Topology and Nematic Ordering II: Observable Critical Behavior

This paper is the second in a pair treating a new lattice model for nematic media. In addition to the familiar isotropic (I) and nematically ordered (N) phases, the phase diagram established in the previous paper (Paper I) contains a new, topologically ordered phase (T) occuring at large suppression of topological defects and weak nematic interactions. This paper (Paper II) is concerned with the experimental signatures of the proposed phase diagram. Specific heat, light scattering and magnetic susceptibility near both the N/T and I/T transitions are studied, and critical behavior determined. The singular dependences of the Frank constants ($K_1$, $K_2$, $K_3$) and the dielectric tensor anisotropy ($\Delta \epsilon$) on temperature upon approaching the N/T transition are also found.Comment: 10 pages, RevTeX 3.

Dissipate locally, couple globally: a sharp transition from decoupling to infinite range coupling in Josephson arrays with on-site dissipation

We study the T=0 normal to superconducting transition of Josephson arrays with {\it on-site} dissipation. A perturbative renormalization group solution is given. Like the previously studied case of {\it bond} dissipation (BD), this is a "floating" to coupled (FC) phase transition. {\it Unlike} the BD transition, at which {\it only} nearest-neighbor couplings become relevant, here {\it all} inter-grain couplings, out to {\it infinitely} large distances, do so simultaneously. We predict, for the first time in an FC transition, a diverging spatial correlation length. Our results show the robustness of floating phases in dissipative quantum systems.Comment: 7+ pages, 3 eps figures, Europhysics Letters preprint format, as publishe

Ginzburg-Landau theory for the conical cycloid state in multiferroics: applications to CoCr2_2O4_4

We show that the cycloidal magnetic order of a multiferroic can arise in the absence of spin and lattice anisotropies, for e.g., in a cubic material, and this explains the occurrence of such a state in CoCr$_2$O$_4$. We discuss the case when this order coexists with ferromagnetism in a so called `conical cycloid' state, and show that a direct transition to this state from the ferromagnet is necessarily first order. On quite general grounds, the reversal of the direction of the uniform magnetization in this state can lead to the reversal of the electric polarization as well, without the need to invoke `toroidal moment' as the order parameter.Comment: 6 pages, 3 figures, accepted for publication in Phys. Rev.

Quenched Dislocation Enhanced Supersolid Ordering

I show using Landau theory that quenched dislocations can facilitate the supersolid (SS) to normal solid (NS) transition, making it possible for the transition to occur even if it does not in a dislocation-free crystal. I make detailed predictions for the dependence of the SS to NS transition temperature T_c(L), superfluid density %\rho_S(T, L), and specific heat C(T,L) on temperature T and dislocation spacing L, all of which can be tested against experiments. The results should also be applicable to an enormous variety of other systems, including, e.g., ferromagnets.Comment: 5 pages, 2 figure

Grothendieck's constant and local models for noisy entangled quantum states

We relate the nonlocal properties of noisy entangled states to Grothendieck's constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states \rho^W_p=p \proj{\psi^-}+(1-p){\one}/{4}, we show that there is a local model for projective measurements if and only if $p \le 1/K_G(3)$, where $K_G(3)$ is Grothendieck's constant of order 3. Known bounds on $K_G(3)$ prove the existence of this model at least for $p \lesssim 0.66$, quite close to the current region of Bell violation, $p \sim 0.71$. We generalize this result to arbitrary quantum states.Comment: 6 pages, 1 figur

Dynamic coordinated control laws in multiple agent models

We present an active control scheme of a kinetic model of swarming. It has been shown previously that the global control scheme for the model, presented in \cite{JK04}, gives rise to spontaneous collective organization of agents into a unified coherent swarm, via a long-range attractive and short-range repulsive potential. We extend these results by presenting control laws whereby a single swarm is broken into independently functioning subswarm clusters. The transition between one coordinated swarm and multiple clustered subswarms is managed simply with a homotopy parameter. Additionally, we present as an alternate formulation, a local control law for the same model, which implements dynamic barrier avoidance behavior, and in which swarm coherence emerges spontaneously.Comment: 20 pages, 6 figure