We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki equation presented in [J. Stat. Mech. 2008 P02004]. By taking terms missing in the latter analysis into account we
arrive at a set of three new equations for correlation functions of the system. These correlations involve the density and its logarithm as local observables. Our new one-loop equations, which must carefully deal with the noninteracting Brownian gas theory, are more general than the historic Mode-Coupling one in that a further and well-defined approximation leads back to the original mode-coupling equation for the density correlations alone. However, without performing any further approximation step, our set of three equations does not feature any ergodic-non ergodic transition, as opposed to the historical mode- coupling approach.
We endow a system of interacting particles with two distinct, local, Markovian and reversible microscopic dynamics. Using common field-theoretic techniques used to investigate the presence of a glass transition, we find that while the first, standard
, dynamical rules lead to glassy behavior, the other one leads to a simple exponential relaxation towards equilibrium. This finding questions the intrinsic link that exists between the underlying, thermodynamical, energy landscape, and the dynamical rules with which this landscape is explored by the system. Our peculiar choice of dynam- ical rules offers the possibility of a direct connection with replica theory, and our findings therefore call for a clarification of the interplay between replica theory and the underlying dynamics of the system.
We investigate the ground state of the irrationally frustrated Josephson junction array with controlling anisotropy parameter lambda that is the ratio of the longitudinal Josephson coupling to the transverse one. We find that the ground state has one
dimensional periodicity whose reciprocal lattice vector depends on lambda and is incommensurate with the substrate lattice. Approaching the isotropic point, lambda=1 the so called hull function of the ground state exhibits analyticity breaking similar to the Aubry transition in the Frenkel-Kontorova model. We find a scaling law for the harmonic spectrum of the hull functions, which suggests the existence of a characteristic length scale diverging at the isotropic point. This critical behavior is directly connected to the jamming transition previously observed in the current-voltage characteristics by a numerical simulation. On top of the ground state there is a gapless, continuous band of metastable states, which exhibit the same critical behavior as the ground state.
The Frenkel Kontorova (FK) model is known to exhibit the so called Aubrys transition which is a jamming or frictional transition at zero temperature. Recently we found similar transition at zero and finite temperatures in a super-conducting Josephson
junction array (JJA) on a square lattice under external magnetic field. In the present paper we discuss how these problems are related.
We find a breakdown of the critical dynamic scaling in the coarsening dynamics of an antiferromagnetic {em XY} model on the kagome lattice when the system is quenched from disordered states into the Kosterlitz-Thouless ({em KT}) phases at low tempera
tures. There exist multiple growing length scales: the length scales of the average separation between fractional vortices are found to be {em not} proportional to the length scales of the quasi-ordered domains. They are instead related through a nontrivial power-law relation. The length scale of the quasi-ordered domains (as determined from optimal collapse of the correlation functions for the order parameter $exp[3 i theta (r)]$) does not follow a simple power law growth but exhibits an anomalous growth with time-dependent effective growth exponent. The breakdown of the critical dynamic scaling is accompanied by unusual relaxation dynamics in the decay of fractional ($3theta$) vortices, where the decay of the vortex numbers is characterized by an exponential function of logarithmic powers in time.
We demonstrate that a highly frustrated anisotropic Josephson junction array(JJA) on a square lattice exhibits a zero-temperature jamming transition, which shares much in common with those in granular systems. Anisotropy of the Josephson couplings al
ong the horizontal and vertical directions plays roles similar to normal load or density in granular systems. We studied numerically static and dynamic response of the system against shear, i. e. injection of external electric current at zero temperature. Current-voltage curves at various strength of the anisotropy exhibit universal scaling features around the jamming point much as do the flow curves in granular rheology, shear-stress vs shear-rate. It turns out that at zero temperature the jamming transition occurs right at the isotropic coupling and anisotropic JJA behaves as an exotic fragile vortex matter : it behaves as superconductor (vortex glass) into one direction while normal conductor (vortex liquid) into the other direction even at zero temperature. Furthermore we find a variant of the theoretical model for the anisotropic JJA quantitatively reproduces universal master flow-curves of the granular systems. Our results suggest an unexpected common paradigm stretching over seemingly unrelated fields - the rheology of soft materials and superconductivity.
Equilibrium and non-equilibrium relaxation behaviors of two-dimensional superconducting arrays are investigated via numerical simulations at low temperatures in the presence of incommensurate transverse magnetic fields, with frustration parameter f=
(3-sqrt{5})/2. We find that the non-equilibrium relaxation, beginning with random initial states quenched to low temperatures, exhibits a three-stage relaxation of chirality autocorrelations. At the early stage, the relaxation is found to be described by the von Schweidler form. Then it exhibits power-law behavior in the intermediate time scale and faster decay in the long-time limit, which together can be fitted to the Ogielski form; for longer waiting times, this crosses over to a stretched exponential form. We argue that the power-law behavior in the intermediate time scale may be understood as a consequence of the coarsening behavior, leading to the local vortex order corresponding to f=2/5 ground-state configurations. High mobility of the vortices in the domain boundaries, generating slow wandering motion of the domain walls, may provide mechanism of dynamic heterogeneity and account for the long-time stretched exponential relaxation behavior. It is expected that such meandering fluctuations of the low-temperature structure give rise to finite resistivity at those low temperatures; this appears consistent with the zero-temperature resistive transition in the limit of irrational frustration.
