Length-scales of Dynamic Heterogeneity in a Driven Binary Colloid

Here we study characteristic length scales in an aqueous suspension of symmetric oppositely charged colloid subject to a uniform electric field by Brownian Dynamics simulations. We consider a sufficiently strong electric field where the like charges in the system form macroscopic lanes. We construct spatial correlation functions characterizing structural order and that of particles of different mobilities in-plane transverse to the electric field at a given time. We call these functions as equal time density correlation function (ETDCF). The ETDCF between particles of different charges, irrespective of mobilities, are called structural ETDCFs, while those between particles of different mobilities are called the dynamic ETDCF. We extract the characteristic length of correlation by fitting the envelopes of the ETDCFs to exponential dependence. We find that structural ETDCF and the dynamical-ETDCFs of the slow particles increase with time. This suggests that the slow particles undergo microphase separation in the background of the fast particles which drive the structural pattern in the plane transverse to the lanes. The ETDCFs can be measured for colloidal systems directly following particle motion by video-microscopy and may be useful to understand patterns out of equilibrium

Maps and twists relating U(sl(2))U(sl(2)) and the nonstandard Uh(sl(2))U_{h}(sl(2)): unified construction

A general construction is given for a class of invertible maps between the classical $U(sl(2))$ and the Jordanian $U_{h}(sl(2))$ algebras. Different maps are directly useful in different contexts. Similarity trasformations connecting them, in so far as they can be explicitly constructed, enable us to translate results obtained in terms of one to the other cases. Here the role of the maps is studied in the context of construction of twist operators between the cocommutative and noncocommutative coproducts of the $U(sl(2))$ and $U_{h}(sl(2))$ algebras respectively. It is shown that a particular map called the `minimal twist map' implements the simplest twist given directly by the factorized form of the ${\cal R}_{h}$-matrix of Ballesteros-Herranz. For other maps the twist has an additional factor obtainable in terms of the similarity transformation relating the map in question to the minimal one. The series in powers of $h$ for the operator performing this transformation may be obtained up to some desired order, relatively easily. An explicit example is given for one particularly interesting case. Similarly the classical and the Jordanian antipode maps may be interrelated by a similarity transformation. For the `minimal twist map' the transforming operator is determined in a closed form.Comment: LaTeX, 13 page

Spatio-temporal correlations in Wigner molecules

The dynamical response of Coulomb-interacting particles in nano-clusters are analyzed at different temperatures characterizing their solid- and liquid-like behavior. Depending on the trap-symmetry, both the spatial and temporal correlations undergo slow, stretched exponential relaxations at long times, arising from spatially correlated motion in string-like paths. Our results indicate that the distinction between the `solid' and `liquid' is soft: While particles in a `solid' flow producing dynamic heterogeneities, motion in `liquid' yields unusually long tail in the distribution of particle-displacements. A phenomenological model captures much of the subtleties of our numerical simulations.Comment: 5 pages, 4 figures, includes supplementary material