Vortex and translational currents due to broken time-space symmetries

Vibrational mechanics in higher dimension: Tuning potential landscapes

This work extends the domain of vibrational mechanics to higher dimensions, with fast vibrations applied to different directions. In particular, the presented analysis considers the case of a split biharmonic drive, where harmonics of frequency ω and 2ω are applied to orthogonal directions in a two-dimensional setting. It is shown, both numerically and with analytic calculations, that this determines a highly tunable effective potential with the same symmetry as the original one. The driving allows one not only to tune the amplitude of the potential, but also to introduce an arbitrary spatial translation in the direction corresponding to the 2ω driving. The setup allows for generalization to implement translations in an arbitrary direction within the two-dimensional landscapes. The same principles also apply to three-dimensional periodic potentials.

Multiple Current Reversals Using Superimposed Driven Lattices

We demonstrate that directed transport of particles in a two dimensional driven lattice can be dynamically reversed multiple times by superimposing additional spatially localized lattices on top of a background lattice. The timescales of such current reversals can be flexibly controlled by adjusting the spatial locations of the superimposed lattices. The key principle behind the current reversals is the conversion of the particle dynamics from chaotic to ballistic, which allow the particles to explore regions of the underlying phase space which are inaccessible otherwise. Our results can be experimentally realized using cold atoms in driven optical lattices and allow for the control of transport of atomic ensembles in such setups.

SQUID ratchet: Statistics of transitions in dynamical localization

We study occupation of certain regions of phase space of an asymmetric superconducting quantum interference device (SQUID) driven by thermal noise, subjected to an external ac current and threaded by a constant magnetic flux. Thermally activated transitions between the states which reflect three deterministic attractors are analyzed in the regime of the noise induced dynamical localization of the Josephson phase velocity, i.e., there is a temperature interval in which the conditional probability of the voltage to remain in one of the states is very close to one. Implications of this phenomenon on the dc voltage drop across the SQUID are discussed. We detect the emergence of the power law tails in a residence time probability distribution of the Josephson phase velocity and discuss the role of symmetry breaking in dynamical localization induced by thermal noise. This phenomenon illustrates how deterministic-like behavior may be extracted from randomness by stochasticity itself. It reveals another face of noise.

Directed motion of spheres induced by unbiased driving forces in viscous fluids beyond the Stokes' law regime

The emergence of directed motion is investigated in a system consisting of a sphere immersed in a viscous fluid and subjected to time-periodic forces of zero average. The directed motion arises from the combined action of a nonlinear drag force and the applied driving forces, in the absence of any periodic substrate potential. Necessary conditions for the existence of such directed motion are obtained and an analytical expression for the average terminal velocity is derived within the adiabatic approximation. Special attention is paid to the case of two mutually perpendicular forces with sinusoidal time dependence, one with twice the period of the other. It is shown that, although neither of these two forces induces directed motion when acting separately, when added together, the resultant force generates directed motion along the direction of the force with the shortest period. The dependence of the average terminal velocity on the system parameters is analyzed numerically and compared with that obtained using the adiabatic approximation. Among other results, it is found that, for appropriate parameter values, the direction of the average terminal velocity can be reversed by varying the forcing strength. Furthermore, certain aspects of the observed phenomenology are explained by means of symmetry arguments.

Symmetry breaking: Abnormal transport induced by mass modulation

Here, we investigate transport of an inertial particle in a symmetric periodic potential and subjected to an external signal, such that mass of the particle is modulated sinusoidally. Our numerical results indicate that the mass modulation can induce abnormal transport in the system, whereas no current appears in the case of constant mass. In the absence of external bias, direction of mean velocity of the particle changes several times as amplitude and frequency of the mass modulation are varied, i.e., a multiple current reversals (CR) phenomenon. The multiple CRs result from temporal symmetry breaking of the system. In the presence of external bias, multiple absolute negative mobilities (ANM) take place in the system. Intrinsic physical mechanisms responsible for the occurrence of the multiple ANMs are analyzed in detail.

Omnidirectional Transport in Fully Reconfigurable Two Dimensional Optical Ratchets

A fully reconfigurable two-dimensional (2D) rocking ratchet system created with holographic optical micromanipulation is presented. We can generate optical potentials with the geometry of any Bravais lattice in 2D and introduce a spatial asymmetry with arbitrary orientation. Nontrivial directed transport of Brownian particles along different directions is demonstrated numerically and experimentally, including on axis, perpendicular, and oblique with respect to an unbiased ac driving. The most important aspect to define the current direction is shown to be the asymmetry and not the driving orientation, and yet we show a system in which the asymmetry orientation of each potential well does not coincide with the transport direction, suggesting an additional symmetry breaking as a result of a coupling with the lattice configuration. Our experimental device, due to its versatility, opens up a new range of possibilities in the study of nonequilibrium dynamics at the microscopic level.

