Imaging Transport Resonances in the Quantum Hall Effect

We use a scanning capacitance probe to image transport in the quantum Hall system. Applying a DC bias voltage to the tip induces a ring-shaped incompressible strip (IS) in the 2D electron system (2DES) that moves with the tip. At certain tip positions, short-range disorder in the 2DES creates a quantum dot island in the IS. These islands enable resonant tunneling across the IS, enhancing its conductance by more than four orders of magnitude. The images provide a quantitative measure of disorder and suggest resonant tunneling as the primary mechanism for transport across ISs.Comment: 4 pages, 4 figures, submitted to PRL. For movies and additional infomation, see http://electron.mit.edu/scanning/; Added scale bars to images, revised discussion of figure 3, other minor change

Sub-linear radiation power dependence of photo-excited resistance oscillations in two-dimensional electron systems

We find that the amplitude of the $R_{xx}$ radiation-induced magnetoresistance oscillations in GaAs/AlGaAs system grows nonlinearly as $A \propto P^{\alpha}$ where $A$ is the amplitude and the exponent $\alpha < 1$. %, with $\alpha \rightarrow 1/2$ in %the low temperature limit. This striking result can be explained with the radiation-driven electron orbits model, which suggests that the amplitude of resistance oscillations depends linearly on the radiation electric field, and therefore on the square root of the power, $P$. We also study how this sub-linear power law varies with lattice temperature and radiation frequency.Comment: 5 pages, 3 figure

Spinful Composite Fermions in a Negative Effective Field

In this paper we study fractional quantum Hall composite fermion wavefunctions at filling fractions \nu = 2/3, 3/5, and 4/7. At each of these filling fractions, there are several possible wavefunctions with different spin polarizations, depending on how many spin-up or spin-down composite fermion Landau levels are occupied. We calculate the energy of the possible composite fermion wavefunctions and we predict transitions between ground states of different spin polarizations as the ratio of Zeeman energy to Coulomb energy is varied. Previously, several experiments have observed such transitions between states of differing spin polarization and we make direct comparison of our predictions to these experiments. For more detailed comparison between theory and experiment, we also include finite-thickness effects in our calculations. We find reasonable qualitative agreement between the experiments and composite fermion theory. Finally, we consider composite fermion states at filling factors \nu = 2+2/3, 2+3/5, and 2+4/7. The latter two cases we predict to be spin polarized even at zero Zeeman energy.Comment: 17 pages, 5 figures, 4 tables. (revision: incorporated referee suggestions, note added, updated references

Anyon Wave Function for the Fractional Quantum Hall Effect

An anyon wave function (characterized by the statistical factor $n$) projected onto the lowest Landau level is derived for the fractional quantum Hall effect states at filling factor $\nu = n/(2pn+1)$ ($p$ and $n$ are integers). We study the properties of the anyon wave function by using detailed Monte Carlo simulations in disk geometry and show that the anyon ground-state energy is a lower bound to the composite fermion one.Comment: Reference adde

Two-subband quantum Hall effect in parabolic quantum wells

The low-temperature magnetoresistance of parabolic quantum wells displays pronounced minima between integer filling factors. Concomitantly the Hall effect exhibits overshoots and plateau-like features next to well-defined ordinary quantum Hall plateaus. These effects set in with the occupation of the second subband. We discuss our observations in the context of single-particle Landau fan charts of a two-subband system empirically extended by a density dependent subband separation and an enhanced spin-splitting g*.Comment: 5 pages, submitte

One-dimensional quantum chaos: Explicitly solvable cases

We present quantum graphs with remarkably regular spectral characteristics. We call them {\it regular quantum graphs}. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly solvable in terms of periodic orbits. We present analytical solutions for the spectrum of regular quantum graphs in the form of explicit and exact periodic orbit expansions for each individual energy level.Comment: 9 pages and 4 figure

Discrete chaotic states of a Bose-Einstein condensate

We find the different spatial chaos in a one-dimensional attractive Bose-Einstein condensate interacting with a Gaussian-like laser barrier and perturbed by a weak optical lattice. For the low laser barrier the chaotic regions of parameters are demonstrated and the chaotic and regular states are illustrated numerically. In the high barrier case, the bounded perturbed solutions which describe a set of discrete chaotic states are constructed for the discrete barrier heights and magic numbers of condensed atoms. The chaotic density profiles are exhibited numerically for the lowest quantum number, and the analytically bounded but numerically unbounded Gaussian-like configurations are confirmed. It is shown that the chaotic wave packets can be controlled experimentally by adjusting the laser barrier potential.Comment: 7 pages, 5 figure

Causal Perturbation Theory and Differential Renormalization

In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions. I show that the pullback of this operation to the distributions yields expressions known from Differential Renormalization. The subtraction is equivalent to BPHZ subtraction in momentum space. Some examples from Euclidean scalar field theory in flat and curved spacetime will be presented.Comment: 15 pages, AMS-LaTeX, feynm