Multifractality of wavefunctions at the quantum Hall transition revisited

We investigate numerically the statistics of wavefunction amplitudes $\psi({\bf r})$ at the integer quantum Hall transition. It is demonstrated that in the limit of a large system size the distribution function of $|\psi|^2$ is log-normal, so that the multifractal spectrum $f(\alpha)$ is exactly parabolic. Our findings lend strong support to a recent conjecture for a critical theory of the quantum Hall transition.Comment: 4 pages Late

Liouvillian Approach to the Integer Quantum Hall Effect Transition

We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and the closed set of commutation relations between the projected densities leads to simple equations for the time evolution of the density operators. These equations can be used to map the problem of calculating the disorder averaged and energetically unconstrained density-density correlation function to the problem of calculating the one-particle density of states of a dynamical system with a novel action. At the self-consistent mean-field level, this approach yields normal diffusion and a finite longitudinal conductivity. While we have not been able to go beyond the saddle point approximation analytically, we show numerically that the critical localization exponent can be extracted from the energetically integrated correlation function yielding $\nu=2.33 \pm 0.05$ in excellent agreement with previous finite-size scaling studies.Comment: 9 pages, submitted to PR

Optimization of macroelement concentrations, pH and osmolarity for triacylglycerol accumulation in Rhodococcus opacus strain PD630

The refinement of biodiesel or renewable diesel from bacterial lipids has a great potential to make a contribution for energy production in the future. This study provides new data concerning suitable nutrient concentrations for cultivation of the Gram-positive Rhodococcus opacus PD630, which is able to accumulate large amounts of lipids during nitrogen limitation. Enhanced concentrations of magnesium have been shown to increase the final optical density and the lipid content of the cells. Elevated phosphate concentrations slowed down the onset of the accumulation phase, without a clear effect on the final optical density and the cell’s lipid content. A robust growth of R. opacus was possible in the presence of ammonium concentrations of up to 1.4 g l-1 and sucrose concentrations of up to 240 g l-1, with an optimum regarding growth and lipid storage observed in the range of 0.2 to 0.4 g l-1 ammonium and 20 to 40 g l-1 sucrose, respectively. Moreover, R. opacus showed tolerance to high salt concentrations

Skill obsolescence, vintage effects and changing tasks

Human capital is no doubt one of the most important factors for future economic growth and well-being. However, human capital is also prone to becoming obsolete over time. Skills that have been acquired at one point in time may perfectly match the skill requirements at that time but may become obsolete as time goes by. Thus, in the following paper, we study the depreciation processes of the human capital of workers performing different types of tasks with different skill requirements over a period of more than twenty years. We argue that two types of tasks must be distinguished: knowledge-based tasks and experience-based tasks. Knowledge-based tasks demand skills depending on the actual stock of technological knowledge in a society whereas experience-based tasks demand skills depending on personal factors and individual experience values. We show, by applying Mincer regressions on four different cross sections, that the human capital of people performing knowledge-based tasks suffers more from depreciation than the human capital of individuals performing experience-based tasks

Effect of Oscillating Landau Bandwidth on the Integer Quantum Hall Effect in a Unidirectional Lateral Superlattice

We have measured activation gaps for odd-integer quantum Hall states in a unidirectional lateral superlattice (ULSL) -- a two-dimensional electron gas (2DEG) subjected to a unidirectional periodic modulation of the electrostatic potential. By comparing the activation gaps with those simultaneously measured in the adjacent section of the same 2DEG sample without modulation, we find that the gaps are reduced in the ULSL by an amount corresponding to the width acquired by the Landau levels through the introduction of the modulation. The decrement of the activation gap varies with the magnetic field following the variation of the Landau bandwidth due to the commensurability effect. Notably, the decrement vanishes at the flat band conditions.Comment: 7 pages, 6 figures, minor revisio

Surface acoustic wave attenuation by a two-dimensional electron gas in a strong magnetic field

The propagation of a surface acoustic wave (SAW) on GaAs/AlGaAs heterostructures is studied in the case where the two-dimensional electron gas (2DEG) is subject to a strong magnetic field and a smooth random potential with correlation length Lambda and amplitude Delta. The electron wave functions are described in a quasiclassical picture using results of percolation theory for two-dimensional systems. In accordance with the experimental situation, Lambda is assumed to be much smaller than the sound wavelength 2*pi/q. This restricts the absorption of surface phonons at a filling factor \bar{\nu} approx 1/2 to electrons occupying extended trajectories of fractal structure. Both piezoelectric and deformation potential interactions of surface acoustic phonons with electrons are considered and the corresponding interaction vertices are derived. These vertices are found to differ from those valid for three-dimensional bulk phonon systems with respect to the phonon wave vector dependence. We derive the appropriate dielectric function varepsilon(omega,q) to describe the effect of screening on the electron-phonon coupling. In the low temperature, high frequency regime T << Delta (omega_q*Lambda /v_D)^{alpha/2/nu}, where omega_q is the SAW frequency and v_D is the electron drift velocity, both the attenuation coefficient Gamma and varepsilon(omega,q) are independent of temperature. The classical percolation indices give alpha/2/nu=3/7. The width of the region where a strong absorption of the SAW occurs is found to be given by the scaling law |Delta \bar{\nu}| approx (omega_q*Lambda/v_D)^{alpha/2/nu}. The dependence of the electron-phonon coupling and the screening due to the 2DEG on the filling factor leads to a double-peak structure for Gamma(\bar{\nu}).Comment: 17 pages, 3 Postscript figures, minor changes mad

