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Comment: Added reference
Comment: 50 pages, Figures available upon request, IUCM94-014
Comment: 30 pages: 4 figures available on request
When the chemical potential of an electron system has a discontinuity at a density $n^{*}$, the system is said to be incompressible and a finite energy is required to create mobile charges in the bulk of the system. The quantum Hall effect is associated with incompressibilities in a two-dimensional electron system that occur at magnetic-field dependent densities, $n^{*}(B)$. In these notes we discuss two aspects of the physics of quantum Hall systems that follow directly from this association.
Comment: 22 pages including 4 figures, submitted to Solid State Communications
Comment: Based on talk at MBIX conference, Sydney, July 1997. 12 pages, 3 figures
We present a theory of time-dependent tunneling between a metal and a partially spin-polarized two-dimensional electron system (2DES). We find that the leakage current which flows to screen an electric field between the metal and the 2DES is the sum of two exponential contributions whose relative weights depend on spin-dependent tunneling conductances, on quantum corrections to the electrostatic capacitance of the tunnel junction, and on the rate at which the 2DES spin-polarization approaches equilibrium. For high-mobility and homogeneous 2DES's at Landau level filling factor $\nu=1$, we predict a ratio of the fast and slow leakage rates equal to $(2K+1)^2$ where $K$ is the number of reversed spins in the skyrmionic elementary charged excitations.
Comment: 14 pages, 4 figures. Based on lecture given at the XVI Sitges Conference, June 1999. Proceedings to be published by Springer-Verlag
Comment: 5 pages, 5 figures; QHE eq corrected; added figure 4 and updated discussion
Comment: 25 pages, 15 figures; Expanded version of PRB 77,155416 (2008), arXiv:0711.4333; Published in the proceedings of YKIS2007; Typos corrected
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