Relativity in Introductory Physics

A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski spacetime, displays covariant symmetries, and enables calculations of boosts and spatial rotations without matrices or tensors. The approach is part of a comprehensive geometric algebra with applications in many areas of physics, but only an intuitive subset is needed at the introductory level. The approach and some of its extensions are given here and illustrated with insights into the geometry of spacetime.Comment: 29 pages, 5 figures, several typos corrected, some discussion polishe

Explicit solutions for relativistic acceleration and rotation

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By assuming the Clock Hypothesis and using these solutions, we are able to describe the space-time transformations between two uniformly accelerated and rotating systems.Comment: 15 pages 1 figur

Average Fidelity in n-Qubit systems

This letter generalizes the expression for the average fidelity of single qubits, as found by Bowdrey et al., to the case of n qubits. We use a simple algebraic approach with basis elements for the density-matrix expansion expressed as Kronecker products of n Pauli spin matrices. An explicit integration over initial states is avoided by invoking the invariance of the state average under unitary transformations of the initial density matrix. The results have applications to measurements of quantum information, for example in ion-trap and NMR experiments.Comment: 4 pages, no figures. Revision includes additional references and a more detailed symmetry argumen

Sufficient condition for the coherent control of n -qubit systems

We study quantum systems with even numbers N of levels that are completely state controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1) 2 as discussed by Albertini and D\u27Allesandro [IEEE Trans. Autom. Control 48, 1399 (2003)]. These Lie algebras are smaller than the corresponding su(N) with dimension N2 -1. We show that this reduction constrains the field-free Hamiltonian to have symmetric energy levels. An example of such a system is an n -qubit system with state-independent interaction terms. Using Clifford\u27s geometric algebra to represent the quantum wave function of a finite system, we present an explicit example of a two-qubit system that can be controlled by the elements of the Lie algebra sp(4) [isomorphic to spin(5) and so(5)] with dimension 10 rather than su(4) with dimension 15, but only if its field-free energy levels are symmetrically distributed about an average. These results enable one to envision more efficient algorithms for the design of fields for quantum-state engineering in certain quantum-computing applications, and provide more insight into the fundamental structure of quantum control

Higher spin quaternion waves in the Klein-Gordon theory

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d'Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories

Angular momentum spatial distribution symmetry breaking in Rb by an external magnetic field

Excited state angular momentum alignment -- orientation conversion for atoms with hyperfine structure in presence of an external magnetic field is investigated. Transversal orientation in these conditions is reported for the first time. This phenomenon occurs under Paschen Back conditions at intermediate magnetic field strength. Weak radiation from a linearly polarized diode laser is used to excite Rb atoms in a cell. The laser beam is polarized at an angle of pi/4 with respect to the external magnetic field direction. Ground state hyperfine levels of the 5S_1/2 state are resolved using laser-induced fluorescence spectroscopy under conditions for which all excited 5P_3/2 state hyperfine components are excited simultaneously. Circularly polarized fluorescence is observed to be emitted in the direction perpendicular to both to the direction of the magnetic field B and direction of the light polarization E. The obtained circularity is shown to be in quantitative agreement with theoretical predictions.Comment: Accepted for publication in Phys. Rev.

Speed-up estimation for HW/SW-systems

HW/SW-codesign has been applied to a wide range of applications. Several partitioning methods have been suggested. Thus the designer selects modules for HW or SW-implementation for the best possible performance within a set of performance and design constraints. This paper describes an estimation method to approximate a priori the entire system performance. The estimation method has been integrated into the codesign tool COD and first results could be generated. The estimated speed-up has been determined for a ciphering algorithm and has been compared to the speed-up of the entire HW/SW-system. The estimation speed-up matches the final speedup. (orig.)SIGLEAvailable from TIB Hannover: RR 7264(96,5) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman