Multifractality at the quantum Hall transition: Beyond the parabolic paradigm

We present an ultra-high-precision numerical study of the spectrum of multifractal exponents $\Delta_q$ characterizing anomalous scaling of wave function moments $$ at the quantum Hall transition. The result reads $\Delta_q = 2q(1-q)[b_0 + b_1(q-1/2)^2 + ...]$, with $b_0 = 0.1291\pm 0.0002$ and $b_1 = 0.0029\pm 0.0003$. The central finding is that the spectrum is not exactly parabolic, $b_1\ne 0$. This rules out a class of theories of Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point.Comment: 4 pages, 4 figure

Multifractality at the spin quantum Hall transition

Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $\eta$ characterizing the decay of wave function correlations is equal to 1/4, at variance with the $r^{-1/2}$ decay of the diffusion propagator. The multifractality spectra of eigenfunctions and of two-point conductances are found to be close-to-parabolic, $\Delta_q\simeq q(1-q)/8$ and $X_q\simeq q(3-q)/4$.Comment: 4 pages, 3 figure

On the length of chains of proper subgroups covering a topological group

We prove that if an ultrafilter L is not coherent to a Q-point, then each analytic non-sigma-bounded topological group G admits an increasing chain <G_a : a of its proper subgroups such that: (i) U_{a in b(L)} G_a=G; and $(ii)$ For every sigma-bounded subgroup H of G there exists a such that H is a subset of G_a. In case of the group Sym(w) of all permutations of w with the topology inherited from w^w this improves upon earlier results of S. Thomas

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

Indicators of stock status for large-pelagic fish based on length composition from driftnet fisheries in Zanzibar

Small-scale fisheries (SSF) contribute to approximately half of the total landings of tuna and tuna-like species in the Indian Ocean and are an important form of employment and source of protein. Research into the properties and dynamics of SSF in East Africa are important for the assessment and sustainable management of fish stocks, however, detailed fisheries data are often inadequate or absent. Fisheries-dependent data on driftnet fisheries in Zanzibar, Tanzania, was collected during the northeast monsoon seasons in 2014 and 2015. The data describes the properties of the driftnet fisheries and allows for comparisons of the length composition of the landings of the SSF with large-scale industrial fisheries (IF) fishing in Tanzania’s Exclusive Economic Zone (EEZ). This data also facil- itates the calculation of stock indicators for the five most abundant tuna and tuna-like species landed in Zanzibar. Results show that the two fisheries (SSF and IF) exploit the same stocks, and landings are representative of a similar length composition, while operating in different parts of Tanzania’s EEZ. High exploitation rates, above reference levels for all species were calculated, in agreement with official assessments by the IOTC, and suggest that calls for the expansion of the SSF should be reconsidered. The assessment and management of straddling stocks are dis- cussed, as well as solutions to challenges faced by local observer programmes

Dimensionality dependence of the wave function statistics at the Anderson transition

The statistics of critical wave functions at the Anderson transition in three and four dimensions are studied numerically. The distribution of the inverse participation ratios (IPR) $P_q$ is shown to acquire a scale-invariant form in the limit of large system size. Multifractality spectra governing the scaling of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR statistics and the multifractality at the Anderson transition in a high spatial dimensionality are formulated.Comment: 4 pages, 4 figure

Surface modification of mineral dust particles by sulphuric acid processing: Implications for ice nucleation abilities

The ability of coated mineral dust particles to act as ice nuclei (IN) was investigated at LACIS (Leipzig Aerosol Cloud Interaction Simulator) during the FROST1- and FROST2-campaigns (Freezing of dust). Sulphuric acid was condensed on the particles which afterwards were optionally humidified, treated with ammonia vapour and/or heat. By means of aerosol mass spectrometry we found evidence that processing of mineral dust particles with sulphuric acid leads to surface modifications of the particles. These surface modifications are most likely responsible for the observed reduction of the IN activation of the particles. The observed particle mass spectra suggest that different treatments lead to different chemical reactions on the particle surface. Possible chemical reaction pathways and products are suggested and the implications on the IN efficiency of the treated dust particles are discussed