We build upon work by C. K. Law [Phys. Rev. A 71, 034306 (2005)10.1103/PhysRevA.71.034306] to show in general that the entanglement between two fermions largely determines the extent to which the pair behaves like an elementary boson. Specifically, we derive upper and lower bounds on a quantity chi{N+1}/chi{N} that governs the bosonic character of a pair of fermions when N such pairs approximately share the same wave function. Our bounds depend on the purity of the single-particle density matrix, an indicator of entanglement, and demonstrate that if the entanglement is sufficiently strong, the quantity chi{N+1}/chi{N} approaches its ideal bosonic value.
Urban mobility significantly contributes to global carbon dioxide emissions. Given the rapid expansion and growth in urban areas, cities thus require innovative policies to ensure efficient and sustainable mobility. Urban typologies can serve as a vehicle for understanding dynamics of cities, which exhibit high variability in form, economic output, mobility behavior, among others. Yet, typologies relevant for sustainable urban mobility analyses are few, outdated and not large enough in scope. In this paper, we present a new typologization spanning 331 cities in 124 countries. Our sample represents 40% of the global urban population and contains the most recent data from 2008 to date. Using a factor analytic and agglomerative clustering approach, we identify 9 urban factors and 12 typologies. We discuss the implications of this new framework for researchers and planners and investigate the relationships between mobility and environmental sustainability indicators. Notably, we show an immediate application of the urban typologies to better understanding travel behavior and also describe their usage for detailed large-scale simulation in representative prototype cities for insights into sustainable future mobility policy pathways. Our data and results are publicly available for further exploration and will serve as a foundation for future analyses toward desirable urban and environmental outcomes.
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