Oscillatory Tunneling between Quantum Hall Systems

Electron tunneling between quantum Hall systems on the same two dimensional plane separated by a narrow barrier is studied. We show that in the limit where inelastic scattering time is much longer than the tunneling time, which can be achieved in practice, electrons can tunnel back and forth through the barrier continously, leading to an oscillating current in the absence of external drives. The oscillatory behavior is dictated by a tunneling gap in the energy spectrum. We shall discuss ways to generate oscillating currents and the phenomenon of natural ``dephasing" between the tunneling currents of edge states. The noise spectra of these junctions are also studied. They contain singularites reflecting the existence of tunneling gaps as well as the inherent oscillation in the system. (Figures will be given upon requests).Comment: 20 pages, OS

Transport in Luttinger Liquids

We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some important results on tunneling through barriers in a one-dimensional quantum wire and the phenomena of persistent currents in mesoscopic rings. We give a brief description of our own work on transport through doubly-crossed Luttinger liquids and transport in the Schulz-Shastry exactly solvable Luttinger-like model.Comment: Latex file, 15 pages, four eps figure

A Supersymmetry approach to billiards with randomly distributed scatterers

The density of states for a chaotic billiard with randomly distributed point-like scatterers is calculated, doubly averaged over the positions of the impurities and the shape of the billiard. Truncating the billiard Hamiltonian to a N x N matrix, an explicit analytic expression is obtained for the case of broken time-reversal symmetry, depending on rank N of the matrix, number L of scatterers, and strength of the scattering potential. In the strong coupling limit a discontinuous change is observed in the density of states as soon as L exceeds N

Magnitude and crystalline anisotropy of hole magnetization in (Ga,Mn)As

Theory of hole magnetization Mc in zinc-blende diluted ferromagnetic semiconductors is developed relaxing the spherical approximation of earlier approaches. The theory is employed to determine Mc for (Ga,Mn)As over a wide range of hole concentrations and a number of crystallographic orientations of Mn magnetization. It is found that anisotropy of Mc is practically negligible but the obtained magnitude of Mc is significantly greater than that determined in the spherical approximation. Its sign and value compares favorably with the results of available magnetization measurements and ferromagnetic resonance studies.Comment: 5 pages, 3 figure

Density of states near the Mott-Hubbard transition in the limit of large dimensions

The zero temperature Mott-Hubbard transition as a function of the Coulomb repulsion U is investigated in the limit of large dimensions. The behavior of the density of states near the transition at U=U_c is analyzed in all orders of the skeleton expansion. It is shown that only two transition scenarios are consistent with the skeleton expansion for U<U_c: (i) The Mott-Hubbard transition is "discontinuous" in the sense that in the density of states finite spectral weight is redistributed at U_c. (ii) The transition occurs via a point at U=U_c where the system is neither a Fermi liquid nor an insulator.Comment: 4 pages, 1 figure; revised version accepted for publication in Phys. Rev. Let

Bosonization of Fermi liquids

We bosonize a Fermi liquid in any number of dimensions in the limit of long wavelengths. From the bosons we construct a set of coherent states which are related with the displacement of the Fermi surface due to particle-hole excitations. We show that an interacting hamiltonian in terms of the original fermions is quadratic in the bosons. We obtain a path integral representation for the generating functional which in real time, in the semiclassical limit, gives the Landau equation for sound waves and in the imaginary time gives us the correct form of the specific heat for a Fermi liquid even with the corrections due to the interactions between the fermions. We also discuss the similarities between our results and the physics of quantum crystals.Comment: 42 pages, RevteX, preprint UIUC (1993

Magnetic hysteresis in Ising-like dipole-dipole model

Using zero temperature Monte Carlo simulations we have studied the magnetic hysteresis in a three-dimensional Ising model with nearest neighbor exchange and dipolar interaction. The average magnetization of spins located inside a sphere on a cubic lattice is determined as a function of magnetic field varied periodically. The simulations have justified the appearance of hysteresis and allowed us to have a deeper insight into the series of metastable states developed during this process.Comment: REVTEX, 10 pages including 4 figure

Bose-Fermi Mixtures in One Dimension

We analyze the phase stability and the response of a mixture of bosons and spin-polarized fermions in one dimension (1D). Unlike in 3D, phase separation happens for low fermion densities. The dynamics of the mixture at low energy is independent of the spin-statistics of the components, and zero-sound-like modes exist that are essentially undamped.Comment: 5 pages; 1 figur

Transport theory

The usual theories of electrical conductivity suffer from a number of weaknesses. A more general theory will be described which gives the entire density matrix of a system of charge carriers in the steady state. It will be shown that the usual theory is valid under certain limiting conditions, but that in general there are rather complicated corrections to it.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32468/1/0000553.pd

Violation of Luttinger's Theorem in the Two-Dimensional t-J Model

We have calculated the high temperature series for the momentum distribution function n_k of the 2D t-J model to 12th order in inverse temperature. By extrapolating the series to T=0.2J we searched for a Fermi surface of the 2D t-J model. We find that three criteria used for estimating the location of a Fermi surface violate Luttinger's Theorem, implying the 2D t-J model does not have an adiabatic connection to a non-interacting model.Comment: 4 pages, 5 figures. Version with grayscale figures available upon reques