Ordering dynamics of the driven lattice gas model

The evolution of a two-dimensional driven lattice-gas model is studied on an L_x X L_y lattice. Scaling arguments and extensive numerical simulations are used to show that starting from random initial configuration the model evolves via two stages: (a) an early stage in which alternating stripes of particles and vacancies are formed along the direction y of the driving field, and (b) a stripe coarsening stage, in which the number of stripes is reduced and their average width increases. The number of stripes formed at the end of the first stage is shown to be a function of L_x/L_y^\phi, with \phi ~ 0.2. Thus, depending on this parameter, the resulting state could be either single or multi striped. In the second, stripe coarsening stage, the coarsening time is found to be proportional to L_y, becoming infinitely long in the thermodynamic limit. This implies that the multi striped state is thermodynamically stable. The results put previous studies of the model in a more general framework

Properties of a magnetic superconductor with weak magnetization - application to ErNi2B2CErNi_2B_2C

Using a Ginsburg-Landau free energy functional, we study the $H-T$ phase diagram of a weak magnetic superconductor, where the magnetization from the magnetic component is marginal in supporting a spontaneous vortex phase in absence of external magnetic field. In particular, the competition between the spiral state and spontaneous vortex phase is analysed. Our theory is applied to understand the magnetic properties of $ErNi_2B_2C$.Comment: 13 pages, 4 postscript figure

Improving the Fidelity of Optical Zeno Gates via Distillation

We have modelled the Zeno effect Control-Sign gate of Franson et al (PRA 70, 062302, 2004) and shown that high two-photon to one-photon absorption ratios, $\kappa$, are needed for high fidelity free standing operation. Hence we instead employ this gate for cluster state fusion, where the requirement for $\kappa$ is less restrictive. With the help of partially offline one-photon and two-photon distillations, we can achieve a fusion gate with unity fidelity but non-unit probability of success. We conclude that for $\kappa > 2200$, the Zeno fusion gate will out perform the equivalent linear optics gate.Comment: 6 pages, 11 figures, Submitted to PR

On vanishing sums of m \,m\,th roots of unity in finite fields

In an earlier work, the authors have determined all possible weights $n$ for which there exists a vanishing sum $\zeta_1+\cdots +\zeta_n=0$ of $m$th roots of unity $\zeta_i$ in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic $p$. For given $m$ and $p$, results are obtained on integers $n_0$ such that all integers $n\geq n_0$ are in the ``weight set'' $W_p(m)$. The main result $(1.3)$ in this paper guarantees, under suitable conditions, the existence of solutions of $x_1^d+\cdots+x_n^d=0$ with all coordinates not equal to zero over a finite field