Scattering matrix in external field problems

We discuss several aspects of second quantized scattering operators $\hat S$ for fermions in external time dependent fields. We derive our results on a general, abstract level having in mind as a main application potentials of the Yang--Mills type and in various dimensions. We present a new and powerful method for proving existence of $\hat S$ which is also applicable to other situations like external gravitational fields. We also give two complementary derivations of the change of phase of the scattering matrix under generalized gauge transformations which can be used whenever our method of proving existence of $\hat S$ applies. The first is based on a causality argument i.e.\ $\hat S$ (including phase) is determined from a time evolution, and the second exploits the geometry of certain infinite-dimensional group extensions associated with the second quantization of 1-particle operators. As a special case we obtain a Hamiltonian derivation of the the axial Fermion-Yang-Mills anomaly and the Schwinger terms related to it via the descent equations, which is on the same footing and traces them back to a common root.Comment: AmsTex file (uses amstex.tex and amsppt.sty) 22 ouput page

Integrated Educational Project of Theoretical, Experimental, and Computational Analyses

This research demonstrates how to design an integrated capstone project by including theoretical, experimental and computational analyses of a truss bridge. The project mainly focused on leading students to approach engineering problems with various methods and to understand the advantages and disadvantages of each method. The students applied three methods to acquire the values of stresses and deflections of members in the given truss bridge. First, they calculated the stresses and deformations theoretically. Second, they actually conducted an experiment of the truss bridge with electronic measuring equipment. Lastly, they built two simulation models with Autodesk Inventor and Dassault Systèmes SolidWorks. From the comparisons of above three methods, students were guided to the validation of assumptions of theories.Cockrell School of Engineerin

Assessing reservoir operations risk under climate change

Risk-based planning offers a robust way to identify strategies that permit adaptive water resources management under climate change. This paper presents a flexible methodology for conducting climate change risk assessments involving reservoir operations. Decision makers can apply this methodology to their systems by selecting future periods and risk metrics relevant to their planning questions and by collectively evaluating system impacts relative to an ensemble of climate projection scenarios (weighted or not). This paper shows multiple applications of this methodology in a case study involving California\u27s Central Valley Project and State Water Project systems. Multiple applications were conducted to show how choices made in conducting the risk assessment, choices known as analytical design decisions, can affect assessed risk. Specifically, risk was reanalyzed for every choice combination of two design decisions: (1) whether to assume climate change will influence flood-control constraints on water supply operations (and how), and (2) whether to weight climate change scenarios (and how). Results show that assessed risk would motivate different planning pathways depending on decision-maker attitudes toward risk (e.g., risk neutral versus risk averse). Results also show that assessed risk at a given risk attitude is sensitive to the analytical design choices listed above, with the choice of whether to adjust flood-control rules under climate change having considerably more influence than the choice on whether to weight climate scenarios

Closing the question on the continuation of turn-of-the-month effects: evidence from the S&P 500 Index futures contract

Prior research documents unusually high returns on the last trading day of the month and over the next three consecutive trading days. This phenomenon is known as the turn-of-the-month (TOTM) effect. According to Siegel (1998), why these anomalies occur is not well understood, and whether they will continue to be significant in the future is an open question. In this paper, we examine the S&P 500 futures contract for evidence that turn-of-the-month effects have continued. Transaction costs are low for index futures, and the absence of short-sale restrictions makes index futures an attractive venue for testing the continuation of market anomalies because of the low cost of arbitrage. We find that TOTM effects for S&P 500 futures disappear after 1990, and this result carries over to the S&P 500 spot market. We conjecture that a change in the preference of individual investors over time from making direct to making indirect stock purchases through mutual funds is related to the disappearance of the TOTM effect for more recent return data. In this paper, we argue that turn-of-the-month return patterns for both spot and futures prices are dynamic and related to market microstructure and therefore subject to change without notice. Financial economists should be careful when making out-of-sample inferences from observed in-sample return regularities.Financial markets ; Futures

Single plane minimal tomography of double slit qubits

The determination of the density matrix of an ensemble of identically prepared quantum systems by performing a series of measurements, known as quantum tomography, is minimal when the number of outcomes is minimal. The most accurate minimal quantum tomography of qubits, sometimes called a tetrahedron measurement, corresponds to projections over four states which can be represented on the Bloch sphere as the vertices of a regular tetrahedron. We investigate whether it is possible to implement the tetrahedron measurement of double slit qubits of light, using measurements performed on a single plane. Assuming Gaussian slits and free propagation, we demonstrate that a judicious choice of the detection plane and the double slit geometry allows the implementation of a tetrahedron measurement. Finally, we consider possible sets of values which could be used in actual experiments.Comment: 23 pages, 4 figure