Optical Hall Effect in the Integer Quantum Hall Regime

Optical Hall conductivity $\sigma_{xy}(\omega)$ is measured from the Faraday rotation for a GaAs/AlGaAs heterojunction quantum Hall system in the terahertz frequency regime. The Faraday rotation angle ($\sim$ fine structure constant $\sim$ mrad) is found to significantly deviate from the Drude-like behavior to exhibit a plateau-like structure around the Landau-level filling $\nu=2$. The result, which fits with the behavior expected from the carrier localization effect in the ac regime, indicates that the plateau structure, although not quantized, still exists in the terahertz regime.Comment: 4 pages, 4 figure

Laughlin states on the Poincare half-plane and its quantum group symmetry

We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE.Comment: 9 pages,Late

The Moon at thermal infrared wavelengths: A benchmark for asteroid thermal models

Thermal-infrared measurements of asteroids are crucial for deriving the objects' sizes, albedos, and also the thermophysical properties of the surface material. Depending on the available data, a range of simple to complex thermal models are applied to achieve specific science goals. However, testing these models is often a difficult process and the uncertainties of the derived parameters are not easy to estimate. Here, we make an attempt to verify a widely accepted thermophysical model (TPM) against unique thermal infrared (IR), full-disk, and well-calibrated measurements of the Moon. The data were obtained by the High-resolution InfraRed Sounder (HIRS) instruments on board a fleet of Earth weather satellites that serendipitously scan over the Moon. We found 22 Moon intrusions, taken in 19 channels between 3.75 micron and 15.0 micron, and over a wide phase angle range from -73.1 deg to +73.8 deg. The similarity between these Moon data and typical asteroid spectral-IR energy distributions allows us to benchmark the TPM concepts and to point out problematic aspects. The TPM predictions match the HIRS measurements within 5% (10% at the shortest wavelengths below 5 micron when using the Moon's known properties (size, shape, spin, albedo, thermal inertia, roughness) in combination with a newly established wavelength-dependent hemispherical emissivity. In the 5-7.5 micron and in the 9.5 to 11 micron ranges, the global emissivity model deviates considerably from the known lunar sample spectra. Our findings will influence radiometric studies of near-Earth and main-belt asteroids in cases where only short-wavelength data (from e.g., NEOWISE, the warm Spitzer mission, or ground-based M-band measurements) are available. The new, full-disk IR Moon model will also be used for the calibration of IR instrumentation on interplanetary missions (e.g., for Hayabusa-2) and weather satellites.Comment: 21 pages, 9 figures, 7 tables, accepted for publication in Astronomy & Astrophysics in March 202

Behaviour of three charged particles on a plane under perpendicular magnetic field

We consider the problem of three identical charged particles on a plane under a perpendicular magnetic field and interacting through Coulomb repulsion. This problem is treated within Taut's framework, in the limit of vanishing center of mass vector $\vec{R} \to \vec{0}$, which corresponds to the strong magnetic field limit, occuring for example in the Fractional Quantum Hall Effect. Using the solutions of the biconfluent Heun equation, we compute the eigenstates and show that there is two sets of solutions. The first one corresponds to a system of three independent anyons which have their angular momenta fixed by the value of the magnetic field and specified by a dimensionless parameter $C \simeq \frac{l_B}{l_0}$, the ratio of $l_B$, the magnetic length, over $l_0$, the Bohr radius. This anyonic character, consistent with quantum mechanics of identical particles in two dimensions, is induced by competing physical forces. The second one corresponds to the case of the Landau problem when $C \to 0$. Finally we compare these states with the quantum Hall states and find that the Laughlin wave functions are special cases of our solutions under certains conditions.Comment: 15 pages, 3 figures, Accepeted in JP

Universal Multifractality in Quantum Hall Systems with Long-Range Disorder Potential

We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wavefunctions at the transition energy are obtained within the framework of the generalized Chalker--Coddington network model. We determine the critical exponent $\alpha_0$ characterizing the scaling behavior of the local order parameter for systems with potential correlation length $d$ up to $12$ magnetic lengths $l$. Our results show that $\alpha_0$ does not depend on the ratio $d/l$. With increasing $d/l$, effects due to classical percolation only cause an increase of the microscopic length scale, whereas the critical behavior on larger scales remains unchanged. This proves that systems with long-range disorder belong to the same universality class as those with short-range disorder.Comment: 4 pages, 2 figures, postsript, uuencoded, gz-compresse

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

Assessing and countering reaction attacks against post-quantum public-key cryptosystems based on QC-LDPC codes

Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are promising post-quantum candidates to replace quantum vulnerable classical alternatives. However, a new type of attacks based on Bob's reactions have recently been introduced and appear to significantly reduce the length of the life of any keypair used in these systems. In this paper we estimate the complexity of all known reaction attacks against QC-LDPC and QC-MDPC code-based variants of the McEliece cryptosystem. We also show how the structure of the secret key and, in particular, the secret code rate affect the complexity of these attacks. It follows from our results that QC-LDPC code-based systems can indeed withstand reaction attacks, on condition that some specific decoding algorithms are used and the secret code has a sufficiently high rate.Comment: 21 pages, 2 figures, to be presented at CANS 201

Analysis of reaction and timing attacks against cryptosystems based on sparse parity-check codes

In this paper we study reaction and timing attacks against cryptosystems based on sparse parity-check codes, which encompass low-density parity-check (LDPC) codes and moderate-density parity-check (MDPC) codes. We show that the feasibility of these attacks is not strictly associated to the quasi-cyclic (QC) structure of the code but is related to the intrinsically probabilistic decoding of any sparse parity-check code. So, these attacks not only work against QC codes, but can be generalized to broader classes of codes. We provide a novel algorithm that, in the case of a QC code, allows recovering a larger amount of information than that retrievable through existing attacks and we use this algorithm to characterize new side-channel information leakages. We devise a theoretical model for the decoder that describes and justifies our results. Numerical simulations are provided that confirm the effectiveness of our approach

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

Coulomb gas representation of quantum Hall effect on Riemann surfaces

Using the correlation function of chiral vertex operators of the Coulomb gas model, we find the Laughlin wavefunctions of quantum Hall effect, with filling factor $\nu =1/m$, on Riemann sufaces with Poincare metric. The same is done for quasihole wavefunctions. We also discuss their plasma analogy.Comment: 10 pages, LaTex, the paper is completely rewritten, It will be appeared in : Jour. Phys. A 32 (1999