Fluctuations of the inverse participation ratio at the Anderson transition

Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale-invariant, with a power-law asymptotic ``tail''. This scale invariance implies that the fractal dimensions $D_q$ are non-fluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between $D_2$ and the spectral compressibility $\chi$ is violated in the regime of strong multifractality, with $\chi\to 1$ in the limit $D_2\to 0$.Comment: 4 pages, 3 eps figure

Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition

We present a numerical finite size scaling study of the localization length in long cylinders near the integer quantum Hall transition (IQHT) employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical problem. In this work we develop a novel method of stability analysis that allows for a better estimate of error bars. Applying the new method we find consistent results when keeping second (or higher) order terms of the leading irrelevant scaling field. The knowledge of the associated (negative) irrelevant exponent $y$ is crucial for a precise determination of other critical exponents, including multifractal spectra of wave functions. We estimate $|y| > 0.4$, which is considerably larger than most recently reported values. Within this approach we obtain the localization length exponent $2.62 \pm 0.06$ confirming recent results. Our stability analysis has broad applicability to other observables at IQHT, as well as other critical points where corrections to scaling are present.Comment: 6 pages and 3 figures, plus supplemental material

Wave function statistics at the symplectic 2D Anderson transition: bulk properties

The wavefunction statistics at the Anderson transition in a 2d disordered electron gas with spin-orbit coupling is studied numerically. In addition to highly accurate exponents ($\alpha_0{=}2.172\pm 0.002, \tau_2{=}1.642\pm 0.004$), we report three qualitative results: (i) the anomalous dimensions are invariant under $q\to (1-q)$ which is in agreement with a recent analytical prediction and supports the universality hypothesis. (ii) The multifractal spectrum is not parabolic and therefore differs from behavior suspected, e.g., for (integer) quantum Hall transitions in a fundamental way. (iii) The critical fixed point satisfies conformal invariance.Comment: 4 pages, 3 figure

Loading atom lasers by collectivity-enhanced optical pumping

The effect of collectivity on the loading of an atom laser via optical pumping is discussed. In our model, atoms in a beam are laser-excited and subsequently spontaneously decay into a trapping state. We consider the case of sufficiently high particle density in the beam such that the spontaneous emission is modified by the particle interaction. We show that the collective effects lead to a better population of the trapping state over a wide range of system parameters, and that the second order correlation function of the atoms can be controlled by the applied laser field.Comment: 5 pages, 7 figure

Jacob: An Educational Agent in a Virtual Environment

The Jacob Project involves the construction of a virtual environment where an animated human-like agent called Jacob gives instruction to the user. The project focuses on three issues: the software engineering aspects of building a virtual reality system, the integration of natural language interaction and other interaction modalities, and the use of agent technology. Jacob has been given a task model and an instruction model in order to teach a particular task. The results of the project can be generalized so that the agent can be used to instruct other tasks in other virtual environments

Towards Informative Path Planning for Acoustic SLAM

Acoustic scene mapping is a challenging task as microphone arrays can often localize sound sources only in terms of their directions. Spatial diversity can be exploited constructively to infer source-sensor range when using microphone arrays installed on moving platforms, such as robots. As the absolute location of a moving robot is often unknown in practice, Acoustic Simultaneous Localization And Mapping (a-SLAM) is required in order to localize the moving robot’s positions and jointly map the sound sources. Using a novel a-SLAM approach, this paper investigates the impact of the choice of robot paths on source mapping accuracy. Simulation results demonstrate that a-SLAM performance can be improved by informatively planning robot paths

Non-diffracting Optical Beams in a Three-level Raman System

Diffractionless propagation of optical beams through atomic vapors is investigated. The atoms in the vapor are operated in a three-level Raman configuration. A suitably chosen control beam couples to one of the transitions, and thereby creates a spatially varying index of refraction modulation in the warm atomic vapor for a probe beam which couples to the other transition in the atoms. We show that a Laguerre-Gaussian control beam allows to propagate single Gaussian probe field modes as well as multi-Gaussian modes and non-Gaussian modes over macroscopic distances without diffraction. This opens perspectives for the propagation of arbitrary images through warm atomic vapors.Comment: 8 pages, 7 figure