Sterile neutrino Dark Matter production from scalar decay in a thermal bath

We calculate the production rate of singlet fermions from the decay of neutral or charged scalar fields in a hot plasma. We find that there are considerable thermal corrections when the temperature of the plasma exceeds the mass of the decaying scalar. We give analytic expressions for the temperature-corrected production rates in the regime where the decay products are relativistic. We also study the regime of non-relativistic decay products numerically. Our results can be used to determine the abundance and momentum distribution of Dark Matter particles produced in scalar decays. The inclusion of thermal corrections helps to improve predictions for the free streaming of the Dark Matter particles, which is crucial to test the compatibility of a given model with cosmic structure formation. With some modifications, our results may be generalised to the production of other Dark Matter candidates in scalar decays.Comment: This version matches the one published in JHEP. 44 pages, 10 figure

Fast and Accurate Random Walk with Restart on Dynamic Graphs with Guarantees

Given a time-evolving graph, how can we track similarity between nodes in a fast and accurate way, with theoretical guarantees on the convergence and the error? Random Walk with Restart (RWR) is a popular measure to estimate the similarity between nodes and has been exploited in numerous applications. Many real-world graphs are dynamic with frequent insertion/deletion of edges; thus, tracking RWR scores on dynamic graphs in an efficient way has aroused much interest among data mining researchers. Recently, dynamic RWR models based on the propagation of scores across a given graph have been proposed, and have succeeded in outperforming previous other approaches to compute RWR dynamically. However, those models fail to guarantee exactness and convergence time for updating RWR in a generalized form. In this paper, we propose OSP, a fast and accurate algorithm for computing dynamic RWR with insertion/deletion of nodes/edges in a directed/undirected graph. When the graph is updated, OSP first calculates offset scores around the modified edges, propagates the offset scores across the updated graph, and then merges them with the current RWR scores to get updated RWR scores. We prove the exactness of OSP and introduce OSP-T, a version of OSP which regulates a trade-off between accuracy and computation time by using error tolerance {\epsilon}. Given restart probability c, OSP-T guarantees to return RWR scores with O ({\epsilon} /c ) error in O (log ({\epsilon}/2)/log(1-c)) iterations. Through extensive experiments, we show that OSP tracks RWR exactly up to 4605x faster than existing static RWR method on dynamic graphs, and OSP-T requires up to 15x less time with 730x lower L1 norm error and 3.3x lower rank error than other state-of-the-art dynamic RWR methods.Comment: 10 pages, 8 figure

Effective Action for Cosmological Scalar Fields at Finite Temperature

Scalar fields appear in many theories beyond the Standard Model of particle physics. In the early universe, they are exposed to extreme conditions, including high temperature and rapid cosmic expansion. Understanding their behavior in this environment is crucial to understand the implications for cosmology. We calculate the finite temperature effective action for the field expectation value in two particularly important cases, for damped oscillations near the ground state and for scalar fields with a flat potential. We find that the behavior in both cases can in good approximation be described by a complex valued effective potential that yields Markovian equations of motion. Near the potential minimum, we recover the solution to the well-known Langevin equation. For large field values we find a very different behavior, and our result for the damping coefficient differs from the expressions frequently used in the literature. We illustrate our results in a simple scalar model, for which we give analytic approximations for the effective potential and damping coefficient. We also provide various expressions for loop integrals at finite temperature that are useful for future calculations in other models.Comment: 34 pages plus appendix, 17 figures: minor corrections, modifications of discussions, added references, version published in JHE

Detecting Photon-Photon Interactions in a Superconducting Circuit

A local interaction between photons can be engineered by coupling a nonlinear system to a transmission line. The required high impedance transmission line can be conveniently formed from a chain of Josephson junctions. The nonlinearity is generated by side-coupling this chain to a Cooper pair box. We propose to probe the resulting photon-photon interactions via their effect on the current-voltage characteristic of a voltage-biased Josephson junction connected to the transmission line. Considering the Cooper pair box to be in the weakly anharmonic regime, we find that the dc current through the probe junction yields features around the voltages $2eV=n\hbar\omega_s$, where $\omega_s$ is the plasma frequency of the superconducting circuit. The features at $n\ge 2$ are a direct signature of the photon-photon interaction in the system.Comment: 10 pages, 7 figure