Uncertainty Relations in the Madelung Picture Including a Dissipative Environment.

In a recent paper, we have shown how in Madelung's hydrodynamic formulation of quantum mechanics, the uncertainties are related to the phase and amplitude of the complex wave function. Now we include a dissipative environment via a nonlinear modified Schrödinger equation. The effect of the environment is described by a complex logarithmic nonlinearity that vanishes on average. Nevertheless, there are various changes in the dynamics of the uncertainties originating from the nonlinear term. Again, this is illustrated explicitly using generalized coherent states as examples. With particular focus on the quantum mechanical contribution to the energy and the uncertainty product, connections can be made with the thermodynamic properties of the environment.

Separate collection rates for plastic packaging in Austria - A regional analysis taking collection systems and urbanization into account.

According to the EU Circular Economy Package, recycling of plastic packaging waste (PPW) has to be enhanced significantly by 2025 and 2030. Although a set of measures will be required along the whole value chain of plastic packaging, the process of separate collection remains the backbone. Hence, a detailed understanding of the performance of current separate collection systems is crucial. As a case study, the separate collection of PPW was analyzed within a single country, Austria, where a variety of collection procedures are implemented. By using the method of material flow analysis, separate collection rates in terms of quantities and qualities were analyzed for separate collection systems of different settlement patterns, target fractions, and service levels provided. Results show that the highest performance was achieved in systems that cover mainly rural areas and where all plastic packaging wastes are collected through curbside collection, with separate collection rates of 74-77%. With additional collection via collection centers, these values increased to 78%-83%. In comparison, the results for urban areas showed the lowest separate collection rate of 56%. In the case that separate collection targeted plastic bottles only, maximum collection rates of around 50 % were observed, with the tendency towards higher collection rates if co-mingled with metals. To enhance separate collection, a general shift to the target fraction "all plastic packaging" instead of "plastic bottles only" is crucial. Modelling of optimized collection systems in all Austrian regions would lead to a theoretical total separation collection rate of 74%.

Uncertainty Relations in the Madelung Picture.

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position-momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.

On the importance of adjusting for distorting factors in benchmarking analysis, as illustrated by a cost comparison of the different forms of implementation of the EU Packaging Directive.

Benchmarking is a proven and widely used business tool for identifying best practice. To produce robust results, the objects of comparison used in benchmarking analysis need to be structurally comparable and distorting factors need to be eliminated. We focus on a specific example - a benchmark study commissioned by the European Commission's Directorate-General for Environment on the implementation of Extended Producer Responsibility (EPR) for packaging at the national level - to discuss potential distorting factors and take them into account in the calculation. The cost of compliance per inhabitant and year, which is used as the key cost efficiency indicator in the study, is adjusted to take account of seven factors. The results clearly show that differences in performance may play a role, but the (legal) implementation of EPR - which is highly heterogeneous across countries - is the single most important cost determinant and must be taken into account to avoid misinterpretation and false conclusions.