CORSIKA 8 - Towards a modern framework for the simulation of extensive air showers

Current and future challenges in astroparticle physics require novel simulation tools to achieve higher precision and more flexibility. For three decades the FORTRAN version of CORSIKA served the community in an excellent way. However, the effort to maintain and further develop this complex package is getting increasingly difficult. To overcome existing limitations, and designed as a very open platform for all particle cascade simulations in astroparticle physics, we are developing CORSIKA 8 based on modern C++ and Python concepts. Here, we give a brief status report of the project.Comment: 4 pages, 3 figures; Proceedings of Ultra High Energy Cosmic Rays 201

Kondo model in nonequilibrium: Interplay between voltage, temperature, and crossover from weak to strong coupling

We consider an open quantum system in contact with fermionic metallic reservoirs in a nonequilibrium setup. For the case of spin, orbital or potential fluctuations, we present a systematic formulation of real-time renormalization group at finite temperature, where the complex Fourier variable of an effective Liouvillian is used as flow parameter. We derive a universal set of differential equations free of divergencies written as a systematic power series in terms of the frequency-independent two-point vertex only, and solve it in different truncation orders by using a universal set of boundary conditions. We apply the formalism to the description of the weak to strong coupling crossover of the isotropic spin-1/2 nonequilibrium Kondo model at zero magnetic field. From the temperature and voltage dependence of the conductance in different energy regimes we determine various characteristic low-energy scales and compare their universal ratio to known results. For a fixed finite bias voltage larger than the Kondo temperature, we find that the temperature-dependence of the differential conductance exhibits non-monotonic behavior in the form of a peak structure. We show that the peak position and peak width scale linearly with the applied voltage over many orders of magnitude in units of the Kondo temperature. Finally, we compare our calculations with recent experiments.Comment: 48 pages, 10 figure

Distributed computation of persistent homology

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not exhaust the available memory. Following up on a recently presented parallel method for persistence computation on shared memory systems, we demonstrate that a simple adaption of the standard reduction algorithm leads to a variant for distributed systems. Our algorithmic design ensures that the data is distributed over the nodes without redundancy; this permits the computation of much larger instances than on a single machine. Moreover, we observe that the parallelism at least compensates for the overhead caused by communication between nodes, and often even speeds up the computation compared to sequential and even parallel shared memory algorithms. In our experiments, we were able to compute the persistent homology of filtrations with more than a billion (10^9) elements within seconds on a cluster with 32 nodes using less than 10GB of memory per node

A Stable Multi-Scale Kernel for Topological Machine Learning

Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes

Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices

This paper proposes an efficient probabilistic method that computes combinatorial gradient fields for two dimensional image data. In contrast to existing algorithms, this approach yields a geometric Morse-Smale complex that converges almost surely to its continuous counterpart when the image resolution is increased. This approach is motivated using basic ideas from probability theory and builds upon an algorithm from discrete Morse theory with a strong mathematical foundation. While a formal proof is only hinted at, we do provide a thorough numerical evaluation of our method and compare it to established algorithms.Comment: 17 pages, 7 figure

Scaling of the Kondo zero bias peak in a hole quantum dot at finite temperatures

We have measured the zero bias peak in differential conductance in a hole quantum dot. We have scaled the experimental data with applied bias and compared to real time renormalization group calculations of the differential conductance as a function of source-drain bias in the limit of zero temperature and at finite temperatures. The experimental data show deviations from the T=0 calculations at low bias, but are in very good agreement with the finite T calculations. The Kondo temperature T_K extracted from the data using T=0 calculations, and from the peak width at 2/3 maximum, is significantly higher than that obtained from finite T calculations.Comment: Accepted to Phys. Rev. B (Rapid

Fingerprints of the Magnetic Polaron in Nonequilibrium Electron Transport through a Quantum Wire Coupled to a Ferromagnetic Spin Chain

We study nonequilibrium quantum transport through a mesoscopic wire coupled via local exchange to a ferromagnetic spin chain. Using the Keldysh formalism in the self-consistent Born approximation, we identify fingerprints of the magnetic polaron state formed by hybridization of electronic and magnon states. Because of its low decoherence rate, we find coherent transport signals. Both elastic and inelastic peaks of the differential conductance are discussed as a function of external magnetic fields, the polarization of the leads and the electronic level spacing of the wire.Comment: 5 pages, 4 figure

Real-time renormalization group and cutoff scales in nonequilibrium applied to an arbitrary quantum dot in the Coulomb blockade regime

We apply the real-time renormalization group (RG) in nonequilibrium to an arbitrary quantum dot in the Coulomb blockade regime. Within one-loop RG-equations, we include self-consistently the kernel governing the dynamics of the reduced density matrix of the dot. As a result, we find that relaxation and dephasing rates generically cut off the RG flow. In addition, we include all other cutoff scales defined by temperature, energy excitations, frequency, and voltage. We apply the formalism to transport through single molecular magnets, realized by the fully anisotropic Kondo model (with three different exchange couplings J_x, J_y, and J_z) in a magnetic field h_z. We calculate the differential conductance as function of bias voltage V and discuss a quantum phase transition which can be tuned by changing the sign of J_x J_y J_z via the anisotropy parameters. Finally, we calculate the noise S(Omega) at finite frequency Omega for the isotropic Kondo model and find that the dephasing rate determines the height of the shoulders in dS(\Omega)/d Omega near Omega=V.Comment: 16 pages, 7 figure

Psychometric precision in phenotype definition is a useful step in molecular genetic investigation of psychiatric disorders

Affective disorders are highly heritable, but few genetic risk variants have been consistently replicated in molecular genetic association studies. The common method of defining psychiatric phenotypes in molecular genetic research is either a summation of symptom scores or binary threshold score representing the risk of diagnosis. Psychometric latent variable methods can improve the precision of psychiatric phenotypes, especially when the data structure is not straightforward. Using data from the British 1946 birth cohort, we compared summary scores with psychometric modeling based on the General Health Questionnaire (GHQ-28) scale for affective symptoms in an association analysis of 27 candidate genes (249 single-nucleotide polymorphisms (SNPs)). The psychometric method utilized a bi-factor model that partitioned the phenotype variances into five orthogonal latent variable factors, in accordance with the multidimensional data structure of the GHQ-28 involving somatic, social, anxiety and depression domains. Results showed that, compared with the summation approach, the affective symptoms defined by the bi-factor psychometric model had a higher number of associated SNPs of larger effect sizes. These results suggest that psychometrically defined mental health phenotypes can reflect the dimensions of complex phenotypes better than summation scores, and therefore offer a useful approach in genetic association investigations