One of the folk theorems in quantum lattice models claims the equivalence of the existence of a nonvanishing spectral gap and exponential decay of spatial correlations in the ground state. It has been known for some time that there are exceptions to one direction of this equivalence. There are models with a unique ground state with exponential decay of correlations but without a gap in the exci...

Analytical expressions for the contributions of sun and shade leaves to instantaneous canopy photosynthesis are derived. The analysis is based on four assumptions. First, that the canopy is closed in the sense that it is horizontally uniform. Secondly, that there is an exponential profile of light down the canopy with the same decay constant for light from different parts of the sky. Thirdly, t...