Characterization of the Local Density of States Fluctuations near the Integer Quantum Hall Transition in a Quantum Dot Array

We present a calculation for the second moment of the local density of states in a model of a two-dimensional quantum dot array near the quantum Hall transition. The quantum dot array model is a realistic adaptation of the lattice model for the quantum Hall transition in the two-dimensional electron gas in an external magnetic field proposed by Ludwig, Fisher, Shankar and Grinstein. We make use of a Dirac fermion representation for the Green functions in the presence of fluctuations for the quantum dot energy levels. A saddle-point approximation yields non-perturbative results for the first and second moments of the local density of states, showing interesting fluctuation behaviour near the quantum Hall transition. To our knowledge we discuss here one of the first analytic characterizations of chaotic behaviour for a two-dimensional mesoscopic structure. The connection with possible experimental investigations of the local density of states in the quantum dot array structures (by means of NMR Knight-shift or single-electron-tunneling techniques) and our work is also established.Comment: 11 LaTeX pages, 1 postscript figure, to appear in Phys.Rev.

Localized states in strong magnetic field: resonant scattering and the Dicke effect

We study the energy spectrum of a system of localized states coupled to a 2D electron gas in strong magnetic field. If the energy levels of localized states are close to the electron energy in the plane, the system exhibits a kind of collective behavior analogous to the Dicke effect in optics. The latter manifests itself in ``trapping'' of electronic states by localized states. At the same time, the electronic density of states develops a gap near the resonance. The gap and the trapping of states appear to be complementary and reflect an intimate relation between the resonant scattering and the Dicke effect. We reveal this relation by presenting the exact solution of the problem for the lowest Landau level. In particular, we show that in the absence of disorder the system undergoes a phase transition at some critical concentration of localized states.Comment: 28 pages + 9 fig

Turbulence in the Solar Atmosphere: Manifestations and Diagnostics via Solar Image Processing

Intermittent magnetohydrodynamical turbulence is most likely at work in the magnetized solar atmosphere. As a result, an array of scaling and multi-scaling image-processing techniques can be used to measure the expected self-organization of solar magnetic fields. While these techniques advance our understanding of the physical system at work, it is unclear whether they can be used to predict solar eruptions, thus obtaining a practical significance for space weather. We address part of this problem by focusing on solar active regions and by investigating the usefulness of scaling and multi-scaling image-processing techniques in solar flare prediction. Since solar flares exhibit spatial and temporal intermittency, we suggest that they are the products of instabilities subject to a critical threshold in a turbulent magnetic configuration. The identification of this threshold in scaling and multi-scaling spectra would then contribute meaningfully to the prediction of solar flares. We find that the fractal dimension of solar magnetic fields and their multi-fractal spectrum of generalized correlation dimensions do not have significant predictive ability. The respective multi-fractal structure functions and their inertial-range scaling exponents, however, probably provide some statistical distinguishing features between flaring and non-flaring active regions. More importantly, the temporal evolution of the above scaling exponents in flaring active regions probably shows a distinct behavior starting a few hours prior to a flare and therefore this temporal behavior may be practically useful in flare prediction. The results of this study need to be validated by more comprehensive works over a large number of solar active regions.Comment: 26 pages, 7 figure

Metal-insulator transitions in anisotropic 2d systems

Several phenomena related to the critical behaviour of non-interacting electrons in a disordered 2d tight-binding system with a magnetic field are studied. Localization lengths, critical exponents and density of states are computed using transfer matrix techniques. Scaling functions of isotropic systems are recovered once the dimension of the system in each direction is chosen proportional to the localization length. It is also found that the critical point is independent of the propagation direction, and that the critical exponents for the localization length for both propagating directions are equal to that of the isotropic system (approximately 7/3). We also calculate the critical value of the scaling function for both the isotropic and the anisotropic system. It is found that the isotropic value equals the geometric mean of the two anisotropic values. Detailed numerical studies of the density of states for the isotropic system reveals that for an appreciable amount of disorder the critical energy is off the band center.Comment: 6 pages RevTeX, 6 figures included, submitted to Physical Review