.

We consider a system of two coupled Brownian particles fluctuating between two states. The fluctuations are produced by both equilibrium thermal and external nonthermal noise, the transition rates depending on the interparticle distance. An externally induced modulation of the transition rates acts on the internal degree of freedom (the interparticle distance) and generates reciprocating motion along this coordinate. The system moves unidirectionally due to rectification of the internal motion by asymmetric friction fluctuations and thus operates as a dimeric motor that converts input energy into net movement. The properties of the motor are primarily determined by the properties of the reciprocating engine, represented by the interparticle distance dynamics. Two main mechanisms are recognized by which the engine operates: energetic and informational. In the physically important cases where only one of the motion-inducing mechanisms is operative, exact solutions can be found for the model with linearly coupled particles. We focus on the informational mechanism, in which thermal noise is involved as a vital component and the reciprocating velocity exhibits a rich behavior as a function of the model parameters. An efficient rectification method for the reciprocating motion is also discussed.

Photoinduced molecular transport in biological environments based on dipole moment fluctuations.

Consideration is given to the possibility of a molecule moving unidirectionally in an electric field of a polar periodic substrate as a result of the fluctuations of molecular dipole moment occurring on the photoexcitation of the molecule. As estimated for such motion, molecules with sufficiently long fluorescence and strongly differing dipole moments in the ground and excited states can move with an average velocity of the same order as that typical of protein motors such as kinesin. This effect results from the mutual compensation of two opposite factors acting in dipole photomotors, namely, a lower energy of interaction with the substrate relative to that for protein motors and a shorter excited-state lifetime as compared with the duration of the hydrolytic splitting of adenosinetriphosphate in protein motors.