Solution of the Lindblad Equation in the Kraus Representation

The so-called Lindblad equation, a typical master equation describing the dissipative quantum dynamics, is shown to be solvable for finite-level systems in a compact form without resort to writing it down as a set of equations among matrix elements. The solution is then naturally given in an operator form, known as the Kraus representation. Following a few simple examples, the general applicability of the method is clarified.Comment: 9 page

Energy Spectra of Elemental Groups of Cosmic Rays: Update on the KASCADE Unfolding Analysis

The KASCADE experiment measures extensive air showers induced by cosmic rays in the energy range around the so-called knee. The data of KASCADE have been used in a composition analysis showing the knee at 3-5 PeV to be caused by a steepening in the light-element spectra. Since the applied unfolding analysis depends crucially on simulations of air showers, different high energy hadronic interaction models (QGSJet and SIBYLL) were used. The results have shown a strong dependence of the relative abundance of the individual mass groups on the underlying model. In this update of the analysis we apply the unfolding method with a different low energy interaction model (FLUKA instead of GHEISHA) in the simulations. While the resulting individual mass group spectra do not change significantly, the overall description of the measured data improves by using the FLUKA model. In addition data in a larger range of zenith angle are analysed. The new results are completely consistent, i.e. there is no hint to any severe problem in applying the unfolding analysis method to KASCADE data.Comment: accepted for publication in Astroparticle Physic

A comparison of the cosmic-ray energy scales of Tunka-133 and KASCADE-Grande via their radio extensions Tunka-Rex and LOPES

The radio technique is a promising method for detection of cosmic-ray air showers of energies around $100\,$PeV and higher with an array of radio antennas. Since the amplitude of the radio signal can be measured absolutely and increases with the shower energy, radio measurements can be used to determine the air-shower energy on an absolute scale. We show that calibrated measurements of radio detectors operated in coincidence with host experiments measuring air showers based on other techniques can be used for comparing the energy scales of these host experiments. Using two approaches, first via direct amplitude measurements, and second via comparison of measurements with air shower simulations, we compare the energy scales of the air-shower experiments Tunka-133 and KASCADE-Grande, using their radio extensions, Tunka-Rex and LOPES, respectively. Due to the consistent amplitude calibration for Tunka-Rex and LOPES achieved by using the same reference source, this comparison reaches an accuracy of approximately $10\,\%$ - limited by some shortcomings of LOPES, which was a prototype experiment for the digital radio technique for air showers. In particular we show that the energy scales of cosmic-ray measurements by the independently calibrated experiments KASCADE-Grande and Tunka-133 are consistent with each other on this level

Radio detection of cosmic ray air showers with LOPES

In the last few years, radio detection of cosmic ray air showers has experienced a true renaissance, becoming manifest in a number of new experiments and simulation efforts. In particular, the LOPES project has successfully implemented modern interferometric methods to measure the radio emission from extensive air showers. LOPES has confirmed that the emission is coherent and of geomagnetic origin, as expected by the geosynchrotron mechanism, and has demonstrated that a large scale application of the radio technique has great potential to complement current measurements of ultra-high energy cosmic rays. We describe the current status, most recent results and open questions regarding radio detection of cosmic rays and give an overview of ongoing research and development for an application of the radio technique in the framework of the Pierre Auger Observatory.Comment: 8 pages; Proceedings of the CRIS2006 conference, Catania, Italy; to be published in Nuclear Physics B, Proceedings Supplement

A new method to measure the attenuation of hadrons in extensive air showers

Extensive air showers are generated through interactions of high-energy cosmic rays impinging the Earth's atmosphere. A new method is described to infer the attenuation of hadrons in air showers. The numbers of electrons and muons, registered with the scintillator array of the KASCADE experiment are used to estimate the energy of the shower inducing primary particle. A large hadron calorimeter is used to measure the hadronic energy reaching observation level. The ratio of energy reaching ground level to the energy of the primary particle is used to derive an attenuation length of hadrons in air showers. In the energy range from $10^6$ GeV to $3\cdot10^7$ GeV the attenuation length obtained increases from 170 \gcm2 to 210 \gcm2. The experimental results are compared to predictions of simulations based on contemporary high energy interaction models.Comment: accepted for publication in Physical Review

Radio Emission in Atmospheric Air Showers: First Measurements with LOPES-30

When Ultra High Energy Cosmic Rays interact with particles in the Earth's atmosphere, they produce a shower of secondary particles propagating toward the ground. LOPES-30 is an absolutely calibrated array of 30 dipole antennas investigating the radio emission from these showers in detail and clarifying if the technique is useful for largescale applications. LOPES-30 is co-located and measures in coincidence with the air shower experiment KASCADE-Grande. Status of LOPES-30 and first measurements are presented.Comment: Proceedings of ARENA 06, June 2006, University of Northumbria, U

