Deviations from Gaussianity in deterministic discrete time dynamical systems

In this paper we examine the deviations from Gaussianity for two types of random variable converging to a normal distribution, namely sums of random variables generated by a deterministic discrete time map and a linearly damped variable driven by a deterministic map. We demonstrate how Edgeworth expansions provide a universal description of the deviations from the limiting normal distribution. We derive explicit expressions for these asymptotic expansions and provide numerical evidence of their accuracy

Quantum processes

A number of ideas and questions related to the construction of quantum processes are discussed. Quantum state extension, entanglement and asymptotic behaviour of the entropy are some of the issues explored. These topics are studied in more detail for a class of quantum processes known as finitely correlated states. Several examples of such processes are presented, specifically a Free Fermionic model.Comment: 20 pages, 2 figures, to appear in the proceedings of the 46th Karpacz Winter School of Theoretical Physics "Quantum Dynamics and Information: Theory and Experiment

Accessible teaching with GNU TeXmacs

In this article I give a brief overview of some of the challenges in creating accessible documents for STEM education, as well as why and how GNU TeXmacs can be used to address some of these

Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems

In this paper we provide a connection between the geometrical properties of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan-Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.Comment: 16 pages, 3 Figure

Classical capacity of a qubit depolarizing channel with memory

The classical product state capacity of a noisy quantum channel with memory is investigated. A forgetful noise-memory channel is constructed by Markov switching between two depolarizing channels which introduces non-Markovian noise correlations between successive channel uses. The computation of the capacity is reduced to an entropy computation for a function of a Markov process. A reformulation in terms of algebraic measures then enables its calculation. The effects of the hidden-Markovian memory on the capacity are explored. An increase in noise-correlations is found to increase the capacity

Stochastic model reduction for slow-fast systems with moderate time-scale separation

We propose a stochastic model reduction strategy for deterministic and stochastic slow-fast systems with finite time-scale separation. The stochastic model reduction relaxes the assumption of infinite time-scale separation of classical homogenization theory by incorporating deviations from this limit as described by an Edgeworth expansion. A surrogate system is constructed the parameters of which are matched to produce the same Edgeworth expansions up to any desired order of the original multi-scale system. We corroborate our analytical findings by numerical examples, showing significant improvements to classical homogenized model reduction

Language and thought in Hildegard of Bingen’s visionary trilogy : close and distant readings of a thinker’s development

By combining the methods of distant reading (computational stylistics) and close reading, the authors discuss the development of language and thought in Hildegard of Bingen's visionary works (Sciuias, Liber uite meritorum and Liber diuinorum operum). The visionary trilogy, although written over the course of three decades, raises the impression of a monolithic and seemingly unchanging voice. Moving beyond this impression, the interdisciplinary analysis presented here reveals that the trilogy exhibits interesting differences at the word level which cannot simply be explained through external historical circumstances (e.g. manuscript transmission or different secretaries). Instead, the results raise pertinent questions regarding the trilogy's internal development in didactic method, style, and philosophy

Computation of extreme heat waves in climate models using a large deviation algorithm

Studying extreme events and how they evolve in a changing climate is one of the most important current scientific challenges. Starting from complex climate models, a key difficulty is to be able to run long enough simulations to observe those extremely rare events. In physics, chemistry, and biology, rare event algorithms have recently been developed to compute probabilities of events that cannot be observed in direct numerical simulations. Here we propose such an algorithm, specifically designed for extreme heat or cold waves, based on statistical physics. This approach gives an improvement of more than two orders of magnitude in the sampling efficiency. We describe the dynamics of events that would not be observed otherwise. We show that European extreme heat waves are related to a global teleconnection pattern involving North America and Asia. This tool opens up a wide range of possible studies to quantitatively assess the impact of climate change

A large deviation theory-based analysis of heat waves and cold spells in a simplified model of the general circulation of the atmosphere

We study temporally persistent and spatially extended extreme events of temperature anomalies, i.e. heat waves and cold spells, using large deviation theory. To this end, we consider a simplified yet Earth-like general circulation model of the atmosphere and numerically estimate large deviation rate functions of near-surface temperature in the mid-latitudes. We find that, after a renormalisation based on the integrated autocorrelation, the rate function one obtains at a given latitude by looking, locally in space, at long time averages agrees with what is obtained, instead, by looking, locally in time, at large spatial averages along the latitude. This is a result of scale symmetry in the spatial-temporal turbulence and of the fact that advection is primarily zonal. This agreement hints at the universality of large deviations of the temperature field. Furthermore, we discover that the obtained rate function is able to describe spatially extended and temporally persistent heat waves or cold spells, if we consider temporal averages of spatial averages over intermediate spatial scales. Finally, we find out that large deviations are relatively more likely to occur when looking at these spatial averages performed over intermediate scales, thus pointing to the existence of weather patterns associated to the low-frequency variability of the atmosphere. Extreme value theory is used to benchmark our results