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

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

Protection of entanglement from sudden death using continuous dynamical decoupling

We show that continuous dynamical decoupling can protect a two-qubit entangled state from sudden death at finite temperature due to uncorrelated dephasing, bit flipping, and dissipation. We consider a situation where an entangled state shared between two non-interacting qubits is initially prepared and left evolve under the environmental perturbations and the protection of external fields. To illustrate the protection of the entanglement, we solve numerically a master equation in the Born approximation, considering independent boson fields at the same temperature coupled to the different error agents of each qubit

Exact Solutions of a (2+1)-Dimensional Nonlinear Klein-Gordon Equation

The purpose of this paper is to present a class of particular solutions of a C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry reduction. Using the subgroups of similitude group reduced ordinary differential equations of second order and their solutions by a singularity analysis are classified. In particular, it has been shown that whenever they have the Painlev\'e property, they can be transformed to standard forms by Moebius transformations of dependent variable and arbitrary smooth transformations of independent variable whose solutions, depending on the values of parameters, are expressible in terms of either elementary functions or Jacobi elliptic functions.Comment: 16 pages, no figures, revised versio

Creation and Implementation of a Tracking Module for a Small-Geometry, Vertex Time Projection Chamber

A charged-particle tracking module was written and tested using pixel data generated from CERN\u27s Monte Carlo detector-modeling program GEANT. This tracking module was customized for testing the design of a micro-strip gas time project chamber, designed by Drs. Margetis and Wieman of the Relativistic Nuclear Collisions Group at Lawrence Berkeley Laboratory. This low-mass, high-resolution, small-geometry vertex time projection chamber was designed for possible use with a larger instrument in an experiment using the relativistic heavy ion collider, RHIC, under construction at Brookhaven National Laboratory in New York. Implementing this tracking module involved generating tables and source code in a manner which is accessible to any user who is familiar with general purpose programming, using event-based data-processing. This charged-particle tracking module project was initiated in Summer-1994 as part of a 10-week, undergraduate research project at Lawrence Berkeley Laboratory, sponsored by LBL\u27s Office of Science and Engineering Education. Further research on this project is underway at UALR

Using the CERN Program-Library Graphics and Interactive Data Display

Small scale Monte Carlo programming is growing rapidly due to the ease with which complex problems may be formulated by any programmer. These programmers may choose to exploit graphics and interactive displays available in the program library developed and maintained by CERN (the Center for European Nuclear Research). This paper outlines the use of graphics and interactive data display features of the CERN program library, developed for visualizing simulated data events in particle detectors. One example uses GEANT, CERN\u27s Monte Carlo modeling program, to simulate 300 MeV/c protons incident on a silicon slab. Display packages for GEANT are available both on-line and off-line for 3-D tracking of particles through any detector system. On-line displays provide the user a qualitative sense of the inner workings of various detector components. On-line displays may be updated for each particle track in the detector system, so any design change in detector geometry or component material may have its consequences visualized immediately. This visualization is useful for repeatedly making gross changes in the detector system. CERN has been very generous in making its program library available to any institution tied to groups working on experiments at CERN, however peripherally