Cohomology ring of the BRST operator associated to the sum of two pure spinors

In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure.

Ab initio investigation of hydrogen bonding and electronic structure of high-pressure phases of ice

We report a detailed ab initio investigation on hydrogen bonding, geometry, electronic structure, and lattice dynamics of ice under a large high pressure range, including the ice X phase (55-380GPa), the previous theoretically proposed higher-pressure phase ice XIIIM (Refs. 1-2) (380GPa), ice XV (a new structure we derived from ice XIIIM) (300-380GPa), as well as the ambient pressure low-temperature phase ice XI. Different from many other materials, the band gap of ice X is found to be increasing linearly with pressure from 55GPa up to 290GPa, the electronic density of states (DOS) shows that the valence bands have a tendency of red shift (move to lower energies) referring to the Fermi energy while the conduction bands have a blue shift (move to higher energies). This behavior is interpreted as the high pressure induced change of s-p charge transfers between hydrogen and oxygen. It is found that ice X exists in the pressure range from 75GPa to about 290GPa. Beyond 300GPa, a new hydrogen-bonding structure with 50% hydrogen atoms in symmetric positions in O-H-O bonds and the other half being asymmetric, ice XV, is identified. The physical mechanism for this broken symmetry in hydrogen bonding is revealed.