Earth magnetic field effects on the cosmic electron flux as background for Cherenkov Telescopes at low energies

Cosmic ray electrons and positrons constitute an important component of the background for imaging atmospheric Cherenkov Telescope Systems with very low energy thresholds. As the primary energy of electrons and positrons decreases, their contribution to the background trigger rate dominates over protons, at least in terms of differential rates against actual energies. After event reconstruction, this contribution might become comparable to the proton background at energies of the order of few GeV. It is well known that the flux of low energy charged particles is suppressed by the Earth's magnetic field. This effect strongly depends on the geographical location, the direction of incidence of the charged particle and its mass. Therefore, the geomagnetic field can contribute to diminish the rate of the electrons and positrons detected by a given array of Cherenkov Telescopes. In this work we study the propagation of low energy primary electrons in the Earth's magnetic field by using the backtracking technique. We use a more realistic geomagnetic field model than the one used in previous calculations. We consider some sites relevant for new generations of imaging atmospheric Cherenkov Telescopes. We also study in detail the case of 5@5, a proposed low energy Cherenkov Telescope array.Comment: To appear in Astroparticle Physic

Theory of Incompressible States in a Narrow Channel

We report on the properties of a system of interacting electrons in a narrow channel in the quantum Hall effect regime. It is shown that an increase in the strength of the Coulomb interaction causes abrupt changes in the width of the charge-density profile of translationally invariant states. We derive a phase diagram which includes many of the stable odd-denominator states as well as a novel fractional quantum Hall state at lowest half-filled Landau level. The collective mode evaluated at the half-filled case is strikingly similar to that for an odd-denominator fractional quantum Hall state.Comment: 4 pages, REVTEX, and 4 .ps file

The transverse magnetoresistance of the two-dimensional chiral metal

We consider the two-dimensional chiral metal, which exists at the surface of a layered, three-dimensional sample exhibiting the integer quantum Hall effect. We calculate its magnetoresistance in response to a component of magnetic field perpendicular to the sample surface, in the low temperature, but macroscopic, regime where inelastic scattering may be neglected. The magnetoresistance is positive, following a Drude form with a field scale, $B_0=\Phi_0/al_{\text{el}}$, given by the transverse field strength at which one quantum of flux, $\Phi_0$, passes through a rectangle with sides set by the layer-spacing, $a$, and the elastic mean free path, $l_{\text{el}}$. Experimental measurement of this magnetoresistance may therefore provide a direct determination of the elastic mean free path in the chiral metal.Comment: submitted to Phys Rev

Barycentric decomposition of quantum measurements in finite dimensions

We analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme points of the convex set are operator valued measures concentrated on a finite set of k \le d^2 points of the outcome space, d< \infty being the dimension of the Hilbert space. We prove that for second countable outcome spaces any POVM admits a Choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure. In the general case, Krein-Milman theorem is invoked to represent POVMs as barycenters of a certain set of POVMs concentrated on k \le d^2 points of the outcome space.Comment: !5 pages, no figure

A Fermi Fluid Description of the Half-Filled Landau Level

We present a many-body approach to calculate the ground state properties of a system of electrons in a half-filled Landau level. Our starting point is a simplified version of the recently proposed trial wave function where one includes the antisymmetrization operator to the bosonic Laughlin state. Using the classical plasma analogy, we calculate the pair-correlation function, the static structure function and the ground state energy in the thermodynamic limit. These results are in good agreement with the expected behavior at $\nu=\frac12$.Comment: 4 pages, REVTEX, and 4 .ps file

Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials

We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a single but arbitrary Landau level. For a wide class of Gaussian random potentials we rigorously prove that the associated restricted integrated density of states is absolutely continuous with respect to the Lebesgue measure. We construct explicit upper bounds on the resulting derivative, the restricted density of states. As a consequence, any given energy is seen to be almost surely not an eigenvalue of the restricted random Landau Hamiltonian.Comment: 16 pages, to appear in "Journal of Mathematical Physics

Quantum Hall Effect in Three Dimensional Layered Systems

Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram, which exhibit a metallic phase for a finite range of energies and magnetic fields, and the calculated associated critical exponent, $\nu=4/3$, agree excellently with existing numerical calculations. The implication of this work for the quantum Hall effect in three dimensions is discussed.Comment: 4 pages + 4 figure

Spectral Properties of Three Dimensional Layered Quantum Hall Systems

We investigate the spectral statistics of a network model for a three dimensional layered quantum Hall system numerically. The scaling of the quantity $J_0={1/2}$ is used to determine the critical exponent $\nu$ for several interlayer coupling strengths. Furthermore, we determine the level spacing distribution $P(s)$ as well as the spectral compressibility $\chi$ at criticality. We show that the tail of $P(s)$ decays as $\exp(-\kappa s)$ with $\kappa=1/(2\chi)$ and also numerically verify the equation $\chi=(d-D_2)/(2d)$, where $D_2$ is the correlation dimension and $d=3$ the spatial dimension.Comment: 4 pages, 5 figures submitted to J. Phys. Soc. Jp

Electron Correlations in Partially Filled Lowest and Excited Landau Levels

The electron correlations near the half-filling of the lowest and excited Landau levels (LL's) are studied using numerical diagonalization. It is shown that in the low lying states electrons avoid pair states with relative angular momenta ${\cal R}$ corresponding to positive anharmonicity of the interaction pseudopotential $V({\cal R})$. In the lowest LL, the super-harmonic behavior of $V({\cal R})$ causes Laughlin correlations (avoiding pairs with ${\cal R}=1$) and the Laughlin-Jain series of incompressible ground states. In the first excited LL, $V({\cal R})$ is harmonic at short range and a different series of incompressible states results. Similar correlations occur in the paired Moore-Read $\nu={5\over2}$ state and in the $\nu={7\over3}$ and ${8\over3}$ states, all having small total parentage from ${\cal R}=1$ and 3 and large parentage from ${\cal R}=5$. The $\nu={7\over3}$ and ${8\over3}$ states are different from Laughlin $\nu={1\over3}$ and ${2\over3}$ states and, in finite systems, occur at a different LL degeneracy (flux). The series of Laughlin correlated states of electron pairs at $\nu=2+2/(q_2+2)={8\over3}$, ${5\over2}$, ${12\over5}$, and ${7\over3}$ is proposed, although only in the $\nu={5\over2}$ state pairing has been confirmed numerically. In the second excited LL, $V({\cal R})$ is sub-harmonic at short range and (near the half-filling) the electrons group into spatially separated larger $\nu=1$ droplets to minimize the number of strongly repulsive pair states at ${\cal R}=3$ and 5.Comment: 10 pages, 8 figures, submitted to PR