Abstract:
We report on the results of molecular dynamics simulation (MD) studies of the classical two-dimensional electron crystal in the presence disorder. Our study is motivated by recent experiments on this system in modulation doped semiconductor systems in very strong magnetic fields, where the magnetic length is much smaller than the average interelectron spacing $a_0$, as well as by recent studies of electrons on the surface of helium. We investigate the low temperature state of this system using a simulated annealing method. We find that the low temperature state of the system always has isolated dislocations, even at the weakest disorder levels investigated. We also find evidence for a transition from a hexatic glass to an isotropic glass as the disorder is increased. The former is characterized by quasi-long range orientational order, and the absence of disclination defects in the low temperature state, and the latter by short range orientational order and the presence of these defects. The threshold electric field is also studied as a function of the disorder strength, and is shown to have a characteristic signature of the transition. Finally, the qualitative behavior of the electron flow in the depinned state is shown to change continuously from an elastic flow to a channel-like, plastic flow as the disorder strength is increased.

Abstract:
Elastic systems driven in a disordered medium exhibit a depinning transition at zero temperature and a creep regime at finite temperature and slow drive $f$. We derive functional renormalization group equations which allow to describe in details the properties of the slowly moving states in both cases. Since they hold at finite velocity $v$, they allow to remedy some shortcomings of the previous approaches to zero temperature depinning. In particular, they enable us to derive the depinning law directly from the equation of motion, with no artificial prescription or additional physical assumptions. Our approach provides a controlled framework to establish under which conditions the depinning regime is universal. It explicitly demonstrates that the random potential seen by a moving extended system evolves at large scale to a random field and yields a self-contained picture for the size of the avalanches associated with the deterministic motion. At $T>0$ we find that the effective barriers grow with lenghtscale as the energy differences between neighboring metastable states, and demonstrate the resulting activated creep law $v\sim \exp (-C f^{-\mu}/T)$ where the exponent $\mu$ is obtained in a $\epsilon=4-D$ expansion ($D$ is the internal dimension of the interface). Our approach also provides quantitatively a new scenario for creep motion as it allows to identify several intermediate lengthscales. In particular, we unveil a novel ``depinning-like'' regime at scales larger than the activation scale, with avalanches spreading from the thermal nucleus scale up to the much larger correlation length $R_{V}$. We predict that $R_{V}\sim T^{-\sigma}f^{-\lambda }$ diverges at small $f$ and $T$ with exponents $\sigma ,\lambda$ that we determine.

Abstract:
We consider one-dimensional bosonic chains with a repulsive boson-boson interaction that decays exponentially on large length-scales. This model describes transport of Cooper-pairs in a Josepshon junction array, or transport of magnetic flux quanta in quantum-phase-slip ladders, i.e. arrays of superconducting wires in a ladder-configuration that allow for the coherent tunnelling of flux quanta. In the low-frequency, long wave-length regime these chains can be mapped to an effective model of a one-dimensional elastic field in a disordered potential. The onset of transport in these systems, when biased by external voltage, is described by the standard depinning theory of elastic media in disordered pinning potentials. We numerically study the regimes that are of relevance for quantum-phase-slip ladders. These are (i) very short chains and (ii) the regime of weak disorder. For chains shorter than the typical pinning length, i.e., the Larkin length, the chains reach a saturation regime where the depinning voltage does not depend on the decay length of the repulsive interaction. In the regime of weak disorder we find an emergent correlation length-scale that depends on the disorder strength. For arrays shorter than this length the onset of transport is similar to the clean arrays, i.e., is due to the penetration of solitons into the array. We discuss the depinning scenarios for longer arrays in this regime.

Abstract:
Two classes of models of driven disordered systems that exhibit history-dependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The second class allows for proliferation of topological defects due to the interplay of strong disorder and drive. In mean field theory both models exhibit a tricritical point as a function of disorder strength. At weak disorder depinning is continuous and the sliding state is unique. At strong disorder depinning is discontinuous and hysteretic.

