A Large Blue Shift of the Biexciton State in Tellurium Doped CdSe Colloidal Quantum Dots

The exciton-exciton interaction energy of Tellurium doped CdSe colloidal quantum dots is experimentally investigated. The dots exhibit a strong Coulomb repulsion between the two excitons, which results in a huge measured biexciton blue shift of up to 300 meV. Such a strong Coulomb repulsion implies a very narrow hole wave function localized around the defect, which is manifested by a large Stokes shift. Moreover, we show that the biexciton blue shift increases linearly with the Stokes shift. This result is highly relevant for the use of colloidal QDs as optical gain media, where a large biexciton blue shift is required to obtain gain in the single exciton regime.Comment: 9 pages, 4 figure

Dynamics of Perfectly Wetting Drops under Gravity

We study the dynamics of small droplets of polydimethylsiloxane (PDMS) silicone oil on a vertical, perfectly-wetting, silicon wafer. Interference videomicroscopy allows us to capture the dynamics of these droplets. We use droplets with a volumes typically ranging from 100 to 500 nanolitres (viscosities from 10 to 1000 centistokes) to understand long time derivations from classical solutions. Past researchers used one dimensional theory to understand the typical $t^{1/3}$ scaling for the position of the tip of the droplet in time $t$. We observe this regime in experiment for intermediate times and discover a two-dimensional, similarity solution of the shape of the droplet. However, at long times our droplets start to move more slowly down the plane than the $t^{1/3}$ scaling suggests and we observe deviations in droplet shape from the similarity solution. We match experimental data with simulations to show these deviations are consistent with retarded van der Waals forcing which should become significant at the small heights observed

Exact Results for 1D Kondo Lattice from Bosonization

We find a solvable limit to the problem of the 1D electron gas interacting with a lattice of Kondo scattering centers. In this limit, we present exact results for the problems of incommensurate filling, commensurate filling, impurity vacancy states, and the commensurate-incommensurate transition.Comment: 4 pages, two columns, Latex fil

Stripes Disorder and Correlation lengths in doped antiferromagnets

For stripes in doped antiferromagnets, we find that the ratio of spin and charge correlation lenghts, $\xi_{s}/\xi_{c}$, provide a sharp criterion for determining the dominant form of disorder in the system. If stripes disorder is controlled by topological defects then $\xi_{s}/\xi_{c}\lesssim 1$. In contast, if stripes correlations are disordered primarily by non-topological elastic deformations (i.e., a Bragg-Glass type of disorder) then $1<\xi _{s}/\xi_{c}\lesssim 4$ is expected. Therefore, the observation of $\xi _{s}/\xi_{c}\approx 4$ in $(LaNd)_{2-x}Sr_{x}CuO_{4}$ and $\xi_{s}/\xi _{c}\approx 3$ in $La_{2/3}Sr_{1/3}NiO_{4}$ invariably implies that the stripes are in a Bragg glass type state, and topological defects are much less relevant than commonly assumed. Expected spectral properties are discussed. Thus, we establish the basis for any theoretical analysis of the experimentally obsereved glassy state in these material.Comment: 4 pages, 2 figure

Contact Line Instability and Pattern Selection in Thermally Driven Liquid Films

Liquids spreading over a solid substrate under the action of various forces are known to exhibit a long wavelength contact line instability. We use an example of thermally driven spreading on a horizontal surface to study how the stability of the flow can be altered, or patterns selected, using feedback control. We show that thermal perturbations of certain spatial structure imposed behind the contact line and proportional to the deviation of the contact line from its mean position can completely suppress the instability. Due to the presence of mean flow and a spatially nonuniform nature of spreading liquid films the dynamics of disturbances is governed by a nonnormal evolution operator, opening up a possibility of transient amplification and nonlinear instabilities. We show that in the case of thermal driving the nonnormality can be significant, especially for small wavenumber disturbances, and trace the origin of transient amplification to a close alignment of a large group of eigenfunctions of the evolution operator. However, for values of noise likely to occur in experiments we find that the transient amplification is not sufficiently strong to either change the predictions of the linear stability analysis or invalidate the proposed control approach.Comment: 13 pages, 14 figure

On the principal bifurcation branch of a third order nonlinear long-wave equation

We study the principal bifurcation curve of a third order equation which describes the nonlinear evolution of several systems with a long--wavelength instability. We show that the main bifurcation branch can be derived from a variational principle. This allows to obtain a close estimate of the complete branch. In particular, when the bifurcation is subcritical, the large amplitude stable branch can be found in a simple manner.Comment: 11 pages, 3 figure

Stripes: Why hole rich lines are antiphase domain walls?

For stripes of hole rich lines in doped antiferromagnets, we investigate the competition between anti-phase and in-phase domain wall ground state configurations. We argue that a phase transition must occure as a function of the electron/hole filling fraction of the domain wall. Due to {\em transverse} kinetic hole fluctuations, empty domain walls are always anti-phase. At arbitrary electron filling fraction ($\delta$) of the domain wall (and in particular for $\delta \approx 1/4$ as in LaNdSrCuO), it is essential to account also for the transverse magnetic interactions of the electrons and their mobility {\em along} the domain wall. We find that the transition from anti-phase to in-phase stripe domain wall occurs at a critical filling fraction $0.28<\delta_{c}<0.30$, for any value of $\frac{J}{t}<{1/3}$. We further use our model to estimate the spin-wave velocity in a stripe system. Finally, relate the results of our microscopic model to previous Landau theory approach to stripes.Comment: 11 pages, 3 figure

Dynamics and Scaling of 2D Polymers in a Dilute Solution

The breakdown of dynamical scaling for a dilute polymer solution in 2D has been suggested by Shannon and Choy [Phys. Rev. Lett. {\bf 79}, 1455 (1997)]. However, we show here both numerically and analytically that dynamical scaling holds when the finite-size dependence of the relevant dynamical quantities is properly taken into account. We carry out large-scale simulations in 2D for a polymer chain in a good solvent with full hydrodynamic interactions to verify dynamical scaling. This is achieved by novel mesoscopic simulation techniques

Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear diffusion--convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.Comment: 25 page

Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II