Background field method in the large NfN_f expansion of scalar QED

Using the background field method, we, in the large $N_f$ approximation, calculate the beta function of scalar quantum electrodynamics at the first nontrivial order in $1/N_f$ by two different ways. In the first way, we get the result by summing all the graphs contributing directly. In the second way, we begin with the Borel transform of the related two point Green's function. The main results are that the beta function is fully determined by a simple function and can be expressed as an analytic expression with a finite radius of convergence, and the scheme-dependent renormalized Borel transform of the two point Green's function suffers from renormalons.Comment: 13 pages, 4 figures, 1 table, to appear in the European Physical Journal

Symbolic bisimulation for quantum processes

With the previous notions of bisimulation presented in literature, to check if two quantum processes are bisimilar, we have to instantiate the free quantum variables of them with arbitrary quantum states, and verify the bisimilarity of resultant configurations. This makes checking bisimilarity infeasible from an algorithmic point of view because quantum states constitute a continuum. In this paper, we introduce a symbolic operational semantics for quantum processes directly at the quantum operation level, which allows us to describe the bisimulation between quantum processes without resorting to quantum states. We show that the symbolic bisimulation defined here is equivalent to the open bisimulation for quantum processes in the previous work, when strong bisimulations are considered. An algorithm for checking symbolic ground bisimilarity is presented. We also give a modal logical characterisation for quantum bisimilarity based on an extension of Hennessy-Milner logic to quantum processes.Comment: 30 pages, 7 figures, comments are welcom

Ionospheric gravity wave measurements with the USU dynasonde

A method for the measurement of ionospheric Gravity Wave (GW) using the USU Dynasonde is outlined. This method consists of a series of individual procedures, which includes functions for data acquisition, adaptive scaling, polarization discrimination, interpolation and extrapolation, digital filtering, windowing, spectrum analysis, GW detection, and graphics display. Concepts of system theory are applied to treat the ionosphere as a system. An adaptive ionogram scaling method was developed for automatically extracting ionogram echo traces from noisy raw sounding data. The method uses the well known Least Mean Square (LMS) algorithm to form a stochastic optimal estimate of the echo trace which is then used to control a moving window. The window tracks the echo trace, simultaneously eliminating the noise and interference. Experimental results show that the proposed method functions as designed. Case studies which extract GW from ionosonde measurements were carried out using the techniques described. Geophysically significant events were detected and the resultant processed results are illustrated graphically. This method was also developed for real time implementation in mind