Integer quantum Hall effect and Hofstadter's butterfly spectra in three-dimensional metals in external periodic modulations

We propose that Hofstadter's butterfly accompanied by quantum Hall effect that is similar to those predicted to occur in 3D tight-binding systems by Koshino {\it et al.} [Phys. Rev. Lett. {\bf 86}, 1062 (2001)] can be realized in an entirely different system -- 3D metals applied with weak external periodic modulations (e.g., acoustic waves). Namely, an effect of two periodic potentials interferes with Landau's quantization due to an applied magnetic field \Vec{B}, resulting generally in fractal energy gaps as a function of the tilting angle of \Vec{B}, for which the accompanying quantized Hall tensors are computed. The phenomenon arises from the fact that, while the present system has a different physical origin for the butterfly from the 3D tight-binding systems, the mathematical forms are remarkably equivalent.Comment: 4 pages, 2 figure

Evolution of cosmic string configurations

We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance of a randomly chosen segment of left-moving string of given length. The description involves three distinct length scales: $\xi$, related to the overall string density, $\bar\xi$, the persistence length along the string, and $\zeta$, describing the small-scale structure, which is an important feature of the numerical simulations that have been done of this problem. An evolution equation is derived describing how the distribution develops in time due to the combined effects of the universal expansion, of intercommuting and loop formation, and of gravitational radiation. With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study, that if gravitational radiation and small-scale structure effects are neglected, the two dominant length scales both scale in proportion to the horizon size. When the extra effects are included, we find that while $\xi$ and $\bar\xi$ grow, $\zeta$ initially does not. Eventually, however, it does appear to scale, at a much lower level, due to the effects of gravitational back-reaction.Comment: 61 pages, requires RevTex v3.0, SUSSEX-TH-93/3-4, IMPERIAL/TP/92-93/4

Inverse flux quantum periodicity of magnetoresistance oscillations in two-dimensional short-period surface superlattices

Transport properties of the two-dimensional electron gas (2DEG) are considered in the presence of a perpendicular magnetic field $B$ and of a {\it weak} two-dimensional (2D) periodic potential modulation in the 2DEG plane. The symmetry of the latter is rectangular or hexagonal. The well-known solution of the corresponding tight-binding equation shows that each Landau level splits into several subbands when a rational number of flux quanta $h/e$ pierces the unit cell and that the corresponding gaps are exponentially small. Assuming the latter are closed due to disorder gives analytical wave functions and simplifies considerably the evaluation of the magnetoresistivity tensor $\rho_{\mu\nu}$. The relative phase of the oscillations in $\rho_{xx}$ and $\rho_{yy}$ depends on the modulation periods involved. For a 2D modulation with a {\bf short} period $\leq 100$ nm, in addition to the Weiss oscillations the collisional contribution to the conductivity and consequently the tensor $\rho_{\mu\nu}$ show {\it prominent peaks when one flux quantum $h/e$ passes through an integral number of unit cells} in good agreement with recent experiments. For periods $300- 400$ nm long used in early experiments, these peaks occur at fields 10-25 times smaller than those of the Weiss oscillations and are not resolved

Energy Spectrum of Bloch Electrons Under Checkerboard Field Modulations

Two-dimensional Bloch electrons in a uniform magnetic field exhibit complex energy spectrum. When static electric and magnetic modulations with a checkerboard pattern are superimposed on the uniform magnetic field, more structures and symmetries of the spectra are found, due to the additional adjustable parameters from the modulations. We give a comprehensive report on these new symmetries. We have also found an electric-modulation induced energy gap, whose magnitude is independent of the strength of either the uniform or the modulated magnetic field. This study is applicable to experimentally accessible systems and is related to the investigations on frustrated antiferromagnetism.Comment: 8 pages, 6 figures (reduced in sizes), submitted to Phys. Rev.

