Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.

Effects of elevation and land use on the biomass of trees, shrubs and herbs at Mount Kilimanjaro

The protection and sustainable management of forest carbon stocks, particularly in the tropics, is a key factor in the mitigation of global change effects. However, our knowledge of how land use and elevation affect carbon stocks in tropical ecosystems is very limited. We compared aboveground biomass of trees, shrubs and herbs for eleven natural and human-influenced habitat types occurring over a wide elevation gradient (866–4550 m) at the world's highest solitary mountain, Mount Kilimanjaro. Thanks to the enormous elevation gradient, we covered important natural habitat types, e.g., savanna woodlands, montane rainforest and afro-alpine vegetation, as well as important land-use types such as maize fields, grasslands, traditional home gardens, coffee plantations and selectively logged forest. To assess tree and shrub biomass with pantropical allometric equations, we measured tree height, diameter at breast height and wood density and to assess herbaceous biomass, we sampled destructively. Among natural habitats, tree biomass was highest at intermediate elevation in the montane zone (340 Mg ha−1), shrub biomass declined linearly from 7 Mg ha−1 at 900 m to zero above 4000 m, and, inverse to tree biomass, herbaceous biomass was lower at mid-elevations (1 Mg ha−1) than in savannas (900 m, 3 Mg ha−1) or alpine vegetation (above 4000 m, 6 Mg ha−1). While the various land-use types dramatically decreased woody biomass at all elevations, though to various degrees, herbaceous biomass was typically increased. Our study highlights tropical montane forest biomass as important aboveground carbon stock and quantifies the extent of the strong aboveground biomass reductions by the major land-use types, common to East Africa. Further, it shows that elevation and land use differently affect different vegetation strata, and thus the matrix for other organisms.