The Hofstadter Energy Spectrum for an Interacting 2DEG

We study the effects of the Coulomb interactions between electrons on the Hofstadter butterfly, which characterizes the subband structure of the Landau levels of a two-dimensional electron gas in a perpendicular homogeneous magnetic field and a periodic lateral superlattice potential. The interactions essentially preserve the intricate gap structure of the Hofstadter spectra, but with a lower symmetry that depends on the filling of the Landau bands. For short enough periods and strong enough modulation the miniband structure can be resolved in the thermodynamic density of states.Comment: LaTeX 4 pages with 3 PostScript figures, Contribution to EP2DSXI Nottingham August 95 to appear in Surface Scienc

Regarding the editorial by Sau and Ng. 'Hypertrophic cardiomyopathy risk stratification based on clinical or dynamic electrophysiological features: two sides of the same coin'

This Letter to the Editor refers to article ‘Hypertrophic cardiomyopathy risk stratification based on clinical or dynamic electrophysiological features: two sides of the same coin’ by Sau A, Ng, FS https://doi.org/10.1093/europace/euad072. ‘Response to the letter to the editor EUPC-D-23-00362 of Richard Saumarez’, by Arunashis Sau and Fu Siong Ng, https://doi.org/10.1093/europace/euad174

Phase--coherence Effects in Antidot Lattices: A Semiclassical Approach to Bulk Conductivity

We derive semiclassical expressions for the Kubo conductivity tensor. Within our approach the oscillatory parts of the diagonal and Hall conductivity are given as sums over contributions from classical periodic orbits in close relation to Gutzwiller's trace formula for the density of states. Taking into account the effects of weak disorder and temperature we reproduce recently observed anomalous phase coherence oscillations in the conductivity of large antidot arrays.Comment: 11 pages, 2 figures available under request, RevTe

Manifestation of the Hofstadter butterfly in far-infrared absorption

The far-infrared absorption of a two-dimensional electron gas with a square-lattice modulation in a perpendicular constant magnetic field is calculated self-consistently within the Hartree approximation. For strong modulation and short period we obtain intra- and intersubband magnetoplasmon modes reflecting the subbands of the Hofstadter butterfly in two or more Landau bands. The character of the absorption and the correlation of the peaks to the number of flux quanta through each unit cell of the periodic potential depends strongly on the location of the chemical potential with respect to the subbands, or what is the same, on the density of electrons in the system.Comment: RevTeX file + 4 postscript figures, to be published Phys. Rev. B Rapid Com

Duality Relation among Periodic Potential Problems in the Lowest Landau Level

Using a momentum representation of a magnetic von Neumann lattice, we study a two-dimensional electron in a uniform magnetic field and obtain one-particle spectra of various periodic short-range potential problems in the lowest Landau level.We find that the energy spectra satisfy a duality relation between a period of the potential and a magnetic length. The energy spectra consist of the Hofstadter-type bands and flat bands. We also study the connection between a periodic short-range potential problem and a tight-binding model.Comment: 6 pages, 3 figures, final version to appear in PR

Magnetization in short-period mesoscopic electron systems

We calculate the magnetization of the two-dimensional electron gas in a short-period lateral superlattice, with the Coulomb interaction included in Hartree and Hartree-Fock approximations. We compare the results for a finite, mesoscopic system modulated by a periodic potential, with the results for the infinite periodic system. In addition to the expected strong exchange effects, the size of the system, the type and the strength of the lateral modulation leave their fingerprints on the magnetization.Comment: RevTeX4, 10 pages with 14 included postscript figures To be published in PRB. Replaced to repair figure

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

Hall conductance of Bloch electrons in a magnetic field

We study the energy spectrum and the quantized Hall conductance of electrons in a two-dimensional periodic potential with perpendicular magnetic field WITHOUT neglecting the coupling of the Landau bands. Remarkably, even for weak Landau band coupling significant changes in the Hall conductance compared to the one-band approximation of Hofstadter's butterfly are found. The principal deviations are the rearrangement of subbands and unexpected subband contributions to the Hall conductance.Comment: to appear in PRB; Revtex, 9 pages, 5 postscript figures; figures with better resolution may be obtained from http://www.chaos.gwdg.d

Signature of Chaotic Diffusion in Band Spectra

We investigate the two-point correlations in the band spectra of spatially periodic systems that exhibit chaotic diffusion in the classical limit. By including level pairs pertaining to non-identical quasimomenta, we define form factors with the winding number as a spatial argument. For times smaller than the Heisenberg time, they are related to the full space-time dependence of the classical diffusion propagator. They approach constant asymptotes via a regime, reflecting quantal ballistic motion, where they decay by a factor proportional to the number of unit cells. We derive a universal scaling function for the long-time behaviour. Our results are substantiated by a numerical study of the kicked rotor on a torus and a quasi-one-dimensional billiard chain.Comment: 8 pages, REVTeX, 5 figures (eps

Should lethal arrhythmias in hypertrophic cardiomyopathy be predicted using non-electrophysiological methods?

While sudden cardiac death (SCD) in hypertrophic cardiomyopathy (HCM) is due to arrhythmias, the guidelines for prediction of SCD are based solely on non-electrophysiological methods. This study aims to stimulate thinking about whether the interests of patients with HCM are better served by using current, 'risk factor', methods of prediction or by further development of electrophysiological methods to determine arrhythmic risk. Five published predictive studies of SCD in HCM, which contain sufficient data to permit analysis, were analysed to compute receiver operating characteristics together with their confidence bounds to compare their formal prediction either by bootstrapping or Monte Carlo analysis. Four are based on clinical risk factors, one with additional MRI analysis, and were regarded as exemplars of the risk factor approach. The other used an electrophysiological method and directly compared this method to risk factors in the same patients. Prediction methods that use conventional clinical risk factors and MRI have low predictive capacities that will only detect 50-60% of patients at risk with a 15-30% false positive rate [area under the curve (AUC) = ∼0.7], while the electrophysiological method detects 90% of events with a 20% false positive rate (AUC = ∼0.89). Given improved understanding of complex arrhythmogenesis, arrhythmic SCD is likely to be more accurately predictable using electrophysiologically based approaches as opposed to current guidelines and should drive further development of electrophysiologically based methods