Leptonic dark matter annihilation in the evolving universe: constraints and implications

The cosmic electron and positron excesses have been explained as possible dark matter (DM) annihilation products. In this work we investigate the possible effects of such a DM annihilation scenario during the evolution history of the Universe. We first calculate the extragalactic $\gamma$-ray background (EGRB), which is produced through the final state radiation of DM annihilation to charged leptons and the inverse Compton scattering between electrons/positrons and the cosmic microwave background. The DM halo profile and the minimal halo mass, which are not yet well determined from the current N-body simulations, are constrained by the EGRB data from EGRET and Fermi telescopes. Then we discuss the impact of such leptonic DM models on cosmic evolution, such as the reionization and heating of intergalactic medium, neutral Hydrogen 21 cm signal and suppression of structure formation. We show that the impact on the Hydrogen 21 cm signal might show interesting signatures of DM annihilation, but the influence on star formation is not remarkable. Future observations of the 21 cm signals could be used to place new constraints on the properties of DM.Comment: 24 pages, 6 figures and 2 tables. Improved treatment of the energy deposition process, the suppression on structure formation is weaker. Accepted for publication by JCA

Matrix Product Representation of Locality Preserving Unitaries

The matrix product representation provides a useful formalism to study not only entangled states, but also entangled operators in one dimension. In this paper, we focus on unitary transformations and show that matrix product operators that are unitary provides a necessary and sufficient representation of 1D unitaries that preserve locality. That is, we show that matrix product operators that are unitary are guaranteed to preserve locality by mapping local operators to local operators while at the same time all locality preserving unitaries can be represented in a matrix product way. Moreover, we show that the matrix product representation gives a straight-forward way to extract the GNVW index defined in Ref.\cite{Gross2012} for classifying 1D locality preserving unitaries. The key to our discussion is a set of `fixed point' conditions which characterize the form of the matrix product unitary operators after blocking sites. Finally, we show that if the unitary condition is relaxed and only required for certain system sizes, the matrix product operator formalism allows more possibilities than locality preserving unitaries. In particular, we give an example of a simple matrix product operator which is unitary only for odd system sizes, does not preserve locality and carries a `fractional' index as compared to their locality preserving counterparts.Comment: 14 page