The flashing ratchet and unidirectional transport of matter

We study the flashing ratchet model of a Brownian motor, which consists in cyclical switching between the Fokker-Planck equation with an asymmetric ratchet-like potential and the pure diffusion equation. We show that the motor really performs unidirectional transport of mass, for proper parameters of the model, by analyzing the attractor of the problem and the stationary vector of a related Markov chain.Comment: 11 page

Brownian Motors driven by Particle Exchange

We extend the Langevin dynamics so that particles can be exchanged with a particle reservoir. We show that grand canonical ensembles are realized at equilibrium and derive the relations of thermodynamics for processes between equilibrium states. As an application of the proposed evolution rule, we devise a simple model of Brownian motors driven by particle exchange. KEYWORDS: Langevin Dynamics, Thermodynamics, Open SystemsComment: 5 pages, late

Rocking ratchets in 2D Josephson networks: collective effects and current reversal

A detailed numerical study on the directed motion of ac-driven vortices and antivortices in 2D Josephson junction arrays (JJA) with an asymmetric periodic pinning potential is reported. Dc-voltage rectification shows a strong dependence on vortex density as well as an inversion of the vortex flow direction with ac amplitude for a wide range of vortex density around $f$=1/2 ($f$=$Ha^2 / \Phi_0$), in good agreement with recent experiments by Shal\'om and Pastoriza [Phys. Rev. Lett. {\bf 94}, 177001 (2005)]. The study of vortex structures, spatial and temporal correlations, and vortex-antivortex pairs formation gives insight into a purely collective mechanism behind the current reversal effect.Comment: 4 pages, 5 figures. Accepted for publication in Phys. Rev. Let

Interaction of molecular motors can enhance their efficiency

Particles moving in oscillating potential with broken mirror symmetry are considered. We calculate their energetic efficiency, when acting as molecular motors carrying a load against external force. It is shown that interaction between particles enhances the efficiency in wide range of parameters. Possible consequences for artificial molecular motors are discussed.Comment: 6 pages, 8 figure

Symmetry Relations for Trajectories of a Brownian Motor

A Brownian Motor is a nanoscale or molecular device that combines the effects of thermal noise, spatial or temporal asymmetry, and directionless input energy to drive directed motion. Because of the input energy, Brownian motors function away from thermodynamic equilibrium and concepts such as linear response theory, fluctuation dissipation relations, and detailed balance do not apply. The {\em generalized} fluctuation-dissipation relation, however, states that even under strongly thermodynamically non-equilibrium conditions the ratio of the probability of a transition to the probability of the time-reverse of that transition is the exponent of the change in the internal energy of the system due to the transition. Here, we derive an extension of the generalized fluctuation dissipation theorem for a Brownian motor for the ratio between the probability for the motor to take a forward step and the probability to take a backward step

Generic Quantum Ratchet Accelerator with Full Classical Chaos

A simple model of quantum ratchet transport that can generate unbounded linear acceleration of the quantum ratchet current is proposed, with the underlying classical dynamics fully chaotic. The results demonstrate that generic acceleration of quantum ratchet transport can occur with any type of classical phase space structure. The quantum ratchet transport with full classical chaos is also shown to be very robust to noise due to the large linear acceleration afforded by the quantum dynamics. One possible experiment allowing observation of these predictions is suggested.Comment: 4 pages, 4 figure

Equilibrium Chemical Engines

An equilibrium reversible cycle with a certain engine to transduce the energy of any chemical reaction into mechanical energy is proposed. The efficiency for chemical energy transduction is also defined so as to be compared with Carnot efficiency. Relevance to the study of protein motors is discussed. KEYWORDS: Chemical thermodynamics, Engine, Efficiency, Molecular machine.Comment: 5 pages, late

Rectifying fluctuations in an optical lattice

We have realized a Brownian motor by using cold atoms in a dissipative optical lattice as a model system. In our experiment the optical potential is spatially symmetric and the time-symmetry of the system is broken by applying appropriate zero-mean ac forces. We identify a regime of rectification of forces and a regime of rectification of fluctuations, the latter corresponding to the realization of a Brownian motor

Efficiency of Energy Transduction in a Molecular Chemical Engine

A simple model of the two-state ratchet type is proposed for molecular chemical engines that convert chemical free energy into mechanical work and vice versa. The engine works by catalyzing a chemical reaction and turning a rotor. Analytical expressions are obtained for the dependences of rotation and reaction rates on the concentrations of reactant and product molecules, from which the performance of the engine is analyzed. In particular, the efficiency of energy transduction is discussed in some detail.Comment: 4 pages, 4 fugures; title modified, figures 2 and 3 modified, content changed (pages 1 and 4, mainly), references adde