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

Very-high energy gamma-ray astronomy: A 23-year success story in high-energy astroparticle physics

Very-high energy (VHE) gamma quanta contribute only a minuscule fraction - below one per million - to the flux of cosmic rays. Nevertheless, being neutral particles they are currently the best "messengers" of processes from the relativistic/ultra-relativistic Universe because they can be extrapolated back to their origin. The window of VHE gamma rays was opened only in 1989 by the Whipple collaboration, reporting the observation of TeV gamma rays from the Crab nebula. After a slow start, this new field of research is now rapidly expanding with the discovery of more than 150 VHE gamma-ray emitting sources. Progress is intimately related with the steady improvement of detectors and rapidly increasing computing power. We give an overview of the early attempts before and around 1989 and the progress after the pioneering work of the Whipple collaboration. The main focus of this article is on the development of experimental techniques for Earth-bound gamma-ray detectors; consequently, more emphasis is given to those experiments that made an initial breakthrough rather than to the successors which often had and have a similar (sometimes even higher) scientific output as the pioneering experiments. The considered energy threshold is about 30 GeV. At lower energies, observations can presently only be performed with balloon or satellite-borne detectors. Irrespective of the stormy experimental progress, the success story could not have been called a success story without a broad scientific output. Therefore we conclude this article with a summary of the scientific rationales and main results achieved over the last two decades.Comment: 45 pages, 38 figures, review prepared for EPJ-H special issue "Cosmic rays, gamma rays and neutrinos: A survey of 100 years of research

Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections

We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2 quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur

Time-Varying Dark Energy Constraints From the Latest SN Ia, BAO and SGL

Based on the latest SNe Ia data provided by Hicken et al. (2009) with using MLCS17 light curve fitter, together with the Baryon Acoustic Oscillation(BAO) and strong gravitational lenses(SGL), we investigate the constraints on the dark energy equation-of-state parameter $w$ in the flat universe, especially for the time-varying case $w(z)=w_0+w_zz/(1+z)$. The constraints from SNe data alone are found to be: (a) $(\Omega_M, w)=(0.358, -1.09)$ as the best-fit results; (b) $(w_0, w_z)=(-0.73^{+0.23}_{-0.97}, 0.84^{+1.66}_{-10.34})$ for the two parameters in the time-varying case after marginalizing the parameter $\Omega_M$; (c) the likelihood of parameter $w_z$ has a high non-Gaussian distribution; (d) an extra restriction on $\Omega_M$ is necessary to improve the constraint of the SNe Ia data on the parameters ($w_0$, $w_z$). A joint analysis of SNe Ia data and BAO is made to break the degeneracy between $w$ and $\Omega_M$, and leads to the interesting maximum likelihoods $w_0 = -0.94$ and $w_z = 0$. When marginalizing the parameter $\Omega_M$, the fitting results are found to be $(w_0, w_z)=(-0.95^{+0.45}_{-0.18}, 0.41^{+0.79}_{-0.96})$. After adding the splitting angle statistic of SGL data, a consistent constraint is obtained $(\Omega_M, w)=(0.298, -0.907)$ and the constraints on time-varying dark energy are further improved to be $(w_0, w_z) = (-0.92^{+0.14}_{-0.10}, 0.35^{+0.47}_{-0.54})$, which indicates that the phantom type models are disfavored.Comment: 24 pages, 9 figures, to be published in JCA

A measurement of the tau mass and the first CPT test with tau leptons

We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV using tau pairs from Z0 decays. To test CPT invariance we compare the masses of the positively and negatively charged tau leptons. The relative mass difference is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.

Measurement of the branching fraction for Υ(1S)→τ+τ−\Upsilon (1S) \to \tau^+ \tau^-

We have studied the leptonic decay of the $\Upsilon (1S)$ resonance into tau pairs using the CLEO II detector. A clean sample of tau pair events is identified via events containing two charged particles where exactly one of the particles is an identified electron. We find $B(\Upsilon(1S) \to \tau^+ \tau^-) = (2.61~\pm~0.12~{+0.09\atop{-0.13}})$. The result is consistent with expectations from lepton universality.Comment: 9 pages, RevTeX, two Postscript figures available upon request, CLNS 94/1297, CLEO 94-20 (submitted to Physics Letters B