Kinetics in one-dimensional lattice gas and Ising models from time-dependent density functional theory

Time-dependent density functional theory, proposed recently in the context of atomic diffusion and non-equilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the representation of non-equilibrium states by a local equilibrium distribution function, we focus on one-dimensional lattice models, where all equilibrium properties can be worked exactly from the known free energy as a functional of the density. This functional determines the thermodynamic driving forces away from equilibrium. In our studies of the interfacial kinetics of atomic hopping and spin relaxation, we find excellent agreement with simulations, suggesting that the method is useful also for treating more complex problems.Comment: 8 pages, 5 figures, submitted to Phys. Rev.

Magnetic Field Effect in a Two-dimensional Array of Short Josephson Junctions

We study analytically the effect of a constant magnetic field on the dynamics of a two dimensional Josephson array. The magnetic field induces spatially dependent states and coupling between rows, even in the absence of an external load. Numerical simulations support these conclusions

Disorder Effects in Superconducting Multiple Loop Quantum Interferometers

A theoretical study is presented on a number N of resistively shunted Josephson junctions connected in parallel as a disordered 1D array by superconducting wiring in such a manner that there are N-1 individual SQUID loops with arbitrary shape formed.Comment: 4 pages, 2 figure

Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system

We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to obtain uniqueness results for the Vlasov-Poisson system.Comment: AMS-LaTeX, 21 page

Screening current effects in Josephson junction arrays

The purpose of this work is to compare the dynamics of arrays of Josephson junctions in presence of magnetic field in two different frameworks: the so called XY frustrated model with no self inductance and an approach that takes into account the screening currents (considering self inductances only). We show that while for a range of parameters the simpler model is sufficiently accurate, in a region of the parameter space solutions arise that are not contained in the XY model equations.Comment: Figures available from the author

Lattice density-functional theory of surface melting: the effect of a square-gradient correction

I use the method of classical density-functional theory in the weighted-density approximation of Tarazona to investigate the phase diagram and the interface structure of a two-dimensional lattice-gas model with three phases -- vapour, liquid, and triangular solid. While a straightforward mean-field treatment of the interparticle attraction is unable to give a stable liquid phase, the correct phase diagram is obtained when including a suitably chosen square-gradient term in the system grand potential. Taken this theory for granted, I further examine the structure of the solid-vapour interface as the triple point is approached from low temperature. Surprisingly, a novel phase (rather than the liquid) is found to grow at the interface, exhibiting an unusually long modulation along the interface normal. The conventional surface-melting behaviour is recovered only by artificially restricting the symmetries being available to the density field.Comment: 16 pages, 6 figure

Row-switched states in two-dimensional underdamped Josephson junction arrays

When magnetic flux moves across layered or granular superconductor structures, the passage of vortices can take place along channels which develop finite voltage, while the rest of the material remains in the zero-voltage state. We present analytical studies of an example of such mixed dynamics: the row-switched (RS) states in underdamped two-dimensional Josephson arrays, driven by a uniform DC current under external magnetic field but neglecting self-fields. The governing equations are cast into a compact differential-algebraic system which describes the dynamics of an assembly of Josephson oscillators coupled through the mesh current. We carry out a formal perturbation expansion, and obtain the DC and AC spatial distributions of the junction phases and induced circulating currents. We also estimate the interval of the driving current in which a given RS state is stable. All these analytical predictions compare well with our numerics. We then combine these results to deduce the parameter region (in the damping coefficient versus magnetic field plane) where RS states can exist.Comment: latex, 48 pages, 15 figs using psfi

Superconducting states and depinning transitions of Josephson ladders

We present analytical and numerical studies of pinned superconducting states of open-ended Josephson ladder arrays, neglecting inductances but taking edge effects into account. Treating the edge effects perturbatively, we find analytical approximations for three of these superconducting states -- the no-vortex, fully-frustrated and single-vortex states -- as functions of the dc bias current $I$ and the frustration $f$. Bifurcation theory is used to derive formulas for the depinning currents and critical frustrations at which the superconducting states disappear or lose dynamical stability as $I$ and $f$ are varied. These results are combined to yield a zero-temperature stability diagram of the system with respect to $I$ and $f$. To highlight the effects of the edges, we compare this dynamical stability diagram to the thermodynamic phase diagram for the infinite system where edges have been neglected. We briefly indicate how to extend our methods to include self-inductances.Comment: RevTeX, 22 pages, 17 figures included; Errata added, 1 page, 1 corrected figur

Reentrant AC magnetic susceptibility in Josephson-junction arrays: An alternative explanation for the paramagnetic Meissner effect

The paramagnetic Meissner effect (PME) measured in high $T_{C}$ granular superconductors has been attributed to the presence of $\pi$-junctions between the grains. Here we present measurements of complex AC magnetic susceptibility from two-dimensional arrays of conventional (non $\pi$) Nb/Al/AlOx/Nb Josephson junctions. We measured the susceptibility as a function of the temperature $T$, the AC amplitude of the excitation field, $h_{AC}$, and the external magnetic field, $H_{DC}$. The experiments show a strong paramagnetic contribution from the multi-junction loops, which manifests itself as a reentrant screening at low temperature, for values of $h_{AC}$ higher than 50 mOe. A highly simplified model, based on a single loop containing four junction, accounts for this paramagnetic contribution and the range of parameters in which it appears. This model offers an alternative explanation of PME which does not involve $\pi$-junctions.Comment: PDF file, 6 two-columns pages, 9 figure