Open systems with error bounds: spin boson model with spectral density variations

In the study of open quantum systems, one of the most common ways to describe environmental effects on the reduced dynamics is through the spectral density. However, in many models this object cannot be computed from first principles and needs to be inferred on phenomenological grounds or fitted to experimental data. Consequently, some uncertainty regarding its form and parameters is unavoidable; this in turn calls into question the accuracy of any theoretical predictions based on a given spectral density. Here, we focus on the spin-boson model as a prototypical open quantum system, and find two error bounds on predicted expectation values in terms of the spectral density variation considered, and state a sufficient condition for the strongest one to apply. We further demonstrate an application of our result, by bounding the error brought about by the approximations involved in the Hierarchical Equations of Motion resolution method for spin-boson dynamics.Comment: 5+5 pages, minor edits since last unpublished versio

Optimized auxiliary oscillators for the simulation of general open quantum systems

A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and that of the target environment, the error induced in the reduced dynamics of the system is brought under rigorous control. The interactions among the effective modes provide remarkable flexibility in replicating non-Markovian effects on the system even with a small number of oscillators, and the resulting Lindblad equation may therefore be integrated at a very reasonable computational cost using standard methods for Markovian problems, even in strongly non-perturbative coupling regimes and at arbitrary temperatures including zero. We apply the method to an exactly solvable problem in order to demonstrate its accuracy, and present a study based on current research in the context of coherent transport in biological aggregates as a more realistic example of its use; performance and versatility are highlighted, and theoretical and numerical advantages over existing methods, as well as possible future improvements, are discussed.Comment: 23 + 9 pages, 11 + 2 figures. No changes from previous version except publication info and updated author affiliation

Urban NO2 Atlas

The Atlas shows, for selected cities, the likely effects of the implementation of “Traffic Policies” intended to reduce urban NO2 concentrations. As NO2 pollution in urban areas is mainly caused by traffic, the analysis focuses on assessing the relative contribution to the NO2 concentration in ambient air from different types of vehicles. The results, obtained for a selected number of cities in Europe show that, depending on the size of the selected “Inner Area” (by this name, we mean the area over which traffic measures are applied), one could reduce on average up to 40% the NO2 urban background concentrations. Of this average reduction, roughly 15% is linked to passenger diesel cars, 13% to trucks and 6% to vans (mostly diesel); while the remaining share is associated to other type of vehicles (buses, gasoline cars, etc…). This Atlas provides a first indication of the relative effectiveness of mobility policies aimed at reducing urban NO2 pollution concentrations in European cities. However, considering the specific assumptions in the applied approach, as on traffic flows, fleet composition, emission factors, size of the “Inner Area”, etc…, the results may not be as accurate as they would be when using detailed local data. The SHERPA-City methodology and tool applied in this Atlas can be used by local authorities to assess a broad range of air quality measures, including technological (e.g. fleet renewal, new technologies) and soft measures (i.e. promotion of walking and cycling). Such measures can be assessed alone or in combination.JRC.C.5-Air and Climat

A new quantitative approach to general bosonic environments in open quantum systems : rigorous error bounds and a novel numerical method for finite systems

A Dissertation on open quantum systems, containing a general review of the current standing of the field, in particular regarding systems interacting with Gaussian environments, as well as original analytical and numerical results. The problem of the impact of a variation in the environmental properties on the reduced dynamics of an open system is investigated analytically, and a new computational technique for the simulation of non-perturbative, non-Markovian open quantum system dynamics based on devising error-certified effective environments is presented