Short-term social memory in the laboratory rat: its susceptibility to disturbance.

Short-term social memory in the laboratory rat: its susceptibility to disturbance

Integer quantum Hall effect for hard-core bosons and a failure of bosonic Chern-Simons mean-field theories for electrons at half-filled Landau level

Field-theoretical methods have been shown to be useful in constructing simple effective theories for two-dimensional (2D) systems. These effective theories are usually studied by perturbing around a mean-field approximation, so the question whether such an approximation is meaningful arises immediately. We here study 2D interacting electrons in a half-filled Landau level mapped onto interacting hard-core bosons in a magnetic field. We argue that an interacting hard-core boson system in a uniform external field such that there is one flux quantum per particle (unit filling) exhibits an integer quantum Hall effect. As a consequence, the mean-field approximation for mapping electrons at half-filling to a boson system at integer filling fails.Comment: 13 pages latex with revtex. To be published in Phys. Rev.

Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar

The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical formula for the localisation length is derived, describing the dimensional crossover as function of width $L_y$, conductance $g$ and perpendicular magnetic field $B$ . On the basis of these results, the scaling analysis of the quantum Hall effect in high Landau levels, and the delocalisation transition in a quantum Hall wire are reconsidered.Comment: 12 pages, 7 figure

Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems

We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers satisfying Fermi statistics (or those related to fermions by the action of the group), the resulting group is known to imply many, if not all, of the remarkable features of Quantum Hall systems. For conductors with boson charge carriers (modulo group transformations) a different group is predicted, implying equally striking implications for the conductivities of these systems, including a super-universality of the critical exponents for conductor/insulator and superconductor/insulator transitions in two dimensions and a hierarchical structure, analogous to that of the quantum Hall effect but different in its details. Our derivation shows how this symmetry emerges at low energies, depending only weakly on the details of dynamics of the underlying systems.Comment: 22 pages, LaTeX, 2 figures, uses revte