Nonequilibrium structures and dynamic transitions in driven vortex lattices with disorder

We review our studies of elastic lattices driven by an external force $F$ in the presence of random disorder, which correspond to the case of vortices in superconducting thin films driven by external currents. Above a critical force $F_c$ we find two dynamical phase transitions at $F_p$ and $F_t$, with $F_c<F_p<F_t$. At $F_p$ there is a transition from plastic flow to smectic flow where the noise is isotropic and there is a peak in the differential resistance. At $F_t$ there is a sharp transition to a frozen transverse solid where both the transverse noise and the diffussion fall down abruptly and therefore the vortex motion is localized in the transverse direction. From a generalized fluctuation-dissipation relation we calculate an effective transverse temperature in the fluid moving phases. We find that the effective temperature decreases with increasing driving force and becomes equal to the equilibrium melting temperature when the dynamic transverse freezing occurs.Comment: 8 pages, 3 fig

Pinning Induced Fluctuations on Driven Vortices

We use a simple model to study the long time fluctuations induced by random pinning on the motion of driven non--interacting vortices. We find that vortex motion seen from the co--moving frame is diffusive and anisotropic, with velocity dependent diffusion constants. Longitudinal and transverse diffusion constants cross at a characteristic velocity where diffusion is isotropic. The diffusion front is elongated in the direction of the drive at low velocities and elongated in the transverse direction at large velocities. We find that the mobility in the driven direction is always larger than the transverse mobility, and becomes isotropic only in the large velocity limit.Comment: 4 pages, 3 figs, Vortex IV Proceedings, Sep. 3-9, 2005, Crete, Greec

Anisotropic finite-size scaling of an elastic string at the depinning threshold in a random-periodic medium

We numerically study the geometry of a driven elastic string at its sample-dependent depinning threshold in random-periodic media. We find that the anisotropic finite-size scaling of the average square width $\bar{w^2}$ and of its associated probability distribution are both controlled by the ratio $k=M/L^{\zeta_{\mathrm{dep}}}$, where $\zeta_{\mathrm{dep}}$ is the random-manifold depinning roughness exponent, $L$ is the longitudinal size of the string and $M$ the transverse periodicity of the random medium. The rescaled average square width $\bar{w^2}/L^{2\zeta_{\mathrm{dep}}}$ displays a non-trivial single minimum for a finite value of $k$. We show that the initial decrease for small $k$ reflects the crossover at $k \sim 1$ from the random-periodic to the random-manifold roughness. The increase for very large $k$ implies that the increasingly rare critical configurations, accompanying the crossover to Gumbel critical-force statistics, display anomalous roughness properties: a transverse-periodicity scaling in spite that $\bar{w^2} \ll M$, and subleading corrections to the standard random-manifold longitudinal-size scaling. Our results are relevant to understanding the dimensional crossover from interface to particle depinning.Comment: 11 pages, 7 figures, Commentary from the reviewer available in Papers in Physic

Non-equilibrium relaxation of an elastic string in random media

We study the relaxation of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length, $L(t)$, separating the equilibrated short length scales from the flat long distance geometry that keep memory of the initial condition. We find that, in the long time limit, $L(t)$ has a non--algebraic growth, consistent with thermally activated jumps over barriers with power law scaling, $U(L) \sim L^\theta$.Comment: 2 pages, 1 figure, Proceedings of ECRYS-2005 International Workshop on Electronic Crysta

Creep motion of an elastic string in a random potential

We study the creep motion of an elastic string in a two dimensional pinning landscape by Langevin dynamics simulations. We find that the Velocity-Force characteristics are well described by the creep formula predicted from phenomenological scaling arguments. We analyze the creep exponent $\mu$, and the roughness exponent $\zeta$. Two regimes are identified: when the temperature is larger than the strength of the disorder we find $\mu \approx 1/4$ and $\zeta \approx 2/3$, in agreement with the quasi-equilibrium-nucleation picture of creep motion; on the contrary, lowering enough the temperature, the values of $\mu$ and $\zeta$ increase showing a strong violation of the latter picture.Comment: 4 pages, 3 figure

Non-steady relaxation and critical exponents at the depinning transition

We study the non-steady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units (GPUs). We compute the time-dependent velocity and roughness as the interface relaxes from a flat initial configuration at the thermodynamic random-manifold critical force. Above a first, non-universal microscopic time-regime, we find a non-trivial long crossover towards the non-steady macroscopic critical regime. This "mesoscopic" time-regime is robust under changes of the microscopic disorder including its random-bond or random-field character, and can be fairly described as power-law corrections to the asymptotic scaling forms yielding the true critical exponents. In order to avoid fitting effective exponents with a systematic bias we implement a practical criterion of consistency and perform large-scale (L~2^{25}) simulations for the non-steady dynamics of the continuum displacement quenched Edwards Wilkinson equation, getting accurate and consistent depinning exponents for this class: \beta = 0.245 \pm 0.006, z = 1.433 \pm 0.007, \zeta=1.250 \pm 0.005 and \nu=1.333 \pm 0.007. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent \beta) found in the literature. It might also be relevant for the analysis of experimental protocols with driven interfaces keeping a long-term memory of the initial condition.Comment: Published version (including erratum). Codes and Supplemental Material available at https://bitbucket.org/ezeferrero/qe

Transverse rectification of disorder-induced fluctuations in a driven system

We study numerically the overdamped motion of particles driven in a two dimensional ratchet potential. In the proposed design, of the so-called geometrical-ratchet type, the mean velocity of a single particle in response to a constant force has a transverse component that can be induced by the presence of thermal or other unbiased fluctuations. We find that additional quenched disorder can strongly enhance the transverse drift at low temperatures, in spite of reducing the transverse mobility. We show that, under general conditions, the rectified transverse velocity of a driven particle fluid is equivalent to the response of a one dimensional flashing ratchet working at a drive-dependent effective temperature, defined through generalized Einstein relations.Comment: 4.5 pages, 3 fig

Direct determination of the collective pinning radius in high temperature superconductors

We study finite-size effects at the onset of the irreversible magnetic behaviour of micron-sized Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ single crystals by using silicon micro-oscillators. We find an irreversibility line appearing well below the thermodynamic Bragg-glass melting line at a magnetic field which increases both with increasing the sample radius and with decreasing the temperature. We show that this size-dependent irreversibility line can be identified with the crossover between the Larkin and the random manifold regimes of the vortex lattice transverse roughness. Our method allows to determine the three-dimensional weak collective pinning Larkin radius in a {\it direct way}.Comment: 4 pages, 3 fig

Infinite family of second-law-like inequalities

The probability distribution function for an out of equilibrium system may sometimes be approximated by a physically motivated "trial" distribution. A particularly interesting case is when a driven system (e.g., active matter) is approximated by a thermodynamic one. We show here that every set of trial distributions yields an inequality playing the role of a generalization of the second law. The better the approximation is, the more constraining the inequality becomes: this suggests a criterion for its accuracy, as well as an optimization procedure that may be implemented numerically and even experimentally. The fluctuation relation behind this inequality, -a natural and practical extension of the Hatano-Sasa theorem-, does not rely on the a priori knowledge of the stationary probability distribution.Comment: 9 pages, 3 figure