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We consider the lowest Landau level on a torus as a function of its circumference L 1 . When L 1 → 0, the ground state at general rational filling fraction is a crystal with a gap-a Tao-Thouless state. For filling fractions ν = p/(2pm + 1), these states are the limits of Laughlin's or Jain's wavefunctions describing the gapped quantum Hall states when L 1 → ∞. For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral fermions (dipoles), or rather to a Luttinger liquid modification thereof, at L 1 ∼ 5 magnetic lengths. Using exact diagonalization we identify this state as a version of the Rezayi-Read state, and find that it develops continuously into the state that is believed to describe the observed metallic phase as L 1 → ∞. Furthermore, the effective Landau level structure that emerges within the lowest Landau level is found to be a consequence of the magnetic symmetries.

We present a systematic treatment of the linear theory of scalar gravitational perturbations of various matter (including baryons, cold dark matter, photons, massless neutrinos, and massive neutrino) for the Hat, open and close universes, concentrating on the treatment of the massive neutrino component which has been either ignored or approximated crudely for the nonBat universe in previous literatures. PACS numbers: 98.80.Cq, 98.70.Vc

Eigenmodes play an important role in the dynamics of spatially extended systems. Using arrays of probes, it is possible to measure the spatial structure of experimentally observed fluctuations. But the interpretation of the measured data becomes very difficult if the number of probes is low, the probes are not evenly spaced or different sample rates are used. This is a common situation in magnetically confined fusion plasmas. A method is proposed that allows the time-resolved reconstruction of the mode numbers and frequencies of eigenmodes in such a situation. It is based on the well known Lomb periodogram and has the following properties: statistical interpretation of the results, combined analysis of spatial and temporal data and effective noise reduction. Though this method can be generalized to arbitrary geometries, this work is dedicated to the analysis of Alfvén eigenmodes in stellarators. The method is applied to Mirnov probes which are found in many stellarators to diagnose Alfvén eigenmodes.

Rotational properties of actinide nuclei are studied in the cranked Hartree-Fock-Bogoliubov model with pairing and quadrupole interactions. General conditions for the backbending anomaly are studied as a function of charge, 2, and neutron number, N, with the aim of comparing the rotation alignment in the rare-earth and actinide regions. It is found that the smooth increase of the moment of inertia with increasing angular momentum is due to a gradual alignment of both the i13/2 proton pair and the jlsIz neutron pair. At 2 -9 2 the critical rotational frequency is smaller for nil312 than for ujIs/2 and therefore the behaviour of the proton pair i13,2 at high spins seems to be decisive for the appearance of the backbending anomaly in this mass region. It is found that the core moment of inertia depends strongly on the rotational frequency and largely determines the slope of the J ( w 2 ) curve.