Melting a Hubbard dimer: benchmarks of 'ALDA' for quantum thermodynamics

The competition between evolution time, interaction strength, and temperature challenges our understanding of many-body quantum systems out-of-equilibrium. Here we consider a benchmark system, the Hubbard dimer, which allows us to explore all the relevant regimes and calculate exactly the related average quantum work. At difference with previous studies, we focus on the effect of increasing temperature, and show how this can turn competition between many-body interactions and driving field into synergy. We then turn to use recently proposed protocols inspired by density functional theory to explore if these effects could be reproduced by using simple approximations. We find that, up to and including intermediate temperatures, a method which borrows from ground-state adiabatic local density approximation improves dramatically the estimate for the average quantum work, including, in the adiabatic regime, when correlations are strong. However at high temperature and at least when based on the pseudo-LDA, this method fails to capture the counterintuitive qualitative dependence of the quantum work with interaction strength, albeit getting the quantitative estimates relatively close to the exact results

Can we avert an Amazon tipping point? The economic and environmental costs

© 2022 The Author(s). Published by IOP Publishing Ltd.The Amazon biome is being pushed by unsustainable economic drivers towards an ecological tipping point where restoration to its previous state may no longer be possible. This degradation is the result of self-reinforcing interactions between deforestation, climate change and fire. We assess the economic, natural capital and ecosystem services impacts and trade-offs of scenarios representing movement towards an Amazon tipping point and strategies to avert one using the Integrated Economic-Environmental Modeling (IEEM) Platform linked with spatial land use-land cover change and ecosystem services modeling (IEEM + ESM). Our approach provides the first approximation of the economic, natural capital and ecosystem services impacts of a tipping point, and evidence to build the economic case for strategies to avert it. For the five Amazon focal countries, namely, Brazil, Peru, Colombia, Bolivia and Ecuador, we find that a tipping point would create economic losses of US$256.6 billion in cumulative gross domestic product by 2050. Policies that would contribute to averting a tipping point, including strongly reducing deforestation, investing in intensifying agriculture in cleared lands, climate-adapted agriculture and improving fire management, would generate approximately US$339.3 billion in additional wealth and a return on investment of US$29.5 billion. Quantifying the costs, benefits and trade-offs of policies to avert a tipping point in a transparent and replicable manner can support the design of regional development strategies for the Amazon biome, build the business case for action and catalyze global cooperation and financing to enable policy implementation