Condensed Matter Theory

Abstract:

We study statistical properties of the eigenvectors of non-Hermitian random matrices, concentrating on Ginibre’s complex Gaussian ensemble, in which the real and imaginary parts of each element of an N × N matrix, J, are independent random variables. Calculating ensemble averages based on the quantity ⟨Lα|Lβ⟩ ⟨Rβ|Rα⟩, where ⟨Lα| and |Rβ⟩ are left and right eigenvectors of J, we show for large N that eigenvectors associated with a pair of eigenvalues are highly correlated if the two eigenvalues lie close in the complex plane. We examine consequences of these correlations that are likely to be important in physical applications. © 1998 The American Physical Society.

Abstract:

The composite fermion picture has had a remarkable number of recent successes both in the description of the fractional quantized Hall states and in the description on the even denominator Fermi liquid like states. In this review we give an introductory account of the Chern-Simons fermion theory, focusing on the description of the even denominator states as unusual Fermi liquids.

Abstract:

We consider the two-dimensional chiral metal, which exists at the surface of a layered, three-dimensional sample exhibiting the integer quantum Hall effect. We calculate its magnetoresistance in response to a component of magnetic field perpendicular to the sample surface, in the low temperature, but macroscopic, regime where inelastic scattering may be neglected. The magnetoresistance is positive, following a Drude form with a field scale, $B_0=\Phi_0/al_{\text{el}}$, given by the transverse field strength at which one quantum of flux, $\Phi_0$, passes through a rectangle with sides set by the layer-spacing, $a$, and the elastic mean free path, $l_{\text{el}}$. Experimental measurement of this magnetoresistance may therefore provide a direct determination of the elastic mean free path in the chiral metal.