Renormalization of pinned elastic systems: how does it work beyond one loop?

We study the field theories for pinned elastic systems at equilibrium and at depinning. Their beta functions differ to two loops by novel "anomalous" terms. At equilibrium we find a roughness zeta = 0.208 298 04 epsilon + 0.006 858 epsilon(2) (random bond), zeta = epsilon/3 (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find zeta = epsilon/3(1 + 0.143 31 epsilon), epsilon = 4 - d, in violation of the conjecture zeta = epsilon/3, solving the discrepancy with simulations. For long range elasticity zeta = epsilon/3(1 + 0.397 35 epsilon), epsilon = 2 - d, much closer to the experimental value (approximately 0.5 both for liquid helium contact line depinning and slow crack fronts) than the standard prediction 1/3.     

Depinning with dynamic stress overshoots: mean field theory

An infinite-range model of an elastic manifold pulled through a random potential by a force F is analyzed focusing on inertial effects. When the inertial parameter M is small, there is a continuous depinning transition from a small- F static phase to a large- F moving phase. When M is increased to M(c), a novel tricritical point occurs. For M>M(c), the depinning transition becomes discontinuous with hysteresis. Yet, the distribution of discrete "avalanche"-like events as the force is increased in the static phase for M>M(c) has an unusual mixture of first-order-like and critical features. The results may be relevant for the onset of crack propagation and for dynamics of geological faults.     

On the dynamics of sliding elastic manifolds with random interaction

The friction dynamics of contacting D-dimensional disordered elastic manifolds, driven by external forces, is studied, and the existence of a zero-temperature depinning transition below some critical dimensionality is demonstrated for different kinds of elastic response. It is shown that this model falls into the universality class of single interface depinning in a 2D-dimensional random medium. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 532–537 (25 October 1996) Published in English in the original Russian Journal. Edited by Steve Torstveit.     

93Nb NMR spin echo spectroscopy in single crystal NbSe3

We report electric field induced phase displacements of the charge density wave (CDW) in a single crystal of NbSe3 using 93Nb NMR spin-echo spectroscopy. CDW polarizations in the pinned state induced by unipolar and bipolar pulses are linear and reversible up to at least E = (0.96)ET. The polarizations have a broad distribution extending up to phase angles of order 60 degrees for electric fields close to threshold. No evidence for polarizations in excess of a CDW wavelength or for a divergence in polarization near ET are observed. The results are consistent with elastic depinning models, provided that the critical regime expected in large systems is not observable.     

Viscoelastic depinning of driven systems: mean-field plastic scallops

We have investigated the mean-field dynamics of an overdamped viscoelastic medium driven through quenched disorder. The model allows for the coexistence of pinned and sliding regions and can exhibit continuous elastic depinning or first-order hysteretic depinning. Numerical simulations indicate mean-field instabilities that correspond to macroscopic stick-slip events and lead to premature switching. The model describes the elastic and plastic dynamics of driven vortex arrays in superconductors and other extended disordered systems.     

Depinning dynamics of two-dimensional magnetized colloids on a substrate with periodic pinning centers

We study, by Langevin simulations, the depinning dynamics of two-dimensional magnetized colloids on a substrate with periodic pinning centers. When the number ratios of pinnings to colloids are 1:1 matching and at finite temperature, we find for the first time crossovers from plastic flow through elastic smectic flow to elastic crystal flow near the depinning with increasing the pinning strength. There exists a power-law scaling relationship between the average velocity of colloids and the external driving force for all the three types of flows. It is found that the critical driving force and the power-law scaling exponent as well as the average intensity of Bragg peaks are invariant basically in the region of elastic smectic flow. We also examine the temperature effect and it reveals that the above dynamic moving phases and their transitions could be attributed to the interplay between thermal fluctuation and pinning potential. At sufficiently low temperature, the thermal fluctuation could be neglected and the colloids near the depinning move in the elastic crystal flow no matter what the pinning strength. In addition, the number of pinning centers is changed and when it is close to the number of colloids, there appears a peak in the critical driving force and a dip in the power-law scaling exponent, respectively. The peak and dip are more pronounced for higher pinning strength.     

Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dlmensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling fit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic depinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

Nonuniversality of Critical Exponents in a Fractional Quenched Kardar–Parisi–Zhang Equation

In this article we address the problem of the depinning transition for driven interfaces in random media. We introduce a fractional Kardar–Parisi–Zhang equation with quenched noise, in which the normal diffusion term is replaced by a fractional Laplacian accounting for long-range interactions through quenched disorder. The critical values of the external driving force and nonlinear term coefficient evidently depend on the system size at the depinning transition. For a fixed value of the external driving force, the fractional order much determines the value of the nonlinear term coefficient that leads to a depinned interface. Near the depinning threshold, the critical exponent obtained numerically is nonuniversal, and weakly depends on the fractional order.     

Driven depinning of strongly disordered media and anisotropic mean-field limits

Extended systems driven through strong disorder are modeled generically using coarse-grained degrees of freedom that interact elastically in the directions parallel to the drive and slip along at least one of the directions transverse to the motion. In the limit of infinite-range elastic and viscous coupling this model has a tricritical point separating a region where the depinning is continuous, in the universality class of elastic depinning, from a region where depinning is hysteretic. Many of the collective transport models discussed in the literature are special cases of the generic model.     

Quantum depinning transition of quantum Hall stripes

We examine the effect of disorder on the electromagnetic response of quantum Hall stripes using an effective elastic theory to describe their low-energy dynamics, and replicas and the Gaussian variational method to handle disorder effects. Within our model we demonstrate the existence of a depinning transition at a critical partial Landau level filling factor Deltanu(c). For DeltanuDeltanu(c). For Deltanu> or =Deltanu(c), we find a partial RSB solution in which there is free sliding only along the stripe direction. The transition is analogous to the Kosterlitz-Thouless phase transition.     

