Search for isotropic γ radiation in the cosmological window between 65 and 200 TeV

Electromagnetic energy injected into the universe above a few hundred TeV is expected to pile up as γ radiation in a relatively narrow energy interval below 100 TeV due to its interaction with the 2.7^°K background radiation. We present an upper limit (90% C.L.) on the ratio of primary γ to charged cosmic rays in the energy interval 65–160 TeV (80–200 TeV) of 10.3 • 10^−3 (7.8 • 10^−3). Data from the HEGRA cosmic-ray detector complex consisting of a wide angle Čerenkov array (AIROBICC) measuring the lateral distribution of air Čerenkov light and a scintillator array, were used with a novel method to discriminate γ-ray and hadron induced air showers. If the presently unmeasured universal far infrared background radiation is not too intense, the result rules out a topological-defect origin of ultrahigh energy cosmic rays for masses of the X particle released by the defects equal to or larger than about 10^16 GeV.

Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced density matrix of a block of Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, where the coefficient a is equal to (m  −  k)/2 in the ground state phase with k vanishing magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi entropy R_q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1) Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3). This is also true in the su(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m  +  1)-simplex in R^m whose vertices are the weights of the fundamental representation of su(m+1).