Effects of Electron Correlations on Hofstadter Spectrum

By allowing interactions between electrons, a new Harper's equation is derived to examine the effects of electron correlations on the Hofstadter energy spectra. It is shown that the structure of the Hofstadter butterfly ofr the system of correlated electrons is modified only in the band gaps and the band widths, but not in the characteristics of self-similarity and the Cantor set.Comment: 13 pages, 5 Postscript figure

Diffusion of electrons in random magnetic fields,

Diffusion of electrons in a two-dimensional system in static random magnetic fields is studied by solving the time-dependent Schr\"{o}dinger equation numerically. The asymptotic behaviors of the second moment of the wave packets and the temporal auto-correlation function in such systems are investigated. It is shown that, in the region away from the band edge, the growth of the variance of the wave packets turns out to be diffusive, whereas the exponents for the power-law decay of the temporal auto- correlation function suggest a kind of fractal structure in the energy spectrum and in the wave functions. The present results are consistent with the interpretation that the states away from the band edge region are critical.Comment: 22 pages (8 figures will be mailed if requested), LaTeX, to appear in Phys. Rev.

Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?

We find that a 2D periodic potential with different modulation amplitudes in x- and y-direction and a perpendicular magnetic field may lead to a transition to electron transport along the direction of stronger modulation and to localization in the direction of weaker modulation. In the experimentally accessible regime we relate this new quantum transport phenomenon to avoided band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea

The Flux-Phase of the Half-Filled Band

The conjecture is verified that the optimum, energy minimizing magnetic flux for a half-filled band of electrons hopping on a planar, bipartite graph is $\pi$ per square plaquette. We require {\it only} that the graph has periodicity in one direction and the result includes the hexagonal lattice (with flux 0 per hexagon) as a special case. The theorem goes beyond previous conjectures in several ways: (1) It does not assume, a-priori, that all plaquettes have the same flux (as in Hofstadter's model); (2) A Hubbard type on-site interaction of any sign, as well as certain longer range interactions, can be included; (3) The conclusion holds for positive temperature as well as the ground state; (4) The results hold in $D \geq 2$ dimensions if there is periodicity in $D-1$ directions (e.g., the cubic lattice has the lowest energy if there is flux $\pi$ in each square face).Comment: 9 pages, EHL14/Aug/9

Wavefunction and level statistics of random two dimensional gauge fields

Level and wavefunction statistics have been studied for two dimensional clusters of the square lattice in the presence of random magnetic fluxes. Fluxes traversing lattice plaquettes are distributed uniformly between - (1/2) Phi_0 and (1/2) Phi_0 with Phi_0 the flux quantum. All considered statistics start close to the corresponding Wigner-Dyson distribution for small system sizes and monotonically move towards Poisson statistics as the cluster size increases. Scaling is quite rapid for states close to the band edges but really difficult to observe for states well within the band. Localization properties are discussed considering two different scenarios. Experimental measurement of one of the considered statistics --wavefunction statistics seems the most promising one-- could discern between both possibilities. A real version of the previous model, i.e., a system that is invariant under time reversal, has been studied concurrently to get coincidences and differences with the Hermitian model.Comment: 12 twocolumnn pages in revtex style, 17 postscript figures, to be published in PRB, send comments to [email protected]

Metal-insulator transitions in cyclotron resonance of periodic nanostructures due to avoided band crossings

A recently found metal-insulator transition in a model for cyclotron resonance in a two-dimensional periodic potential is investigated by means of spectral properties of the time evolution operator. The previously found dynamical signatures of the transition are explained in terms of avoided band crossings due to the change of the external electric field. The occurrence of a cross-like transport is predicted and numerically confirmed

How to escape Aharonov-Bohm cages ?

We study the effect of disorder and interactions on a recently proposed magnetic field induced localization mechanism. We show that both partially destroy the extreme confinement of the excitations occuring in the pure case and give rise to unusual behavior. We also point out the role of the edge states that allows for a propagation of the electrons in these systems.Comment: 22 pages, 20 EPS figure

Pressure drawdown analysis for the Travale 22 well

This work presents preliminary results on the analysis of drawdown data for Travale 22. Both wellhead pressure and flow rate data were recorded in this well for over a period of almost two years. In the past, Barelli et al. (1975) and Atkinson et al. (1977) presented the analysis of five pressure buildup tests. Figure 1 shows the Horner plot for these cases. They found that to have a good match in all cases, it was necessary to assume that the Travale 22 well is intersected by a partially penetrating vertical fracture in a parallel-piped whose bottom side is maintained at constant pressure (boiling front), as shown in Fig. 2. Atkinson et al. also presented an analysis for a pressure interface test run in the Travale-Radicondoli area. In this case, the Travale 22 well was flowing and the pressure recorded at wells R1, R3, R5, R6, R9, and Chl (see Fig. 3 ) . Analysis of these data showed that pressure interference in this reservoir can be matched by considering pure linear flow (Figs. 4 and 5 ) . This indicated the possible presence of a vertical fracture intersecting the Travale 22 well. It was determined that fracture is oriented along the N73{sup o}W direction. In addition, the pressure interference data showed that no boundary exists within 2 kilometers from the fracture plane. It was mentioned that linear flow should take place in both horizontal and vertical directions