The Solution of the Relativistic Schrodinger Equation for the δ′\delta'-Function Potential in 1-dimension Using Cutoff Regularization

We study the relativistic version of Schr\"odinger equation for a point particle in 1-d with potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultra-violet divergent, and the resultant expression cannot be renormalized in the usual sense. Therefore a general procedure has been developed to derive different physical properties of the system. The procedure is used first on the non-relativistic case for the purpose of clarification and comparisons. The results from the relativistic case show that this system behaves exactly like the delta function potential, which means it also shares the same features with quantum field theories, like being asymptotically free, and in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point.Comment: 32 pages, 5 figure

Functionalized crystalline polyactones as toughners for thermosetting resins

A crystalline polylactone is produced having reactive acrylate end groups. When incorporated into a thermosetting resin which includes reactive C.dbd.CH.sub.2 sites, the present functionalized polylactone acts as a toughener, greatly increasing the impact resistance of the final cured product. Also disclosed are carboxyl-bearing polylactones as tougheners for epoxy resin systems

Functionalized crystalline polylactones as tougheners for thermosetting resins

A crystalline polylactone is produced having reactive acrylate end groups. When incorporated into a thermosetting resin which includes reactive C.dbd.CH.sub.2 sites, the present functionalized polylactone acts as a toughener, greatly increasing the impact resistance of the final cured product. Also disclosed are carboxyl-bearing polylactones as tougheners for epoxy resin systems

Relationship of sea level muon charge ratio to primary composition including nuclear target effects

The discrepancy between the muon charge ratio observed at low energies and that calculated using pp data is removed by including nuclear target effects. Calculations at high energies show that the primary iron spectrum is expected to change slope from 2 to 2.2 to 2.4 to 2.5 for energies approx. 4 x 10 to the 3 GeV/nucleon if scaling features continue to the highest energies

Vacuum Stability of the wrong sign (−ϕ6)(-\phi^{6}) Scalar Field Theory

We apply the effective potential method to study the vacuum stability of the bounded from above $(-\phi^{6})$ (unstable) quantum field potential. The stability ($\partial E/\partial b=0)$ and the mass renormalization ($\partial^{2} E/\partial b^{2}=M^{2})$ conditions force the effective potential of this theory to be bounded from below (stable). Since bounded from below potentials are always associated with localized wave functions, the algorithm we use replaces the boundary condition applied to the wave functions in the complex contour method by two stability conditions on the effective potential obtained. To test the validity of our calculations, we show that our variational predictions can reproduce exactly the results in the literature for the $\mathcal{PT}$-symmetric $\phi^{4}$ theory. We then extend the applications of the algorithm to the unstudied stability problem of the bounded from above $(-\phi^{6})$ scalar field theory where classical analysis prohibits the existence of a stable spectrum. Concerning this, we calculated the effective potential up to first order in the couplings in $d$ space-time dimensions. We find that a Hermitian effective theory is instable while a non-Hermitian but $\mathcal{PT}$-symmetric effective theory characterized by a pure imaginary vacuum condensate is stable (bounded from below) which is against the classical predictions of the instability of the theory. We assert that the work presented here represents the first calculations that advocates the stability of the $(-\phi^{6})$ scalar potential.Comment: 21pages, 12 figures. In this version, we updated the text and added some figure

Characterisation and optimisation of the semiconductor optical amplifier for ultra-high speed performance

This research is in the area of high speed telecommunication systems where all- optical technologies are being introduced to meet the ever increasing demand for bandwidth by replacing the costly electro-optical conversion modules. In such systems, all-optical routers are the key technologies capable of supporting networks with high capacity/bandwidth as well as offering lower power consumption. One of the fundamental building blocks in all-optical routers/networks is the semiconductor optical amplifier (SOA), which is used in for clock extraction, wavelength conversion, all-optical gates and optical processing. The SOAs are perfect for optical amplification and optical switching at a very high speed. This is due to their small size, a low switching energy, non-linear characteristics and the seamless integration with other optical devices. Therefore, characterisation of the SOA operational functionalities and optimisation of its performance for amplification and switching are essential and challenging. Existing models on SOA gain dynamics do not address the impact of optical propagating wavelength, the combined input parameters and their adaptation for optimised amplification and switching operations. The SOA operation is limited at high data rates > 2.5 Gb/s to a greater extent by the gain recovery time. A number of schemes have been proposed to overcome this limitation; however no work has been reported on the SOA for improving the gain uniformity. This research aims to characterise the boundaries conditions and optimise the SOA performance for amplification and switching. The research also proposes alternative techniques to maximise the SOA gain uniformity at ultra-high speed data rates theoretically and practically. An SOA model is been developed and used throughout the research for theoretical simulations. Results show that the optimum conditions required to achieve the maximum output gain for best amplification performance depends on the SOA peak gain wavelength. It is also shown that the optimum phase shift of 180º for switching can be induced at lower input power level when the SOA biasing current is at its maximum limit. A gain standard deviation equation is introduced to measure the SOA gain uniformity. New wavelength diversity technique is proposed to achieve an average improvement of 7.82 dB in the SOA gain standard deviation at rates from 10 to 160 Gb/s. Other novel techniques that improved the gain uniformity employing triangular and sawtooth bias currents, as replacements for the uniform biasing, have been proposed. However, these current patterns were not able to improve the SOA gain uniformity at data rates beyond 40 Gb/s. For that reason, an optimised biasing for SOA (OBS) pattern is introduced to maximise the gain uniformity at any input data rates. This OBS pattern was practically generated and compared to the uniform biased SOA at different data rates and with different input bit sequences. All executed experiments showed better output uniformities employing the proposed OBS pattern with an average improvement of 19%