Laughlin’s Ansatz to explain the fractional Quantum Hall effect is derived by coupling a particle associated with “exotic” the two-fold central extension of the planar Galilei group. The reduced system is identical to the one used to describe the dynamics of vortices in an incompressible planar fluid.

The Landau problem is discussed in two similar but still different non-commutative frameworks. The “standard” one, where the coupling to the gauge field is achieved using Poisson brackets, yields all Landau levels. The “exotic” approach, where the coupling to the gauge field is achieved using the symplectic structure, only yields lowest-Landau level states, as advocated by Peierls and used in t...

Anomalous spin Hall effects that belong to the intrinsic type in Dresselhaus (110) quantum wells are discussed. For the out-of-plane spin component, antisymmetric current-induced spin polarization induces opposite spin Hall accumulation, even though there is no spin-orbit force due to Dresselhaus (110) coupling. A surprising feature of this spin Hall induction is that the spin accumulation sign...

The implementation of modular invariance on the torus at the quantum level is discussed in a group-theoretical framework. Two cases must be considered, depending on the cohomology class of the symplectic form on the torus. If it is of integer cohomology class n, then full modular invariance is achieved at the quantum level only for those wave functions on the torus which are periodic if n is ev...

The Landau problem is discussed in two similar but still different non-commutative frameworks. The “standard” one, where the coupling to the gauge field is achieved using Poisson brackets, yields all Landau levels. The “exotic” approach, where the coupling to the gauge field is achieved using the symplectic structure, only yields lowest-Landau level states as advocated by Peierls, and widely us...

Addition formulas for theta functions of arbitrary order are shown and applied to the theoretical understanding of the fractional quantum Hall effect in a multi-layer two-dimensional many-electron system under periodic conditions.

A two-dimensional harmonic oscillator, when rotated by the oscillator frequency, generates Landau-like levels. A further cranking results in condensates and gaps resembling the fractional quantum Hall effect. For a filling fraction ν = p/q, with q odd, the model predicts that the gap is proportional to √ ne/pq, where ne is the electron density of the sample. This agrees well with recent experim...

We study the linear response spin Hall conductivity of a two-dimensional electron gas (2DEG) in the presence of the Rashba spin-orbit interaction in the diffusive transport regime. When defect scattering is modeled by isotropic short-range potential scatterers the spin Hall conductivity vanishes due to the vertex correction. A nonvanishing spin Hall effect may be recovered for dominantly forwar...

The “Laughlin” picture of the Fractional Quantum Hall effect can be derived using the “exotic” model based on the two-fold centrally-extended planar Galilei group. When coupled to a planar magnetic field of critical strength determined by the extension parameters, the system becomes singular, and “Faddeev-Jackiw” reduction yields the “Chern-Simons” mechanics of Dunne, Jackiw, and Trugenberger. ...

Background and objectives: Calamus rotang is used in traditional medicine. Regarding the previous phytochemical screening of methanol extract of Calamus rotang L. fruits (MCR), this study was performed to find out the antidiarrheal and hypoglycemic effects of the experimented extract in rodents. Methods: Castor oil induced diarrheal test...