Freezing, accelerating, and slowing directed currents in real time with superimposed driven lattices

We provide a generic scheme offering real-time control of directed particle transport using superimposed driven lattices. This scheme allows one to accelerate, slow, and freeze the transport on demand by switching one of the lattices subsequently on and off. The underlying physical mechanism hinges on a systematic opening and closing of channels between transporting and nontransporting phase space structures upon switching and exploits cantori structures which generate memory effects in the population of these structures. Our results should allow for real-time control of cold thermal atomic ensembles in optical lattices but might also be useful as a design principle for targeted delivery of molecules or colloids in optical devices.

Hidden Symmetries, Instabilities, and Current Suppression in Brownian Ratchets

The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetry-breaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand. When the appropriate conditions are satisfied, symmetry-related trajectories with opposite current are thought to balance each other, yielding suppression of transport. The direction of the current can be precisely controlled around these symmetry points by finely tuning the driving parameters. Here we demonstrate, by studying a prototypical Brownian ratchet system, the existence of hidden symmetries, which escape identification by the standard symmetry analysis, and which require different theoretical tools for their revelation. Furthermore, we show that system instabilities may lead to spontaneous symmetry breaking with unexpected generation of directed transport.

Robust unidirectional rotation in three-tooth Brownian rotary ratchet systems

We apply a simple Brownian ratchet model to an artificial molecular rotary system mounted in a biological membrane, in which the rotor always maintains unidirectional rotation in response to a linearly polarized weak ac field. Because the rotor and stator compose a ratchet system, we describe the motion of the rotor tip with the Langevin equation for a particle in a two-dimensional three-tooth ratchet potential of threefold symmetry. Unidirectional rotation can be induced under the field and optimized by stochastic resonance, wherein the mean angular momentum (MAM) of the rotor exhibits a bell-shaped curve for the noise strength. We obtain analytical expressions for the MAM and power loss from the corresponding Fokker-Planck equation, via a Markov transition model for coarse-grained states (six-state model). The MAM expression reveals a significant effect depending on the chirality of the ratchet potential: in achiral cases, the MAM approximately vanishes with respect to the polarization angle φ of the field; in chiral cases, the MAM does not crucially depend on φ, but depends on the direction of the ratchet; i.e., the parity of the unidirectional rotation is inherent in the ratchet structure. This feature is useful for artificial rotary systems to maintain robust unidirectional rotation independent of the mounting condition.

Control of transport in two-dimensional systems via dynamical decoupling of degrees of freedom with quasiperiodic driving fields

We consider the problem of the control of transport in higher-dimensional periodic structures by applied ac fields. In a generic crystal, transverse degrees of freedom are coupled, and this makes the control of motion difficult to implement. We show, both with simulations and with an analytical functional expansion on the driving amplitudes, that the use of quasiperiodic driving significantly suppresses the coupling between transverse degrees of freedom. This allows a precise control of the transport, and does not require a detailed knowledge of the crystal geometry.

Design of two-tooth unidirectional rotary-ratchet molecular machines driven by linearly polarized ac fields

An artificial molecular rotor system mounted in a biological membrane, which can unidirectionally rotate in response to weak pumping from a linearly polarized ac field, is modeled. The dynamics of the rotor unit are described by the Langevin equation for a particle in a two-dimensional bistable potential with a two-tooth ratchet structure. This model reveals effects due to the two-dimensionality of the ratchet and the polarization of the applied field. First, we demonstrate that a unidirectional rotation appears with stochastic resonance exhibiting a bell-shaped peak for noise intensity in the mean angular momentum (MAM) of the rotor. An analytical expression for the MAM, (L), is obtained on the basis of a four-state Markov approximation. Second, a significant effect due to torsional nonlinearity (representing the ratchet-like structure) in the potential geometry is quantified: in the absence of torsion, the MAM depends on the polarization angle φ of the applied field as (L) sin(2φ), whereas in the presence of torsion, an additional bias appears in the MAM as (L)(bias + sin(2φ)). It is found that this effect can be used to make the rotor system robustly maintain rotation in a single direction independent of the mounting conditions. Possible designs for an artificial molecular rotor system using the torsion effect are discussed.

Controlling chaotic transport in two-dimensional periodic potentials

We uncover and characterize different chaotic transport scenarios in perfect two-dimensional periodic potentials by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect (i.e., with no directed transport by symmetry breaking of zero-mean forces). After identifying relevant symmetries of the equations of motion, analytical estimates in parameter space for the occurrence of different transport scenarios are provided and confirmed by numerical simulations. These scenarios are highly sensitive to variations of the system's asymmetry parameters, including the eccentricity of the two-dimensional periodic potential and the direction of dc and ac forces, which could be useful for particle sorting purposes in those cases where chaos is unavoidable.

Directing Brownian motion on a periodic surface

We consider an overdamped Brownian particle, exposed to a two-dimensional, square lattice potential and a rectangular ac drive. Depending on the driving amplitude, the linear response to a weak dc force along a lattice symmetry axis consist in a mobility in basically any direction. In particular, motion exactly opposite to the applied dc force may arise. Upon changing the angle of the dc force relatively to the square lattice, the particle motion remains predominantly opposite to the dc force. The basic physical mechanism consists in a spontaneous symmetry breaking of the unbiased deterministic particle dynamics.