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It is well known that at low temperatures, the direction of motion for a quantum rocking ratchet in an asymmetric periodic potential (with a period L and an energy barrier V0), driven by an external fluctuating force F (F=0), can be opposite to the direction for the analogous classical ratchet operating at high temperature (Reimann et al, Phys. Rev. Lett. 1997, 79, 10). In the present work, within the semiclassical approximation and taking into account zero‐point fluctuations of a quantum particle in the minima of a sawtooth potential of an arbitrary asymmetry at the temperature of absolute zero, we obtain analytical expressions for the tunneling current in the rocking ratchet. These expressions allowed us to obtain the dependencies of the ratio FL/V0, at which the motion direction is reversed, on the asymmetry parameter and other parameters of the system. Similar results are obtained for a particle in a two‐sinusoidal potential. [ABSTRACT FROM AUTHOR]

We present a review of analytical approaches involved in developing the ratchet theory, which are based on the model of extremely asymmetric sawtooth potential. Analytical expressions are given for the average velocity of ratchets which operate in various motion modes, namely, motion induced by dichotomous half‐period shifts of potential profiles, adiabatic and high‐temperature modes, and motion induced by small fluctuations of an arbitrary type. The presence of jumps in the periodic extremely asymmetric sawtooth potential profile leads to a number of features of the obtained solutions which follow from the competition of the reverse sliding time tending to infinity with high fluctuation frequencies. The resulting dependences of the average velocity on the ratchet parameters clearly demonstrate that the motion direction can be controlled by tuning the frequency and temperature. The heuristic value of the presented models for controlling nanoparticle transport is discussed. [ABSTRACT FROM AUTHOR]

The operating properties of different‐type Brownian photomotors have been compared in relation to the symmetry interplay between their moving (particle/molecule) and immovable (substrate) units. As found, essentially different symmetry constraints and hence different motor behavior are characteristic of molecules if their electron density redistribution on excitation involves only odd‐order or only even‐order multipole moments. The two respective types of molecules give rise to dipole and quadrupole photomotors. Purely dipole photomotors can operate only on substrates with symmetric charge distribution and their ensemble with random molecular orientations undergoes equidirectional diffusion rather than directed motion. Contrary to this, purely quadrupole photomotors need substrates with antisymmetric charge distribution for directed motion to occur and they can move directionally in an ensemble. Also, quadrupole photomotors provide much smaller velocities of directed motion than their dipole counterparts (as a result of the much weaker interaction of quadrupoles than dipoles with an electric field). The generic distinctions between the two photomotor types are exemplified by donor‐acceptor‐substituted stilbenoids (dipole molecules) and symmetric squaraines (quadrupole molecules). The model used affords the rational design of photomotors by the selection of promising moving molecules and by the continuous wide‐range tuning of charge‐distribution symmetry in substrates. [ABSTRACT FROM AUTHOR]

The directed mechanical motion of nanoscale objects along a phase boundary can result from strongly nonequilibrium processes, which transfer the energy of various external sources to the system. This effect is particularly relevant in Brownian (molecular or biological) motors known for their high efficiency of chemical-to-kinetic energy conversion. Here, we formulate the necessary conditions for nanoparticle surface-parallel motion to occur under the action of external nonequilibrium fluctuations of various nature; the ways to provide such conditions are also considered. As shown, the magnitude and sign of the average directed velocity are dictated by the competition between the spatial and temporal asymmetry of the potential energy. The theoretical models are exemplified by high-efficiency Brownian nanoengines, molecular pumps, dipole rotators, and photo-induced molecular motors. The latter serve to illustrate the kinematic controllability of motors by varying their molecular structure and photoexcitation parameters. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [ABSTRACT FROM AUTHOR]