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We present a microscopic theory of the fractional quantum Hall effect at the filling factor ν with even denominator, which is recently observed in a double-layer electron system. In our approach electrons belonging to different layers are interpreted as different types of anyons with appropriate statistics. The wavefunction of the Hall state is calculated, which is found to coincide with that of Halperin. We also analyze vortex (quasihole) excitations. It is shown that a single vortex carries electric charges on both of the layers; for instance, a vortex at ν=½ has the electric charge [Formula: see text] on one layer and -⅛e on the other layer. The ground state at the vicinity of ν=½ is given by a Wigner crystal made of these vortices.

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We show that fast radio bursts arise from collisions between axion stars and neutron stars. The bursts are emitted in the atmosphere of the neutron stars. The observed frequencies of the bursts are given by the axion mass ma such as ma/2π ≃ 1.4 GHz ma/(6 × 10 −6 eV) . From the event rate ∼ 10 −3 per year in a galaxy, we can determine the mass ∼ 10 −11 M⊙ of the axion stars. Using these values we can explain short durations ( ∼ms ) and amount of radiation energies ( ∼ 10 43 GeV ) of the bursts.PACS numbers: 98.70.Dk, 14.80.Va, 11.27.+d Axion, Neutron Star, Fast Radio Burst Fast Radio Bursts ( FRBs ) have recently been discovered [1][2][3] at around 1.4 GHz frequency. The durations of the bursts are typically a few milliseconds. The origin of the bursts has been suggested to be extra-galactic owing to their large dispersion measures. This suggests that the large amount of the energies ∼ 10 46 GeV/s is produced at the radio frequencies. The event rate of the burst is estimated to be ∼ 10 −3 per year in a galaxy. Furthermore, no gamma ray bursts associated with the bursts have been detected. To find progenitors of the bursts, several models [4] have been proposed.In the letter, we show that FRBs arise from collisions between neutron stars and axion stars [5,6]. The axion star is a boson star ( known as oscillaton [7] ) made of axions bounded gravitationally. The axion stars have been discussed [8] to be formed in an epoch after the period of equal matter and radiation energy density.The production mechanism of FRBs is shown in the following. Under strong magnetic fields of neutron stars, axion stars generate oscillating electric fields [9]. When they collide with the neutron stars, the oscillating electric fields rapidly produce radiations in the atmospheres of the neutron stars. Since the frequency of the oscillating electric field is given by the axion mass m a , the frequency of the radiations produced [10] in the collisions is equal to m a /2π ≃ 2.4 GHz (m a /10 −5 eV). This is the case of electrons accelerated by the electric field initially stopping relative to the axion stars. Actually, we need to take into account Doppler effect owing to the electron motions in the atmosphere of the neutron stars, in order to explain finite band width of the observed FRBs.The observations of FRBs constraint the parameters of the axion stars, that is, the mass of the axion and the mass of the axion stars. The observed frequency ( ≃ 1.4 GHz ) of FRBs gives the mass ( ≃ 6 × 10 −6 eV ) of the axion, while the observed rate of the bursts ( ∼ 10 −3 per year in a galaxy ) gives the mass ( ∼ 10 −11 M ⊙ ) of the axion stars under the assumption that halo of galaxy is composed of the axion stars. Then, with the use of the theoretical formula [6,9] relating radius R a to mass M a of the axion stars, we can find the radius R a ∼ 160km. Since the relative velocity v c at the time when the collisions occur is estimated to be a several ten thousand km/s, we find that the durations of FRBs are given by R a /v c ∼ a few milliseconds.First w...

We study 2+l-dimensional Chern-Simons gauge theories with external magnetic field B and the self-interaction of the matter field. It is shown that the system has three phases depending on the strength g of the self-interaction. They are the symmetry-preserving phase for g > g,, and the symmetry-breaking phase for g, > g > -g,, with kg, the critical coupling constants. When g, > g > 0 the system has an excitation with gap; when 0 > g > -g, its spectrum develops the absolute minimum at a nonzero momentum. The corresponding excitation becomes gapless at g = -g,, and the system is unstable for g < -9,. We then analyze vortex solitons which are anyons. Nontopological (topological) vortices are relevant in the symmetry-preserving (-breaking) phase. The charge, spin, and mass of these vortices are calculated. These vortices can be analyzed analytically at the critical points g = kg,. The static energy of self-dual topological vortices is obtained explicitly, and is expressed as a spin-magnetic interaction. We also present analytic time-dependent solutions of nontopological vortices, which describe vortex solitons moving along the cyclotron orbit in the external magnetic field.

A homogeneous color magnetic field is known to be unstable for the fluctuations perpendicular to the field in the color space (the Nielsen-Olesen instability). We argue that these unstable modes, exponentially growing, generate an azimuthal magnetic field with the original field being in the z-direction, which causes the Nielsen-Olesen instability for another type of fluctuations. The growth rate of the latter unstable mode increases with the momentum p z and can become larger than the former's growth rate which decreases with increasing p z . These features may explain the interplay between the primary and secondary instabilities observed in the real-time simulation of a non-expanding glasma, i.e., stochastically generated anisotropic Yang-Mills fields without expansion.

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