The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bil...

<p style='text-indent:20px;'>We consider a coupled system of nonlinear Lowest Landau Level equations. We first show the existence multi-solitons with an exponentially localised error term in space, and then we prove uniqueness result. also long time stability result sum traveling waves having all same speed, under condition that they are far away enough from each other. Finally, observe t...

The pair distribution function and the static structure factor are computed for composite fermions. Clear and robust evidence for a 2kF structure is seen in a range of filling factors in the vicinity of the half-filled Landau level. Surprisingly, it is found that filled Landau levels of composite fermions, i.e. incompressible FQHE states, bear a stronger resemblance to a Fermi sea than do fille...

A (p, q)-deformation of the Landau problem in a spherically symmetric harmonic potential is considered. The quantum spectrum as well as space noncommutativity are established, whether for the full Landau problem or its quantum Hall projections. The well known noncommutative geometry in each Landau level is recovered in the appropriate limit. PACS numbers: 02.40.Gh, 02.20.-a, 02.20.Uw Submitted ...

We study the quantum mechanical problem of a charged particle moving in a constant magnetic field and an azimuthilly symmetric external potential. We show that the lowest Landau level splits in a definite way if the external potential is a monotone function of the radial distance in the plane orthogonal to the magnetic field. For two-dimensional systems we give sufficient conditions such that a...