Subharmonic Shapiro Steps and Devil's-Staircase Behavior in Driven Charge-Density-Wave Systems

Brown, Stuart; Mozurkewich, George; Grüner, G.

doi:10.1103/physrevlett.52.2277

Cited by 128 publications

(45 citation statements)

References 15 publications

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“…Each step of the ''devil's staircase'', for example, represents a regime where the object's motion is entrained between two driving frequencies of integer ratios. These systems are both physically intriguing as well have practical interest in applications ranging from magnetoresistance 2,3 to colloidal separation.…”

Section: Introductionmentioning

confidence: 99%

“…The flux of objects through periodic potential energy landscapes under the action of external driving force has implications in a number of physical systems, including atom migration on crystal surfaces, 1 the motion of charge density packets in solids, 2,3 the movement of vortices in type II superconductors, 4 fluid driven movement of colloidal particles through optical and magnetic lattices, [5][6][7][8][9] as well as various problems in the life sciences and chemical kinetics. 10 From a physical standpoint, these are fascinating non-linear dynamic systems where small changes in a driving parameter can lead to abrupt changes in the pattern of synchronization of the object relative to the underlying lattice.…”

Section: Introductionmentioning

confidence: 99%

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The synchronization of superparamagnetic beads driven by a micro-magnetic ratchet

et al. 2010

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We present theoretical, numerical, and experimental analyses on the non-linear dynamic behavior of superparamagnetic beads exposed to a periodic array of micro-magnets and an external rotating field. The agreement between theoretical and experimental results revealed that non-linear magnetic forcing dynamics are responsible for transitions between phase-locked orbits, sub-harmonic orbits, and closed orbits, representing different mobility regimes of colloidal beads. These results suggest that the non-linear behavior can be exploited to construct a novel colloidal separation device that can achieve effectively infinite separation resolution for different types of beads, by exploiting minor differences in their bead's properties. We also identify a unique set of initial conditions, which we denote the ''devil's gate'' which can be used to expeditiously identify the full range of mobility for a given bead type.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The synchronization of superparamagnetic beads driven by a micro-magnetic ratchet

et al. 2010

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“…Here we think particularly of dissipative systems driven by periodic forces such as Josephson junctions in the presence of microwave radiation [43,44,45,46,47,48,49], superionic conductors [50,51], and systems exhibiting charge-density waves [52] in which certain features of deterministic diffusion were already observed experimentally. For these systems the equations of motion are typically of the form of some nonlinear pendulum equation.…”

Section: Introductionmentioning

confidence: 99%

Fractality of deterministic diffusion in the nonhyperbolic climbing sine map

Korabel

Klages

2004

Physica D: Nonlinear Phenomena

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The nonlinear climbing sine map is a nonhyperbolic dynamical system exhibiting both normal and anomalous diffusion under variation of a control parameter. We show that on a suitable coarse scale this map generates an oscillating parameterdependent diffusion coefficient, similarly to hyperbolic maps, whose asymptotic functional form can be understood in terms of simple random walk approximations. On finer scales we find fractal hierarchies of normal and anomalous diffusive regions as functions of the control parameter. By using a Green-Kubo formula for diffusion the origin of these different regions is systematically traced back to strong dynamical correlations. Starting from the equations of motion of the map these correlations are formulated in terms of fractal generalized Takagi functions obeying generalized de Rham-type functional recursion relations. We finally analyze the measure of the normal and anomalous diffusive regions in the parameter space showing that in both cases it is positive, and that for normal diffusion it increases by increasing the parameter value.

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“…Variants of this problem appear in areas as diverse as driven charge density waves [1], electronic energy states in twodimensional electron gases [2], atom migration on crystal surfaces [3], chemical kinetics, and flux flow in type-II superconductors [4]. Quite recently, this problem was investigated [5] using a monolayer of colloidal spheres in flowing water as a model system and a square array of holographic optical tweezers [6] to provide the periodic potential energy surface.…”

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confidence: 99%

Statistically Locked-In Transport through Periodic Potential Landscapes

Gopinathan

Grier

2004

Phys. Rev. Lett.

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Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments on colloidal spheres flowing through arrays of optical traps do indeed reveal such a hierarchy, but not with the predicted structure. The microscopic trajectories, moreover, appear to be random, with commensurability emerging only in a statistical sense. We introduce an idealized model for periodically modulated transport in the presence of randomness that captures both the structure and statistics of such statistically locked-in states.Objects driven through periodic potential energy surfaces face a myriad of choices: either they follow the driving force or they become entrained along any of the commensurate directions through the landscape. Variants of this problem appear in areas as diverse as driven charge density waves [1], electronic energy states in twodimensional electron gases [2], atom migration on crystal surfaces [3], chemical kinetics, and flux flow in type-II superconductors [4]. Quite recently, this problem was investigated [5] using a monolayer of colloidal spheres in flowing water as a model system and a square array of holographic optical tweezers [6] to provide the periodic potential energy surface. Depending on the array's orientation with respect to the driving force, the spheres were observed to trace out a Devil's staircase hierarchy of commensurate directions through the array, with particular directions being preferentially selected over certain ranges of orientations [5]. Trajectories deflected by a preference for commensurability are said to be kinetically locked in to the lattice. This anticipated result [7] was accompanied by two surprises. In the first place, not all kinetically lockedin states were centered on simple commensurate directions. Still more surprisingly, particles' microscopic trajectories in high-order locked-in states did not consist of sequences of commensurate jumps, but rather consisted of seemingly random lower-order hops whose combination, nonetheless, were commensurate. The appearance of statistical rather than deterministic commensurability suggests an unexpected role for thermal randomness in structuring transport through periodic potentials, and has been dubbed statistical lock-in [5].This Letter presents a highly simplified model for statistically locked-in transport through mesoscopic potential energy landscapes that nonetheless accounts for the emergence of combination jumps and their statistical commensurability. In particular this model reveals how the potential energy landscape's structure and extent establish the discrete spectrum of travel directions selected by biased random walkers. While our discussion is directed toward the purely classical behavior of flowing colloids, similar results should emerge for biased quantum mechanical hopping through arrays of potential An applied force drives objects through the array...

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Subharmonic Shapiro Steps and Devil's-Staircase Behavior in Driven Charge-Density-Wave Systems

Cited by 128 publications

References 15 publications

The synchronization of superparamagnetic beads driven by a micro-magnetic ratchet

The synchronization of superparamagnetic beads driven by a micro-magnetic ratchet

Fractality of deterministic diffusion in the nonhyperbolic climbing sine map

Statistically Locked-In Transport through Periodic Potential Landscapes

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