Functional Equations and the Generalised Elliptic Genus

We give a new derivation and characterisation of the generalised elliptic genus of Krichever-H\"ohn by means of a functional equation.Comment: To be published in the collection honouring Francesco Calogero's 70-th birthda

Multicomponent Dark Matter in Supersymmetric Hidden Sector Extensions

Most analyses of dark matter within supersymmetry assume the entire cold dark matter arising only from weakly interacting neutralinos. We study a new class of models consisting of $U(1)^n$ hidden sector extensions of the MSSM that includes several stable particles, both fermionic and bosonic, which can be interpreted as constituents of dark matter. In one such class of models, dark matter is made up of both a Majorana dark matter particle, i.e., a neutralino, and a Dirac fermion with the current relic density of dark matter as given by WMAP being composed of the relic density of the two species. These models can explain the PAMELA positron data and are consistent with the anti-proton flux data, as well as the photon data from FERMI-LAT. Further, it is shown that such models can also simultaneously produce spin independent cross sections which can be probed in CDMS-II, XENON-100 and other ongoing dark matter experiments. The implications of the models at the LHC and at the NLC are also briefly discussed.Comment: Journal: Physical Review D, Latex 32 pages, 4 eps figure

Projective measurement in nuclear magnetic resonance

It is demonstrated that nuclear magnetic resonance experiments using pseudopure spin states can give possible outcomes of projective quantum measurement and probabilities of such outcomes. The physical system is a cluster of six dipolar-coupled nuclear spins of benzene in a liquid-crystalline matrix. For this system with the maximum total spin S=3, the results of measuring $S_X$ are presented for the cases when the state of the system is one of the eigenstates of $S_Z$.Comment: 9 pages incluing 3 figure