Continuum elasticity theory of edge excitations in a two-dimensional electron liquid with finite range interactions

We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with the following simplifying assumptions: (i) The system is {\it macroscopically} homogeneous and isotropic in the half-plane delimited by the edge (ii) The electron-electron interaction is of finite range due to screening by external electrodes (iii) The system is nearly incompressible. At sufficiently small wave vector $q$ we find a universal dispersion curve $\omega \sim q$ independent of the shear modulus. At larger wave vectors the dispersion can change its form in a manner dependent on the comparison of various length scales. We obtain analytical formulas for the dispersion and damping of the modes in various physical regimes.Comment: 3 figure

Exact exchange-correlation potential for a time-dependent two electron system

We obtain an exact solution of the time-dependent Schroedinger equation for a two-electron system confined to a plane by an isotropic parabolic potential whose curvature is periodically modulated in time. From this solution we compute the exact time-dependent exchange correlation potential v_xc which enters the Kohn-Sham equation of time-dependent density functional theory. Our exact result provides a benchmark against which various approximate forms for v_xc can be compared. Finally v_xc is separated in an adiabatic and a pure dynamical part and it is shown that, for the particular system studied, the dynamical part is negligible.Comment: 23 pages, 6 figure

Glycine insertion makes yellow fluorescent protein sensitive to hydrostatic pressure

Fluorescent protein-based indicators for intracellular environment conditions such as pH and ion concentrations are commonly used to study the status and dynamics of living cells. Despite being an important factor in many biological processes, the development of an indicator for the physicochemical state of water, such as pressure, viscosity and temperature, however, has been neglected. We here found a novel mutation that dramatically enhances the pressure dependency of the yellow fluorescent protein (YFP) by inserting several glycines into it. The crystal structure of the mutant showed that the tyrosine near the chromophore flipped toward the outside of the β-can structure, resulting in the entry of a few water molecules near the chromophore. In response to changes in hydrostatic pressure, a spectrum shift and an intensity change of the fluorescence were observed. By measuring the fluorescence of the YFP mutant, we succeeded in measuring the intracellular pressure change in living cell. This study shows a new strategy of design to engineer fluorescent protein indicators to sense hydrostatic pressure