Abstract:
We review in these notes the dynamics of extended condensed matter systesm, such as vortex lattices in type-II superconductors and charge density waves in anisotropic metals, driven over quenched disorder. We focus in particular on the case of strong disorder, where topological defects are generated in the driven lattice. In this case the repsonse is plastic and the depinning transition may become discontinuous and hysteretic.

Abstract:
The coupling between the intramolecular vibrational modes and the doped conduction electrons in $M_3C_{60}$ is studied by a calculation of the electronic contributions to the phonon self energies. The calculations are carried out for an orientationally ordered reference solid with symmetry $Fm \bar{3} m$ and for a model with quenched orientational disorder on the fullerene sites. In both cases, the dispersion and symmetry of the renormalized modes is governed by the electronic contributions. The current current correlation functions and frequency dependent conductivity through the midinfrared are calculated for both models. In the disordered structures, the renormalized modes derived from even parity intramolecular phonons are resonant with the dipole excited single particle spectrum, and modulate the predicted midinfrared conductivity. The spectra for this coupled system are calculated for several recently proposed microscopic models for the electron phonon coupling, and a comparison is made with recent experimental data which demonstrate this effect.

Abstract:
We study a model for the depinning and driven steady state phases of a solid tuned across a polymorphic phase transition between ground states of triangular and square symmetry. These include pinned states which may have dominantly triangular or square correlations, a plastically flowing liquid-like phase, a moving phase with hexatic correlations, flowing triangular and square states and a dynamic coexistence regime characterized by the complex interconversion of locally square and triangular regions. We locate these phases in a dynamical phase diagram. We demonstrate that the apparent power-law orientational correlations we obtain in our moving hexatic phase arise from circularly averaging an orientational correlation function with qualitatively different behaviour in the longitudinal (drive) and transverse directions. The intermediate coexistence regime exhibits several novel properties, including substantial enhancement in the current noise, an unusual power-law spectrum of current fluctuations and striking metastability effects. This noise arises from the fluctuations of the interface separating locally square and triangular ordered regions. We demonstrate the breakdown of effective ``shaking temperature'' treatments in the coexistence regime by showing that such shaking temperatures are non-monotonic functions of the drive in this regime. Finally we discuss the relevance of these simulations to the anomalous behaviour seen in the peak effect regime of vortex lines in the disordered mixed phase of type-II superconductors. We propose that this anomalous behavior is directly linked to the behavior exhibited in our simulations in the dynamical coexistence regime, thus suggesting a possible solution to the problem of the origin of peak effect anomalies.

Abstract:
We study depinning of vortex chains in channels formed by static, disordered vortex arrays. Depinning is governed either by the barrier for defect nucleation or for defect motion, depending on whether the chain periodicity is commensurate or incommensurate with the surrounding arrays. We analyze the reduction of the gap between these barriers as function of disorder. At large disorder, commensurability becomes irrelevant and the pinning force is reduced to a small fraction of the ideal shear strength of ordered channels. Implications for experiments on channel devices are discussed.

Abstract:
We simulate the ordering of vortices and its effects on the critical current in superconductors with varied vortex-vortex interaction strength and varied pinning strengths for a two-dimensional system. For strong pinning the vortex lattice is always disordered and the critical depinning force only weakly increases with decreasing vortex-vortex interactions. For weak pinning the vortex lattice is defect free until the vortex-vortex interactions have been reduced to a low value, when defects begin to appear with a simultaneous rapid increase in the critical depinning force. In each case the depinning force shows a maximum for non-interacting vortices. The relative height of the peak increases and the peak width decreases for decreasing pinning strength in excellent agreement with experimental trends associated with the peak effect. We show that scaling relations exist between the distance between defects in the vortex lattice and the critical depinning force.

Abstract:
We present a unified view of orientational ordering in phases I, II, and III of solid hydrogen. Phases II and III are orientationally ordered, while the ordering objects in phase II are angular momenta of rotating molecules, and in phase III the molecules themselves. This concept provides quantitative explanation of the vibron softening, libron and roton spectra, and increase of the IR vibron oscillator strength in phase III. The temperature dependence of the effective charge parallels the frequency shifts of the IR and Raman vibrons. All three quantities are linear in the order parameter.