The Fast Wandering of Slow Birds

I study a single "slow" bird moving with a flock of birds of a different, and faster (or slower) species. I find that every "species" of flocker has a characteristic speed $\gamma\ne v_0$, where $v_0$ is the mean speed of the flock, such that, if the speed $v_s$ of the "slow" bird equals $\gamma$, it will randomly wander transverse to the mean direction of flock motion far faster than the other birds will: its mean-squared transverse displacement will grow in $d=2$ with time $t$ like $t^{5/3}$, in contrast to $t^{4/3}$ for the other birds. In $d=3$, the slow bird's mean squared transverse displacement grows like $t^{5/4}$, in contrast to $t$ for the other birds. If $v_s\neq \gamma$, the mean-squared displacement of the "slow" bird crosses over from $t^{5/2}$ to $t^{4/3}$ scaling in $d=2$, and from $t^{5/4}$ to $t$ scaling in $d=3$, at a time $t_c$ that scales according to $t_c \propto|v_s-\gamma|^{-2}$.Comment: 10 pages; 5 pages of which did not appear in earlier versions, but were added in response to referee's suggestion

A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks

I reanalyze the hydrodynamic theory of fluid, polar ordered flocks. I find new linear terms in the hydrodynamic equations which slightly modify the anisotropy, but not the scaling, of the damping of sound modes. I also find that the nonlinearities allowed {\it in equilibrium} do not stabilize long ranged order in spatial dimensions $d=2$; in accord with the Mermin-Wagner theorem. Nonequilibrium nonlinearities {\it do} stabilize long ranged order in $d=2$, as argued by earlier work. Some of these were missed by earlier work; it is unclear whether or not they change the scaling exponents in $d=2$.Comment: 6 pages, no figures. arXiv admin note: text overlap with arXiv:0909.195

Self-organization in systems of self-propelled particles

We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension, the self-organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges.In two-dimensions, we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions, even in the absence of a confining boundary. Furthermore, we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent.Comment: 4 pages, 5 figure

Kinetic Roughening in Surfaces of Crystals Growing on Disordered Substrates

Substrate disorder effects on the scaling properties of growing crystalline surfaces in solidification or epitaxial deposition processes are investigated. Within the harmonic approach there is a phase transition into a low-temperature (low-noise) superrough phase with a continuously varying dynamic exponent z>2 and a non-linear response. In the presence of the KPZ nonlinearity the disorder causes the lattice efects to decay on large scales with an intermediate crossover behavior. The mobility of the rough surface hes a complex dependence on the temperature and the other physical parameters.Comment: 13 pages, 2 figures (not included). Submitted to Phys. Rev. Letts. Use Latex twic

The Communication Cost of Simulating Bell Correlations

What classical resources are required to simulate quantum correlations? For the simplest and most important case of local projective measurements on an entangled Bell pair state, we show that exact simulation is possible using local hidden variables augmented by just one bit of classical communication. Certain quantum teleportation experiments, which teleport a single qubit, therefore admit a local hidden variables model.Comment: 4 pages, 2 figures; reference adde

Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion

A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity parameter, and a dynamical phase transition exhibiting spontaneous breaking of rotational symmetry occurs at a critical parameter value. The model is analyzed using nonequilibrium mean field theory: Dispersion relations for the critical modes are derived, and a phase diagram is constructed. Mean field predictions for the two critical exponents describing the phase transition as a function of sensitivity and density are obtained analytically.Comment: 4 pages, 4 figures, final version as publishe

Thermodynamics of Mesoscopic Vortex Systems in 1+1 Dimensions

The thermodynamics of a disordered planar vortex array is studied numerically using a new polynomial algorithm which circumvents slow glassy dynamics. Close to the glass transition, the anomalous vortex displacement is found to agree well with the prediction of the renormalization-group theory. Interesting behaviors such as the universal statistics of magnetic susceptibility variations are observed in both the dense and dilute regimes of this mesoscopic vortex system.Comment: 4 pages, REVTEX, 6 figures included. Comments and suggestions can be sent to [email protected]

The Hilbertian Tensor Norm and Entangled Two-Prover Games

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.Comment: 33 pages, some of the results have been obtained independently in arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6 rewritten, v3: completely rewritten in order to improve readability; title changed; references added; published versio

Longitudinal and transverse dissipation in a simple model for the vortex lattice with screening

Transport properties of the vortex lattice in high temperature superconductors are studied using numerical simulations in the case in which the non-local interactions between vortex lines are dismissed. The results obtained for the longitudinal and transverse resistivities in the presence of quenched disorder are compared with the results of experimental measurements and other numerical simulations where the full interaction is considered. This work shows that the dependence on temperature of the resistivities is well described by the model without interactions, thus indicating that many of the transport characteristics of the vortex structure in real materials are mainly a consequence of the topological configuration of the vortex structure only. In addition, for highly anisotropic samples, a regime is obtained where longitudinal coherence is lost at temperatures where transverse coherence is still finite. I discuss the possibility of observing this regime in real samples.Comment: 9 pages, 7 figures included using epsf.st