Effective dynamics of disordered quantum systems

We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective coupling agents and associated rates which encode the specific statistical properties of the Hamiltonian's eigenvectors and eigenvalues, respectively. Spectral disorder and isotropically disordered eigenvector distributions are considered as paradigmatic test cases.Comment: 20 page

Win-wins or trade-offs? Site and strategy determine carbon and local ecosystem service benefits for protection, restoration, and agroforestry

Nature-based solutions (NBS) can deliver many benefits to human wellbeing, including some crucial to climate adaptation. We quantitatively assess the global potential of NBS strategies of protection, restoration, and agroforestry by modeling global climate change mitigation and local ecosystem services (water availability, sediment retention, runoff, pollination, nitrogen retention, green water storage, and coastal protection). The strategies with the most potential to help people do not necessarily deliver the most climate change mitigation: per area of conservation action, agroforestry provides substantial benefits (>20% increase in at least one local ecosystem service) to three times more people on average than reforestation while providing less than one tenth the carbon sequestration per unit area. Each strategy delivers a different suite of ecosystem service benefits; for instance, avoided forest conversion provides a strong increase in nitrogen retention (100% increase to 72 million people if fully implemented globally) while agroforestry increases pollination services (100% increase to 3.0 billion people if fully implemented globally). One common disservice shared by all the NBS strategies modeled here is that increased woody biomass increases transpiration, reducing annual runoff and in some watersheds negatively impacting local water availability. In addition, the places with the greatest potential for climate change mitigation are not necessarily the ones with the most people. For instance, reforestation in Latin America has the greatest climate change mitigation potential, but the greatest ecosystem service benefits are in Africa. Focusing on nations with high climate mitigation potential as well as high local ecosystem service potential, such as Nigeria in the case of reforestation, India for agroforestry, and the Republic of Congo for avoided forest conversion, can help identify win-win sites for implementation. We find that concentrating implementation of these three conservation strategies in critical places, covering 5.8 million km2, could benefit 2.0 billion people with increased local ecosystem services provision. These critical places cover only 35% of the possible area of implementation but would provide 80% of the benefits that are possible globally for the selected set of ecosystem services under the NBS scenarios examined here. We conclude that targeting these critical places for protection, restoration, and agroforestry interventions will be key to achieving adaptation and human wellbeing goals while also increasing nature-based carbon mitigation.Peer Reviewe