A Solvable Model of Interface Depinning in Random Media

We study the mean-field version of a model proposed by Leschhorn to describe the depinning transition of interfaces in random media. We show that evolution equations for the distribution of forces felt by the interface sites can be written directly for an infinite system. For a flat distribution of random local forces the value of the depinning threshold can be obtained exactly. In the case of parallel dynamics (all unstable sites move simultaneously), due to the discrete character of the interface heights allowed in the model, the motion of the center of mass is non-uniform in time in the moving phase close to the threshold, and the mean interface velocity vanishes with a square-root singularity.     

Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dimensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling lit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic de. Pinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

Numerical approaches on driven elastic interfaces in random media

We discuss the universal dynamics of elastic interfaces in quenched random media. We focus on the relation between the rough geometry and collective transport properties in driven steady-states. Specially devised numerical algorithms allow us to analyze the equilibrium, creep, and depinning regimes of motion in minimal models. The relevance of our results for understanding domain wall experiments is outlined.     

Dependence of current and field driven depinning of domain walls on their structure and chirality in permalloy nanowires

A magnetic domain wall (DW) injected and pinned at a notch in a permalloy nanowire is shown to exhibit four well-defined magnetic states, vortex and transverse, each with two chiralities. These states, imaged using magnetic force microscopy, are readily detected from their different resistance values arising from the anisotropic magnetoresistance effect. Whereas distinct depinning fields and critical depinning currents in the presence of magnetic fields are found, the critical depinning currents are surprisingly similar for all four DW states in low magnetic fields. We observe current-induced transformations between these DW states below the critical depinning current which may account for the similar depinning currents.     

Critical Properties and Finite-Size Estimates for the Depinning Transition of Directed Random Polymers

We consider models of directed random polymers interacting with a defect line, which are known to undergo a pinning/depinning (or localization/delocalization) phase transition. We are interested in critical properties and we prove, in particular, finite-size upper bounds on the order parameter (the contact fraction) in a window around the critical point, shrinking with the system size. Moreover, we derive a new inequality relating the free energy F and an annealed exponent μ which describes extreme fluctuations of the polymer in the localized region. For the particular case of a (1+1)-dimensional interface wetting model, we show that this implies an inequality between the critical exponents which govern the divergence of the disorder-averaged correlation length and of the typical one. Our results are based on the recently proven smoothness property of the depinning transition in presence of quenched disorder and on concentration of measure ideas.     

Wavefront depinning in semiconductor superlattices due to discrete-mapping failure

We investigate the wavefronts depinning in current biased, infinitely long semiconductor superlattice systems by the method of discrete mapping and show that the wavefront depinning corresponds to the discrete mapping failure. For parameter values near the lower critical current in both discrete drift model （DD model） and discrete drift-diffusion model （DDD model）, the mapping failure is determined by the important mapping step from the bottom of branch to branch α. For the upper critical parameters in DDD model, the key mapping step is from branch γ to the top of the corresponding branch α and we may need several active wells to describe the wavefronts.     

Domain wall depinning in random media by ac fields

The viscous motion of an interface driven by an ac external field of frequency omega(0) in a random medium is considered here in the nonadiabatic regime. The velocity exhibits a smeared depinning transition showing a double hysteresis which is absent in the adiabatic case omega(0)-->0. Using scaling arguments and an approximate renormalization group calculation we explain the main characteristics of the hysteresis loop. In the low frequency limit these can be expressed in terms of the depinning threshold and the critical exponents of the adiabatic case.     

Driven quasi-one-dimensional classical electron gas in the presence of a constriction: Pinning and depinning

We studied the properties of a quasi-one-dimensional system of charged particles in the presence of a local Lorentzian-shaped constriction. We investigated the response of the system when a time-independent external driving force is applied in the unconfined direction. Langevin molecular dynamics simulations for different values of the drive and temperature are performed. We found that the particles are pinned unless a threshold value of the driving force is reached. We investigated in detail the depinning phenomenon. The system can depin “elastically”, with particles moving together and keeping their neighbors, or “quasi-elastically”, with particles moving together through a complex net of conducting channels without keeping their neighbors. In the case of elastic depinning the velocity vs applied drive curves is characterized by a critical exponent β consistent with the value , while in the case of quasi-elastic depinning the critical exponent β has on average the value 0.94. The model is relevant e.g. for electrons on liquid helium, colloids and dusty plasma.     

The Depinning Transition in Presence of Disorder: A Toy Model

We introduce a toy model, which represents a simplified version of the problem of the depinning transition in the limit of strong disorder. This toy model can be formulated as a simple renormalization transformation for the probability distribution of a single real variable. For this toy model, the critical line is known exactly in one particular case and it can be calculated perturbatively in the general case. One can also show that, at the transition, there is no fixed distribution accessible by renormalization which corresponds to a disordered fixed point. Instead, both our numerical and analytic approaches indicate a transition of infinite order (of the Berezinskii–Kosterlitz–Thouless type). We give numerical evidence that this infinite order transition persists for the problem of the depinning transition with disorder on the hierarchical lattice.     

Dynamics below the depinning threshold in disordered elastic systems

We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T-->0, the steady state is dominated by a single configuration which is occupied with probability 1. We develop an exact algorithm to target this dominant configuration and to analyze its geometrical properties as a function of the driving force. The roughness exponent of the line at large scales is identical to the one at depinning. No length scale diverges in the steady-state regime as the depinning threshold is approached from below. We do find a divergent length, but it is associated only with the transient relaxation between metastable states.