Dynamics and symmetries of a field partitioned by an accelerated frame

The canonical evolution and symmetry generators are exhibited for a Klein-Gordon (K-G) system which has been partitioned by an accelerated coordinate frame into a pair of subsystems. This partitioning of the K-G system is conveyed to the canonical generators by the eigenfunction property of the Minkowski Bessel (M-B) modes. In terms of the M-B degrees of freedom, which are unitarily related to those of the Minkowski plane waves, a near complete diagonalization of these generators can be realized.Comment: 14 pages, PlainTex. Related papers on accelerated frames available at http://www.math.ohio-state.edu/~gerlac

Consistent modeling of the geodetic precession in Earth rotation

A highly precise model for the motion of a rigid Earth is indispensable to reveal the effects of non-rigidity in the rotation of the Earth from observations. To meet the accuracy goal of modern theories of Earth rotation of 1 microarcsecond (muas) it is clear, that for such a model also relativistic effects have to be taken into account. The largest of these effects is the so called geodetic precession. In this paper we will describe this effect and the standard procedure to deal with it in modeling Earth rotation up to now. With our relativistic model of Earth rotation Klioner et al. (2001) we are able to give a consistent post-Newtonian treatment of the rotational motion of a rigid Earth in the framework of General Relativity. Using this model we show that the currently applied standard treatment of geodetic precession is not correct. The inconsistency of the standard treatment leads to errors in all modern theories of Earth rotation with a magnitude of up to 200 muas for a time span of one century.Comment: 6 pages, 4 figures, 1 table, published in the Proceedings of the VII Hotine-Marussi Symposium, Chapter 4

Coulomb field of an accelerated charge: physical and mathematical aspects

The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge invariant "2+2" decomposition is used to see how the Coulomb field of a charge, static in an accelerated frame, has properties that suggest features of electromagnetism which are different from those in an inertial frame. In particular, (1) an illustrative calculation shows that the Larmor radiation reaction equals the electrostatic attraction between the accelerated charge and the charge induced on the surface whose history is the event horizon, and (2) a spectral decomposition of the Coulomb potential in the accelerated frame suggests the possibility that the distortive effects of this charge on the Rindler vacuum are akin to those of a charge on a crystal lattice.Comment: 27 pages, PlainTex. Related papers available at http://www.math.ohio-state.edu/~gerlac

Paired accelerated arames: The perfect interferometer with everywhere smooth wave amplitudes

Rindler's acceleration-induced partitioning of spacetime leads to a nature-given interferometer. It accomodates quantum mechanical and wave mechanical processes in spacetime which in (Euclidean) optics correspond to wave processes in a ``Mach-Zehnder'' interferometer: amplitude splitting, reflection, and interference. These processes are described in terms of amplitudes which behave smoothly across the event horizons of all four Rindler sectors. In this context there arises quite naturally a complete set of orthonormal wave packet histories, one of whose key properties is their "explosivity index". In the limit of low index values the wave packets trace out fuzzy world lines. By contrast, in the asymptotic limit of high index values, there are no world lines, not even fuzzy ones. Instead, the wave packet histories are those of entities with non-trivial internal collapse and explosion dynamics. Their details are described by the wave processes in the above-mentioned Mach-Zehnder interferometer. Each one of them is a double slit interference process. These wave processes are applied to elucidate the amplification of waves in an accelerated inhomogeneous dielectric. Also discussed are the properties and relationships among the transition amplitudes of an accelerated finite-time detector.Comment: 38 pages, RevTex, 10 figures, 4 mathematical tutorials. Html version of the figures and of related papers available at http://www.math.ohio-state.edu/~gerlac

High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schroedinger equation

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schroedinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS - a hotly debated subject in current scientific literature.Comment: 5 Figures, Physics Letters A (accepted

Ion-tracer anemometer

Gas velocity measuring instrument measures transport time of ion-trace traveling fixed distance between ionization probe and detector probe. Electric field superimposes drift velocity onto flow velocity so travel times can be reduced to minimize ion diffusion effects