Via measurements of commensurability features near the Landau filling factor ν=1/2, we probe the shape of the Fermi contour for hole-flux composite fermions confined to a wide GaAs quantum well. The data reveal that the composite fermions are strongly influenced by the characteristics of the Landau level in which they are formed. In particular, their Fermi contour is warped when their Landau le...

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...

We point out a close relation between a family of Gödel-type solutions of 3+1 General Relativity and the Landau problem in S2,R2 and H2; in particular, the classical geodesics correspond to Larmor orbits in the Landau problem. We discuss the extent of this relation, by analyzing the solutions of the Klein-Gordon equation in these backgrounds. Guided by the analogy with the Landau problem, we sp...

In the asymptotic limit of a large Ginzburg-Landau parameter, we give a new asymptotic formula for the L-norm of the Ginzburg-Landau order parameter. The formula is valid in the bulk regime where the intensity of the applied magnetic eld is of the same order as the Ginzburg-Landau parameter and strictly below the second critical eld. Our formula complements the celebrated one of Sandier-Serfaty...

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 ...

Homogeneous Fokker-Planck-Landau equation is investigated for Coulombic potential and isotropic distribution function i.e. when the distribution function depends only on time and on the modulus of the velocity. We derive a conservative and entropy decaying semi-discretized Landau equation for which we prove the existence of global in time positive solutions. This scheme is not based on the so-c...

While a large number of fractional quantized Hall states have been discovered in the lowest Landau level, such states become increasingly rare in higher Landau levels. Few quantized Hall states have been observed in the first Landau level (Landau level filling factor 2 ≤ ν < 4) and no such states have so far been found for filling factors ν ≥ 4. Correspondingly, the role of electron-electron in...

We introduce a duality construction for toric Landau-Ginzburg models, applicable to complete intersections in toric varieties via the sigma model / Landau-Ginzburg model correspondence. This construction is shown to reconstruct those of Batyrev-Borisov, Berglund-Hübsch, Givental, and HoriVafa. It can be done in more general situations, and provides partial resolutions when the above constructio...

We report on the experimental results of interlayer magnetoresistance in the multilayer massless Dirac fermion system alpha-(BEDT-TTF)2I3 under hydrostatic pressure and its interpretation. We succeeded in detecting the zero-mode Landau level (n=0 Landau level) that is expected to appear at the contact points of Dirac cones in the magnetic field normal to the two-dimensional plane. The character...

5 Simplification procedures 72 5.1 Simplification under Landau symbols . . . . . . . . . . . . . . 72 5.2 Simproc setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.3 Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.3.1 Product simplification tests . . . . . . . . . . . . . . . 74 5.3.2 Real product decision procure tests . . . . . . . . . . . 74 5.3.3 Su...