Scaling the localisation lengths for two interacting particles in one-dimensional random potentials

Using a numerical decimation method, we compute the localisation length $\lambda_{2}$ for two onsite interacting particles (TIP) in a one-dimensional random potential. We show that an interaction $U>0$ does lead to $\lambda_2(U) > \lambda_2(0)$ for not too large $U$ and test the validity of various proposed fit functions for $\lambda_2(U)$. Finite-size scaling allows us to obtain infinite sample size estimates $\xi_{2}(U)$ and we find that $\xi_{2}(U) \sim \xi_2(0)^{\alpha(U)}$ with $\alpha(U)$ varying between $\alpha(0)\approx 1$ and $\alpha(1) \approx 1.5$. We observe that all $\xi_2(U)$ data can be made to coalesce onto a single scaling curve. We also present results for the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs.Comment: proceedings of "Percolation98", 5 Elsart pages with 5 figures to be published in Physica

Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential

We present calculations of the localisation length, $\lambda_{2}$, for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength $U$ and system size. $\lambda_{2}(U)$ is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates $\xi_{2}(U)$ are obtained by finite-size scaling. For U=0 we reproduce approximately the well-known dependence of the one-particle localisation length on disorder while for finite $U$, we find that $\xi_{2}(U) \sim \xi_2(0)^{\beta(U)}$ with $\beta(U)$ varying between $\beta(0)=1$ and $\beta(1) \approx 1.5$. We test the validity of various other proposed fit functions and also study the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs. As a check of our method and data, we also reproduce well-known results for the two-dimensional Anderson model without interaction.Comment: 34 RevTeX 3.0 pages with 16 figures include

Non-linear conductivity and quantum interference in disordered metals

We report on a novel non-linear electric field effect in the conductivity of disordered conductors. We find that an electric field gives rise to dephasing in the particle-hole channel, which depresses the interference effects due to disorder and interaction and leads to a non-linear conductivity. This non-linear effect introduces a field dependent temperature scale $T_E$ and provides a microscopic mechanism for electric field scaling at the metal-insulator transition. We also study the magnetic field dependence of the non-linear conductivity and suggest possible ways to experimentally verify our predictions. These effects offer a new probe to test the role of quantum interference at the metal-insulator transition in disordered conductors.Comment: 5 pages, 3 figure

Disordered vortex arrays in a two-dimensional condensate

We suggest a method to create turbulence in a Bose-Einstein condensate. The method consists in, firstly, creating an ordered vortex array, and, secondly, imprinting a phase difference in different regions of the condensate. By solving numerically the two-dimensional Gross-Pitaevskii equation we show that the motion of the resulting positive and negative vortices is disordered.Comment: 14 pages, 18 figures, accepted by Geophysical and Astrophysical Fluid Dynamic

Three-dimensional images of choanoflagellate loricae

Choanoflagellates are unicellular filter-feeding protozoa distributed universally in aquatic habitats. Cells are ovoid in shape with a single anterior flagellum encircled by a funnel-shaped collar of microvilli. Movement of the flagellum creates water currents from which food particles are entrapped on the outer surface of the collar and ingested by pseudopodia. One group of marine choanoflagellates has evolved an elaborate basket-like exoskeleton, the lorica, comprising two layers of siliceous costae made up of costal strips. A computer graphic model has been developed for generating three-dimensional images of choanoflagellate loricae based on a universal set of 'rules' derived from electron microscopical observations. This model has proved seminal in understanding how complex costal patterns can be assembled in a single continuous movement. The lorica, which provides a rigid framework around the cell, is multifunctional. It resists the locomotory forces generated by flagellar movement, directs and enhances water flow over the collar and, for planktonic species, contributes towards maintaining cells in suspension. Since the functional morphology of choanoflagellate cells is so effective and has been highly conserved within the group, the ecological and evolutionary radiation of choanoflagellates is almost entirely dependent on the ability of the external coverings, particularly the lorica, to diversify