Dynamics of multipartite quantum correlations under decoherence

Quantum discord is an optimal resource for the quantification of classical and non-classical correlations as compared to other related measures. Geometric measure of quantum discord is another measure of quantum correlations. Recently, the geometric quantum discord for multipartite states has been introduced by Jianwei Xu [arxiv:quant/ph.1205.0330]. Motivated from the recent study [Ann. Phys. 327 (2012) 851] for the bipartite systems, I have investigated global quantum discord (QD) and geometric quantum discord (GQD) under the influence of external environments for different multipartite states. Werner-GHZ type three-qubit and six-qubit states are considered in inertial and non-inertial settings. The dynamics of QD and GQD is investigated under amplitude damping, phase damping, depolarizing and flipping channels. It is seen that the quantum discord vanishes for p>0.75 in case of three-qubit GHZ states and for p>0.5 for six qubit GHZ states. This implies that multipartite states are more fragile to decoherence for higher values of N. Surprisingly, a rapid sudden death of discord occurs in case of phase flip channel. However, for bit flip channel, no sudden death happens for the six-qubit states. On the other hand, depolarizing channel heavily influences the QD and GQD as compared to the amplitude damping channel. It means that the depolarizing channel has the most destructive influence on the discords for multipartite states. From the perspective of accelerated observers, it is seen that effect of environment on QD and GQD is much stronger than that of the acceleration of non-inertial frames. The degradation of QD and GQD happens due to Unruh effect. Furthermore, QD exhibits more robustness than GQD when the multipartite systems are exposed to environment.Comment: 15 pages, 4 figures, 4 table

Frequency spectra of cosmic ray air shower radio emission measured with LOPES

AIMS: We wish to study the spectral dependence of the radio emission from cosmic-ray air showers around 100 PeV (1017 eV). METHODS: We observe short radio pulses in a broad frequency band with the dipole-interferometer LOPES (LOFAR Prototype Station), which is triggered by a particle detector array named Karlsruhe Shower Core and Array Detector (KASCADE). LOFAR is the Low Frequency Array. For this analysis, 23 strong air shower events are selected using parameters from KASCADE. RESULTS: The resulting electric field spectra fall off to higher frequencies. An average electric field spectrum is fitted with an exponential, or alternatively, with a power law. The spectral slope obtained is not consistent within uncertainties and it is slightly steeper than the slope obtained from Monte Carlo simulations based on air showers simulated with CORSIKA (Cosmic Ray Simulations for KASCADE). One of the strongest events was measured during thunderstorm activity in the vicinity of LOPES and shows the longest pulse length measured of 110 ns and a spectral slope of -3.6. CONCLUSIONS: We show with two different methods that frequency spectra from air shower radio emission can be reconstructed on event-by-event basis, with only two dozen dipole antennae simultaneously over a broad range of frequencies. According to the obtained spectral slopes, the maximum power is emitted below 40 MHz. Furthermore, the decrease in power to higher frequencies indicates a loss in coherence determined by the shower disc thickness. We conclude that a broader bandwidth, larger collecting area, and longer baselines, as will be provided by LOFAR, are necessary to further investigate the relation of the coherence, pulse length, and spectral slope of cosmic ray air showers.Comment: 13 pages, 21 figures. Nigl, A. et al. (LOPES Collaboration), Frequency spectra of cosmic ray air shower radio emission measured with LOPES, accepted by A&A on 17/06/200

Air Shower Measurements with the LOPES Radio Antenna Array

LOPES is set up at the location of the KASCADE-Grande extensive air shower experiment in Karlsruhe, Germany and aims to measure and investigate radio pulses from Extensive Air Showers. Since radio waves suffer very little attenuation, radio measurements allow the detection of very distant or highly inclined showers. These waves can be recorded day and night, and provide a bolometric measure of the leptonic shower component. LOPES is designed as a digital radio interferometer using high bandwidths and fast data processing and profits from the reconstructed air shower observables of KASCADE-Grande. The LOPES antennas are absolutely amplitude calibrated allowing to reconstruct the electric field strength which can be compared with predictions from detailed Monte Carlo simulations. We report about the analysis of correlations present in the radio signals measured by the LOPES 30 antenna array. Additionally, LOPES operates antennas of a different type (LOPES-STAR) which are optimized for an application at the Pierre Auger Observatory. Status, recent results of the data analysis and further perspectives of LOPES and the possible large scale application of this new detection technique are discussed.Comment: 8 pages, 10 figures, Contribution to the Arena 2008 conference, Rome, June 200

Highlights from the Pierre Auger Observatory

The Pierre Auger Observatory is the world's largest cosmic ray observatory. Our current exposure reaches nearly 40,000 km$^2$ str and provides us with an unprecedented quality data set. The performance and stability of the detectors and their enhancements are described. Data analyses have led to a number of major breakthroughs. Among these we discuss the energy spectrum and the searches for large-scale anisotropies. We present analyses of our X$_{max}$ data and show how it can be interpreted in terms of mass composition. We also describe some new analyses that extract mass sensitive parameters from the 100% duty cycle SD data. A coherent interpretation of all these recent results opens new directions. The consequences regarding the cosmic ray composition and the properties of UHECR sources are briefly discussed.Comment: 9 pages, 12 figures, talk given at the 33rd International Cosmic Ray Conference, Rio de Janeiro 201