RESUMO
Quantum many-body systems are typically endowed with a tensor product structure. A structure they inherited from probability theory, where the probability of two independent events is the product of the probabilities. The tensor product structure of a Hamiltonian thus gives a natural decomposition of the system into independent smaller subsystems. It is interesting to understand whether a given Hamiltonian is compatible with some particular tensor product structure. In particular, we ask, is there a basis in which an arbitrary Hamiltonian has a 2-local form, i.e., it contains only pairwise interactions? Here we show, using analytical and numerical calculations, that a generic Hamiltonian (e.g., a large random matrix) can be approximately written as a linear combination of two-body interaction terms with high precision; that is, the Hamiltonian is 2-local in a carefully chosen basis. Moreover, we show that these Hamiltonians are not fine-tuned, meaning that the spectrum is robust against perturbations of the coupling constants. Finally, by analyzing the adjacency structure of the couplings [Formula: see text], we suggest a possible mechanism for the emergence of geometric locality from quantum chaos.
RESUMO
Mobile communication technology has evolved rapidly over the last ten years with a drastic increase in wireless data traffic and the deployment of new telecommunication technologies. The aim of this study was to evaluate the ambient radiofrequency electromagnetic field (RF-EMF) levels and temporal changes in various microenvironments in Switzerland in 2014 and 2021. We measured the ambient RF-EMF levels in V/m in the same 49 outdoor areas and in public transport in 2014 and 2021 using portable RF-EMF exposure meters carried in a backpack. The areas were selected to represent some typical types of microenvironments (e.g. urban city centres, suburban and rural areas). We calculated the summary statistics (mean, percentiles) in mW/m2 and converted back to V/m for each microenvironment. We evaluated the distribution and the variability of the ambient RF-EMF levels per microenvironment types in 2021. Finally, we compared the ambient RF-EMF mean levels in 2014 and 2021 using multilevel regression modelling. In outdoor areas, the average ambient RF-EMF mean levels per microenvironment in 2021 ranged from 0.19 V/m in rural areas to 0.43 V/m in industrial areas (overall mean: 0.27 V/m). In public transports, the mean levels were 0.27 V/m in buses, 0.33 V/m in trains and 0.36 V/m in trams. In 2021, mean levels across all outdoor areas were -0.022 V/m lower (95% confidence interval: -0.072, 0.030) than in 2014. Results from our comprehensive measurement study across Switzerland suggest that RF-EMF levels in public places have not significantly changed between 2014 and 2021 despite an 18-fold increase in mobile data transmission during that period. The absence of temporal changes may be owed to the shift to newer mobile communication technologies, which are more efficient.
RESUMO
PURPOSE: Proton therapy is a limited resource that is not available to all patients who may benefit from it. We investigated combined proton-photon treatments, in which some fractions are delivered with protons and the remaining fractions with photons, as an approach to maximize the benefit of limited proton therapy resources at a population level. METHODS AND MATERIALS: To quantify differences in normal-tissue complication probability (NTCP) between protons and photons, we considered a cohort of 45 patients with head and neck cancer for whom intensity modulated radiation therapy and intensity modulated proton therapy plans were previously created, in combination with NTCP models for xerostomia and dysphagia considered in the Netherlands for proton patient selection. Assuming limited availability of proton slots, we developed methods to optimally assign proton fractions in combined proton-photon treatments to minimize the average NTCP on a population level. The combined treatments were compared with patient selection strategies in which patients are assigned to single-modality proton or photon treatments. RESULTS: There is a benefit of combined proton-photon treatments compared with patient selection, owing to the nonlinearity of NTCP functions; that is, the initial proton fractions are the most beneficial, whereas additional proton fractions have a decreasing benefit when a flatter part of the NTCP curve is reached. This effect was small for the patient cohort and NTCP models considered, but it may be larger if dose-response relationships are better known. In addition, when proton slots are limited, patient selection methods face a trade-off between leaving slots unused and blocking slots for future patients who may have a larger benefit. Combined proton-photon treatments with flexible proton slot assignment provide a method to make optimal use of all available resources. CONCLUSIONS: Combined proton-photon treatments allow for better use of limited proton therapy resources. The benefit over patient selection schemes depends on the NTCP models and the dose differences between protons and photons.
