Iddo Ussishkin

SEMICLASSICAL QUANTIZATION OF BILLIARDS WITH MIXED BOUNDARY CONDITIONS

The semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived. The parametric dependence of the spectrum on the boundary condition is shown to be a very useful diagnostic tool in the semiclassical analysis of the spectrum of billiards. It is also used to check in detail some recently proposed parametric spectral statistics. The methods are illustrated in the analysis of the spectrum of the Sinai billiard and its parametric dependence on the boundary condition on the dispersing arc.

COULOMB DRAG IN COMPRESSIBLE QUANTUM HALL STATES

We consider the Coulomb drag between two layers of two-dimensional electronic gases subject to a strong magnetic field. We first focus on the case in which the electronic density is such that the Landau level filling fraction

Penumbra diffraction in the semiclassical quantization of concave billiards

\nu

COULOMB DRAG AT NU = 1/2 : COMPOSITE FERMION PAIRING FLUCTUATIONS

in each layer is at, or close to,

The smooth spectral counting function and the total phase shift for quantum billiards

\nu=1/2

Signatures of spin-charge separation in scanning probe microscopy.

. Discussing the coupling between the layers in purely electronic terms, we show that the unique dependence of the longitudinal conductivity on wave-vector, observed in surface acoustic waves experiments, leads to a very slow decay of density fluctuations. Consequently, it has a crucial effect on the Coulomb drag, as manifested in the transresistivity

Coulomb drag in the quantum Hall state: Role of disorder

\rho_D

Penumbra diffraction in the quantization of dispersing billiards.

. We find that the transresistivity is very large compared to its typical values at zero magnetic field, and that its temperature dependence is unique --

Inside-outside duality for planar billiards: A numerical study

\rho_D \propto T^{4/3}

Lifetime of a one-dimensional fermion

. For filling factors at or close to