Condensed Matter Theory

Abstract:

An effective field theoretic description of $\nu=1$ bilayer electron systems stabilized by Coulomb repulsion in a single wide quantum well is examined using renormalization group techniques. The system is found to undergo a crossover from a low temperature strongly correlated quantum Hall state to a high temperature compressible state. This picture is used to account for the recent experimental observation of an anomalous transition in bilayer electron systems (T. S. Lay, {\em et al.} Phys. Rev. B {\bf 50}, 17725 (1994)). An estimate for the crossover temperature is provided, and it is shown that its dependence on electron density is in reasonable agreement with i the experiment.

Abstract:

Statistical properties of eigenvectors in non-Hermitian random matrix ensembles are discussed, with an emphasis on correlations between left and right eigenvectors. Two approaches are described. One is an exact calculation for Ginibre's ensemble, in which each matrix element is an independent, identically distributed Gaussian complex random variable. The other is a simpler calculation using $N^{-1}$ as an expansion parameter, where $N$ is the rank of the random matrix: this is applied to Girko's ensemble. Consequences of eigenvector correlations which may be of physical importance in applications are also discussed. It is shown that eigenvalues are much more sensitive to perturbations than in the corresponding Hermitian random matrix ensembles. It is also shown that, in problems with time-evolution governed by a non- Hermitian random matrix, transients are controlled by eigenvector correlations.

Abstract:

Using a generalization of the Poisson-Boltzmann equation, dynamics of counterion condensation is studied. For a single charged plate in the presence of counterions, it is shown that the approach to equilibrium is diffusive. In the far from equilibrium case of a moving charged plate, a dynamical counterion condensation transition occurs at a critical velocity. The complex dynamic behavior of the counterion cloud is shown to lead to a novel nonlinear force-velocity relation for the moving plate.