Quantum states far from the energy eigenstates of any local hamiltonian

What quantum states are possible energy eigenstates of a many-body Hamiltonian? Suppose the Hamiltonian is nontrivial, i.e., not a multiple of the identity, and L local, in the sense of containing interaction terms involving at most L bodies, for some fixed L. We construct quantum states psi which are far away from all the eigenstates E of any nontrivial L-local Hamiltonian, in the sense that parallel topsi-Eparallel to is greater than some constant lower bound, independent of the form of the Hamiltonian.

Assigning dates to thin gneissic veins in high-grade metamorphic terranes: A cautionary tale from Akilia, southwest Greenland

A granodiorite from Akilia, southwest Greenland, previously suggested to date putative life-bearing rocks to greater than or equal to3.84 Ga, is re-investigated using whole-rock major and trace-element geochemistry, and detailed cathodoluminescence image-guided secondary ion mass spectrometer analyses of zircon U-Th-Pb and rare earth elements. Complex zircon internal structure reveals three episodes of zircon growth and/or recrystallization dated to c. 3.84 Ga, 3.62 Ga and 2.71 Ga. Rare earth element abundances imply a significant role for garnet in zircon generation at 3.62 Ga and 2.71 Ga. The 3.62 Ga event is interpreted as partial melting of a c. 3.84 Ga grey gneiss precursor at granulite facies with residual garnet. Migration of this 3.62 Ga magma (or melt-crystal mush) away from the melt source places a maximum age limit on any intrusive relationship. These early Archaean relationships have been complicated further by isotopic reworking in the 2.71 Ga event, which could have included a further episode of partial melting. This study highlights a general problem associated with dating thin gneissic veins in polyphase metamorphic terranes, where field relationships may be ambiguous and zircon inheritance can be expected.

I-Spi: innovative shared practical ideas: a support guide for literacy and numeracy in the early years of schooling, for home tutor/supervisors in distance education

Innovative Shared Practical Ideas (I-Spi) is a guide to help you and your children learn together. It is designed to affirm, support and strengthen your role as home tutor/supervisors in your daily learning sessions with your children. In this guide particular emphasis is given to the value of talk, formal and informal early literacy and numeracy practices (including ideas from distance school lessons, from home tutor/supervisors, research, and beyond), assessment of these practices together with informal assessment ideas for gauging your children’s literacy and numeracy progress, and stepping in and building on strategies