arXiv subjects

Jeroen Wouters

Publications and source records attributed to Jeroen Wouters.

22 records · Page 2Linked to original sources

arXiv2011

Relevance of sampling schemes in light of Ruelle's linear response theory

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We first show that by using a general functional decomposition for space-time dependent forcings, we can define elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the definition of SRB measure, we then study the consequence of taking different sampling schemes for analysing the response of the system. We show that only a specific choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula first presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be fine-tuned to make the definition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.

cond-mat.stat-mech↗

arXiv2011

Universal behavior of extreme value statistics for selected observables of dynamical systems

The main results of the extreme value theory developed for the investigation of the observables of dynamical systems rely, up to now, on the Gnedenko approach. In this framework, extremes are basically identified with the block maxima of the time series of the chosen observable, in the limit of infinitely long blocks. It has been proved that, assuming suitable mixing conditions for the underlying dynamical systems, the extremes of a specific class of observables are distributed according to the so called Generalized Extreme Value (GEV) distribution. Direct calculations show that in the case of quasi-periodic dynamics the block maxima are not distributed according to the GEV distribution. In this paper we show that, in order to obtain a universal behaviour of the extremes, the requirement of a mixing dynamics can be relaxed if the Pareto approach is used, based upon considering the exceedances over a given threshold. Requiring that the invariant measure locally scales with a well defined exponent - the local dimension -, we show that the limiting distribution for the exceedances of the observables previously studied with the Gnedenko approach is a Generalized Pareto distribution where the parameters depends only on the local dimensions and the value of the threshold. This result allows to extend the extreme value theory for dynamical systems to the case of regular motions. We also provide connections with the results obtained with the Gnedenko approach. In order to provide further support to our findings, we present the results of numerical experiments carried out considering the well-known Chirikov standard map.

cond-mat.stat-mech↗

arXiv2010

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.

quant-ph↗

arXiv2009

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.

quant-ph↗