Nonlinear Dynamics of Composite Fermions in Nanostructures

We outline a theory describing the quasi-classical dynamics of composite fermions in the fractional quantum Hall regime in the potentials of arbitrary nanostructures. By an appropriate parametrization of time we show that their trajectories are independent of their mass and dispersion. This allows to study the dynamics in terms of an effective Hamiltonian although the actual dispersion is as yet unknown. The applicability of the theory is verified in the case of antidot arrays where it explains details of magnetoresistance measurements and thus confirms the existence of these quasiparticles.Comment: submitted to Europhys. Lett., 4 pages, postscrip

Umbilical endometriosis

We report two women who presented with a recurrent, mildly painful, bluish nodule in the umbilicus. Both patients complained of local tenderness and occasional bleeding that increased during menstruation. Neither patient had had previous pelvic surgery. Excision of the lesions revealed a primary umbilical endometriosis; in one case, a simultaneous laparoscopy showed a pelvic endometriosis. We review the current literature and discuss the possible etiopathogenesis and when a laparoscopy is indicated to diagnose a concomitant pelvic endometriosis. Umbilical endometriosis is a very rare disease but should be considered in the differential diagnosis of umbilical lesion

Perfectly Translating Lattices on a Cylinder

We perform molecular dynamics simulations on an interacting electron gas confined to a cylindrical surface and subject to a radial magnetic field and the field of the positive background. In order to study the system at lowest energy states that still carry a current, initial configurations are obtained by a special quenching procedure. We observe the formation of a steady state in which the entire electron-lattice cycles with a common uniform velocity. Certain runs show an intermediate instability leading to lattice rearrangements. A Hall resistance can be defined and depends linearly on the magnetic field with an anomalous coefficient reflecting the manybody contributions peculiar to two dimensions.Comment: 13 pages, 5 figure

Devil's Staircase in Magnetoresistance of a Periodic Array of Scatterers

The nonlinear response to an external electric field is studied for classical non-interacting charged particles under the influence of a uniform magnetic field, a periodic potential, and an effective friction force. We find numerical and analytical evidence that the ratio of transversal to longitudinal resistance forms a Devil's staircase. The staircase is attributed to the dynamical phenomenon of mode-locking.Comment: two-column 4 pages, 5 figure

Frequency-dependent magnetotransport and particle dynamics in magnetic modulation systems

We analyze the dynamics of a charged particle moving in the presence of spatially-modulated magnetic fields. From Poincare surfaces of section and Liapunov exponents for characteristic trajectories we find that the fraction of pinned and runaway quasiperiodic orbits {\em vs}. chaotic orbits depends strongly on the ratio of cyclotron radius to the structure parameters, as well as on the amplitude of the modulated field. We present a complete characterization of the dynamical behavior of such structures, and investigate the contribution to the magnetoconductivity from all different orbits using a classical Kubo formula. Although the DC conductivity of the system depends strongly on the pinned and runaway trajectories, the frequency response reflects the topology of all different orbits, and even their unusual temporal behavior.Comment: Submitted to PRB - 14 figure files - REVTEX tex

Flat-band ferromagnetism in quantum dot superlattices

Possibility of flat-band ferromagnetism in quantum dot arrays is theoretically discussed. By using a quantum dot as a building block, quantum dot superlattices are possible. We consider dot arrays on Lieb and kagome lattices known to exhibit flat band ferromagnetism. By performing an exact diagonalization of the Hubbard Hamiltonian, we calculate the energy difference between the ferromagnetic ground state and the paramagnetic excited state, and discuss the stability of the ferromagnetism against the second nearest neighbor transfer. We calculate the dot-size dependence of the energy difference in a dot model and estimate the transition temperature of the ferromagnetic-paramagnetic transition which is found to be accessible within the present fabrication technology. We point out advantages of semiconductor ferromagnets and suggest other interesting possibilities of electronic properties in quantum dot superlattices.Comment: 15 pages, 7 figures (low resolution). High-resolution figures are available at http://www.brl.ntt.co.jp/people/tamura/Research/PublicationPapers.htm

Duality Relation among Periodic Potential Problems in the Lowest Landau Level

Using a momentum representation of a magnetic von Neumann lattice, we study a two-dimensional electron in a uniform magnetic field and obtain one-particle spectra of various periodic short-range potential problems in the lowest Landau level.We find that the energy spectra satisfy a duality relation between a period of the potential and a magnetic length. The energy spectra consist of the Hofstadter-type bands and flat bands. We also study the connection between a periodic short-range potential problem and a tight-binding model.Comment: 6 pages, 3 figures, final version to appear in PR