H^+_2$ in a strong magnetic field described via a solvable model

We consider the hydrogen molecular ion $H^+_2$ in the presence of a strong homogeneous magnetic field. In this regime, the effective Hamiltonian is almost one dimensional with a potential energy which looks like a sum of two Dirac delta functions. This model is solvable, but not close enough to our exact Hamiltonian for relevant strenght of the magnnetic field. However we show that the correct values of the equilibrium distance as well as the binding energy of the ground state of the ion, can be obtained when incorporating perturbative corrections up to second order. Finally, we show that $He_2^{3+}$ exists for sufficiently large magnetic fields

Marine invasion genomics: Revealing ecological and evolutionary consequences of biological invasions

Genomic approaches are increasingly being used to study biological invasions. Here, we first analyse how high-throughput sequencing has aided our understanding of the mechanisms associated with biological invasions. These include the transport of propagules to pre-invaded areas, an exploration of the consequences of hybridisation during range expansions, and the pre- and post- invasion adaptation of colonising populations. We then explore how contemporary genomic methods have been used to probe and monitor the spread of non-indigenous species. More specifically, we focus on the detection of species richness from environmental samples, measures of quantitative traits that may promote invasive- ness, analysis of rapid adaptation, and the study of phenotypic plasticity. Finally, we look to the future, exploring how genomic approaches will assist future biodiversity conservationists in their efforts to mitigate the spread and effects of biological invasions. Ultimately, although the use of genomic tools to study non-indigenous species has so far been rather limited, studies to date indicate that genomic tools offer unparalleled research opportunities to continually improve our understanding of marine biological invasion