Generalized Euler Angle Paramterization for SU(N)

In a previous paper (math-ph/0202002) an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov's volume formula for SU(N) will also be derived. As an example of this parameterization's usefulness, the density matrix parameterization and invariant volume element for a qubit/qutrit, three qubit and two three-state systems, also known as two qutrit systems, will also be given.Comment: 36 pages, no figures; added qubit/qutrit work, corrected minor definition problems and clarified Haar measure derivation. To be published in J. Phys. A: Math. and Ge

Topological structures of adiabatic phase for multi-level quantum systems

The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) have a monopole structure, the curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures.Comment: 15 pages, no figures. Accepted by J.Phys.

Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems

The use of d-state systems, or qudits, in quantum information processing is discussed. Three-state and higher dimensional quantum systems are known to have very different properties from two-state systems, i.e., qubits. In particular there exist qudit states which are not equivalent under local unitary transformations unless a selection rule is violated. This observation is shown to be an important factor in the theory of decoherence-free, or noiseless, subsystems. Experimentally observable consequences and methods for distinguishing these states are also provided, including the explicit construction of new decoherence-free or noiseless subsystems from qutrits. Implications for simulating quantum systems with quantum systems are also discussed.Comment: 13 pages, 1 figures, Version 2: Typos corrected, references fixed and new ones added, also includes referees suggested changes and a new exampl

Soft-Pulse Dynamical Decoupling with Markovian Decoherence

We consider the effect of broadband decoherence on the performance of refocusing sequences, having in mind applications of dynamical decoupling in concatenation with quantum error correcting codes as the first stage of coherence protection. Specifically, we construct cumulant expansions of effective decoherence operators for a qubit driven by a pulse of a generic symmetric shape, and for several sequences of $\pi$- and $\pi/2$-pulses. While, in general, the performance of soft pulses in decoupling sequences in the presence of Markovian decoherence is worse than that of the ideal $\delta$-pulses, it can be substantially improved by shaping.Comment: New version contains minor content clarification

Combined Gamma Ray/neutron Spectroscopy for Mapping Lunar Resources

Some elements in the Moon can be resources, such as hydrogen and oxygen. Other elements, like Ti or the minerals in which they occur, such as ilmenite, could be used in processing lunar materials. Certain elements can also be used as tracers for other elements or lunar processes, such as hydrogen for mature regoliths with other solar-wind-implanted elements like helium, carbon, and nitrogen. A complete knowledge of the elemental composition of a lunar region is desirable both in identifying lunar resources and in lunar geochemical studies, which also helps in identifying and using lunar resources. The use of gamma ray and neutron spectroscopy together to determine abundances of many elements in the top few tens of centimeters of the lunar surface is discussed. To date, very few discussions of elemental mapping of planetary surfaces considered measurements of both gamma rays and the full range of neutron energies. The theories for gamma ray and neutron spectroscopy of the Moon and calculations of leakage fluxes are presented here with emphasis on why combined gamma ray/neutron spectroscopy is much more powerful than measuring either radiation alone

Coherent States For SU(3)

We define coherent states for SU(3) using six bosonic creation and annihilation operators. These coherent states are explicitly characterized by six complex numbers with constraints. For the completely symmetric representations (n,0) and (0,m), only three of the bosonic operators are required. For mixed representations (n,m), all six operators are required. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties. We introduce an explicit parameterization of the group SU(3) and the corresponding integration measure. Finally, we discuss the path integral formalism for a problem in which the Hamiltonian is a function of SU(3) operators at each site.Comment: 18 pages, LaTeX, no figure

Gamma Ray and Neutron Spectrometer for the Lunar Resource Mapper

One of the early Space Exploration Initiatives will be a lunar orbiter to map the elemental composition of the Moon. This mission will support further lunar exploration and habitation and will provide a valuable dataset for understanding lunar geological processes. The proposed payload will consist of the gamma ray and neutron spectrometers which are discussed, an x ray fluorescence imager, and possibly one or two other instruments

A Parametrization of Bipartite Systems Based on SU(4) Euler Angles

In this paper we give an explicit parametrization for all two qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing. To accomplish this we present a generalized Euler angle parametrization for SU(4) and all possible two qubit density matrices. The important group-theoretical properties of such a description are then manifest. We thus obtain the correct Haar (Hurwitz) measure and volume element for SU(4) which follows from this parametrization. In addition, we study the role of this parametrization in the Peres-Horodecki criteria for separability and its corresponding usefulness in calculating entangled two qubit states as represented through the parametrization.Comment: 23 pages, no figures; changed title and abstract and rewrote certain areas in line with referee comments. To be published in J. Phys. A: Math. and Ge

Examining the Correlation between Acute Behavioral Manifestations of Concussion and the Underlying Pathophysiology of Chronic Traumatic Encephalopathy: A Pilot Study

Concussion in athletes can contribute to early neuropsychological changes that may be indicative of future neurodegenerative disease. One of the hallmark findings of chronic traumatic encephalopathy is anxiety and impulsive behavior that often develops early in the course of the disease. The behavioral dysfunction can be grouped into a broader category referred to as cognitive disruption. The current gold standard for diagnosing chronic neurodegeneration is post-mortem evaluation of tauopathy to identify neurofibrillary tau tangles in neurons. Few studies, however, have looked at clinical correlations between acute injury and chronic neurodegeneration in terms of behavior. This lack of focus towards translational study has limited advancements towards treatment. In this pilot investigation, the acute cognitive and emotional (anger, impulsivity, and anxiety) affects of concussion in a cohort of collegiate athletes (n = 30) are examined and compared to findings in the post-mortem pathologic features of chronic traumatic encephalopathy. Specifically, the role of the seroternergic system with alpha synuclein and tauopathy staining and the potential for early clinically relevant behavioral and pharmaceutical interventions was investigated. The purpose was to determine if athletes began demonstrating cognitive disruption present in post-mortem evaluation during the acute phase of injury. The acute data was collected via questionnaires within ten days of the athletes’ concussion diagnosis. Results demonstrated that 11 of 30 athletes (36%) scored in a diagnosable range of anxiety post-concussion, and athletes scored above the norm in state-anger (M = 22.9, SD = 9.99), indicating severe emotional disturbance. A limitation is that due to the long time frame from acute injury to the development of neurodegeneration individual athletes cannot be tracked in longevity thus limiting the findings to the realm of correlation. The findings from this pilot study warrant further investigation into the neuropsychological aspects for how to manage concussion and prevent degenerative disease