On the Exponentials of Some Structured Matrices

In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra isomorphism and basic Lie theory. When used in conjunction with structure preserving similarities, such as Givens rotations, these techniques extend to dimensions bigger than four.Comment: 19 page

Constructive control of quantum systems using factorization of unitary operators

We demonstrate how structured decompositions of unitary operators can be employed to derive control schemes for finite-level quantum systems that require only sequences of simple control pulses such as square wave pulses with finite rise and decay times or Gaussian wavepackets. To illustrate the technique it is applied to find control schemes to achieve population transfers for pure-state systems, complete inversions of the ensemble populations for mixed-state systems, create arbitrary superposition states and optimize the ensemble average of dynamic observables.Comment: 28 pages, IoP LaTeX, principal author has moved to Cambridge University ([email protected]

Comparison of the self-healing behaviour of 60Sn40Pb and 99.3Sn0.7Cu solder alloy reinforced Al6061 MMCs’.

The self-healing characteristics of Al6061 reinforced with CuO have been examined experimentally. The solder alloys 60Pb40Sn and 99.3Sn0.7Cu with low melting points are incorporated to strengthen the Al6061 MMCs'; the self-healing properties have been investigated. Developed self-healing samples have undergone testing for hardness, tensile, and impact characteristics in accordance with ASTM standard test protocols. The findings demonstrate how the solder filling affects the mechanical characteristics of self-healed Al6061 alloy and its MMCs'. The results showed that the composites formed a decent bond between the solder and matrix, confirming successful fabrication. Pb-Sn filled samples demonstrated higher self-healing efficiency for tensile and impact of 90.02% and 90.30% with 6 wt.% of CuO, respectively, and Sn-Cu filled samples witnessed higher self-healing efficiency for tensile and impact of 91.81% and 91.09% with 6 wt.% of CuO respectively. However, the self-healed composite did not split in two when subjected to Charpy impact and tensile strength tests, and the healing efficiency of Sn-Cu-filled composites is higher than that of the Pb-Sn-filled composites

Active Integrated Filters for RF-Photonic Channelizers

A theoretical study of RF-photonic channelizers using four architectures formed by active integrated filters with tunable gains is presented. The integrated filters are enabled by two- and four-port nano-photonic couplers (NPCs). Lossless and three individual manufacturing cases with high transmission, high reflection, and symmetric couplers are assumed in the work. NPCs behavior is dependent upon the phenomenon of frustrated total internal reflection. Experimentally, photonic channelizers are fabricated in one single semiconductor chip on multi-quantum well epitaxial InP wafers using conventional microelectronics processing techniques. A state space modeling approach is used to derive the transfer functions and analyze the stability of these filters. The ability of adapting using the gains is demonstrated. Our simulation results indicate that the characteristic bandpass and notch filter responses of each structure are the basis of channelizer architectures, and optical gain may be used to adjust filter parameters to obtain a desired frequency magnitude response, especially in the range of 1–5 GHz for the chip with a coupler separation of ∼9 mm. Preliminarily, the measurement of spectral response shows enhancement of quality factor by using higher optical gains. The present compact active filters on an InP-based integrated photonic circuit hold the potential for a variety of channelizer applications. Compared to a pure RF channelizer, photonic channelizers may perform both channelization and down-conversion in an optical domain