Nonequilibrium transport and statistics of Schwinger pair production in Weyl semimetals

The non-equilibrium dynamics beyond linear response of Weyl semimetals is studied after a sudden switching on of a DC electric field. The resulting current is a nonmonotonic function of time, with an initial quick increase of polarization current followed by a power-law decay. Particle-hole creation \`a la Schwinger dominates for long times when the conduction current takes over the leading role, with the total current increasing again. The conductivity estimated from a dynamical calculation within a Drude picture agrees with the one obtained from Kubo's formula. The full distribution function of electron-hole pairs changes from Poissonian for short perturbations to a Gaussian in the long perturbation (Landau-Zener) regime. The vacuum persistence probability of high energy physics manifests itself in a finite probability of no pair creation and no induced current at all times.Comment: 7 pages, 4 figure

Sampling-based optimization with mixtures

Sampling-based Evolutionary Algorithms (EA) are of great use when dealing with a highly non-convex and/or noisy optimization task, which is the kind of task we often have to solve in Machine Learning. Two derivative-free examples of such methods are Estimation of Distribution Algorithms (EDA) and techniques based on the Cross-Entropy Method (CEM). One of the main problems these algorithms have to solve is finding a good surrogate model for the normalized target function, that is, a model which has sufficient complexity to fit this target function, but which keeps the computations simple enough. Gaussian mixture models have been applied in practice with great success, but most of these approaches lacked a solid theoretical founding. In this paper we describe a sound mathematical justification for Gaussian mixture surrogate models, more precisely we propose a proper derivation of an EDA/CEM algorithm with mixture updates using Expectation Maximization techniques. It will appear that this algorithm resembles the recent Population MCMC schemes, thus reinforcing the link between Monte- Carlo integration methods and sampling-based optimization. We will concentrate throughout this paper on continuous optimization

Fundamental (f) Oscillations in a Magnetically Coupled Solar Interior-Atmosphere System:An Analytical Approach

Solar fundamental (f) acoustic mode oscillations are investigated analytically in a magnetohydrodynamic (MHD) model. The model consists of three layers in planar geometry, representing the solar interior, the magnetic atmosphere, and a transitional layer sandwiched between them. Since we focus on the fundamental mode here, we assume the plasma is incompressible. A horizontal, canopy-like, magnetic field is introduced to the atmosphere, in which degenerated slow MHD waves can exist. The global (f-mode) oscillations can couple to local atmospheric Alfvén waves, resulting, e.g., in a frequency shift of the oscillations. The dispersion relation of the global oscillation mode is derived, and is solved analytically for the thin-transitional layer approximation and for the weak-field approximation. Analytical formulae are also provided for the frequency shifts due to the presence of a thin transitional layer and a weak atmospheric magnetic field. The analytical results generally indicate that, compared to the fundamental value (ω=gk), the mode frequency is reduced by the presence of an atmosphere by a few per cent. A thin transitional layer reduces the eigen-frequencies further by about an additional hundred microhertz. Finally, a weak atmospheric magnetic field can slightly, by a few percent, increase the frequency of the eigen-mode. Stronger magnetic fields, however, can increase the f-mode frequency by even up to ten per cent, which cannot be seen in observed data. The presence of a magnetic atmosphere in the three-layer model also introduces non-permitted propagation windows in the frequency spectrum; here, f-mode oscillations cannot exist with certain values of the harmonic degree. The eigen-frequencies can be sensitive to the background physical parameters, such as an atmospheric density scale-height or the rate of the plasma density drop at the photosphere. Such information, if ever observed with high-resolution instrumentation and inverted, could help to gain further insight into solar magnetic structures by means of solar magneto-seismology, and could provide further insight into the role of magnetism in solar oscillations

Apportionment and districting by Sum of Ranking Differences

Sum of Ranking Differences is an innovative statistical method that ranks competing solutions based on a reference point. The latter might arise naturally, or can be aggregated from the data. We provide two case studies to feature both possibilities. Apportionment and districting are two critical issues that emerge in relation to democratic elections. Theoreticians invented clever heuristics to measure malapportionment and the compactness of the shape of the constituencies, yet, there is no unique best method in either cases. Using data from Norway and the US we rank the standard methods both for the apportionment and for the districting problem. In case of apportionment, we find that all the classical methods perform reasonably well, with subtle but significant differences. By a small margin the Leximin method emerges as a winner, but—somewhat unexpectedly—the non-regular Imperiali method ties for first place. In districting, the Lee-Sallee index and a novel parametric method the so-called Moment Invariant performs the best, although the latter is sensitive to the function’s chosen parameter

Impact of non-Poisson activity patterns on spreading processes

Halting a computer or biological virus outbreak requires a detailed understanding of the timing of the interactions between susceptible and infected individuals. While current spreading models assume that users interact uniformly in time, following a Poisson process, a series of recent measurements indicate that the inter-contact time distribution is heavy tailed, corresponding to a temporally inhomogeneous bursty contact process. Here we show that the non-Poisson nature of the contact dynamics results in prevalence decay times significantly larger than predicted by the standard Poisson process based models. Our predictions are in agreement with the detailed time resolved prevalence data of computer viruses, which, according to virus bulletins, show a decay time close to a year, in contrast with the one day decay predicted by the standard Poisson process based models.Comment: 4 pages, 3 figure

Quantum Monte Carlo Algorithm Based on Two-Body Density Functional Theory for Fermionic Many-Body Systems: Application to 3He

We construct a quantum Monte Carlo algorithm for interacting fermions using the two-body density as the fundamental quantity. The central idea is mapping the interacting fermionic system onto an auxiliary system of interacting bosons. The correction term is approximated using correlated wave functions for the interacting system, resulting in an effective potential that represents the nodal surface. We calculate the properties of 3He and find good agreement with experiment and with other theoretical work. In particular, our results for the total energy agree well with other calculations where the same approximations were implemented but the standard quantum Monte Carlo algorithm was usedComment: 4 pages, 3 figures, 1 tabl

Global oscillations in a magnetic solar model:II Oblique propagation

The coupling of solar global acoustic oscillations to a magnetised solar atmosphere is studied here. The solar interior – atmosphere interface is modelled by a non-magnetic polytrope interior overlayed by a planar atmosphere embedded in non-uniform horizontal atmospheric magnetic field. Pintér & Goossens (1999, A&A, 347, 321) showed that parallel propagating acoustic waves can couple resonantly to local magnetohydrodynamic (MHD) slow continuum modes only. In general, global acoustic modes can, however, propagate in arbitrary directions with respect to local atmospheric fields giving rise to an additional efficient coupling mechanism that has consequences on mode damping and atmospheric energetics. In this paper we study obliquely propagating global modes that can couple also to local MHD Alfvén continuum modes. The atmospheric magnetic effects on global mode frequencies are still much of a debate. In particular, the resulting frequency shifts and damping rates of global modes caused by the resonant interaction with both local Alfvén and slow waves are investigated. We found the coupling of global f and p modes and the Lamb mode, that penetrate into the magnetic solar atmosphere, will strongly depend on the direction of propagation with respect to the solar atmospheric magnetic field. These frequency shifts, as a function of the propagation direction, give us a further elegant tool and refinement method of local helioseismology techniques. Finally we briefly discuss the importance of studying obliquely propagating waves and discuss the results in the context of possible helioseismic observations