13,728 research outputs found
Variational electrodynamics of Atoms
We generalize Wheeler-Feynman electrodynamics by the minimization of a finite
action functional defined for variational trajectories that are required to
merge continuously into given past and future boundary segments. We prove that
the boundary-value problem is well-posed for two classes of boundary data and
show that the well-posed solution in general has velocity discontinuities,
henceforth broken extrema. Along regular segments, broken extrema satisfy the
Euler-Lagrange neutral differential delay equations with state-dependent
deviating arguments. At points where velocities are discontinuous, broken
extrema satisfy the Weierstrass-Erdmann conditions that energies and momenta
are continuous. The electromagnetic fields of the variational trajectories are
derived quantities that can be extended only to a bounded region B of
space-time. For extrema with a finite number of velocity discontinuities,
extended fields are defined for all point in B with the exception of sets of
zero measure. The extended fields satisfy the integral laws of classical
electrodynamics for most surfaces and curves inside B. As an application, we
study globally bounded trajectories with vanishing far-fields for the
hydrogenoid atomic models of hydrogen, muonium and positronium. Our model uses
solutions of the neutral differential delay equations along regular segments
and a variational approximation for the collisional segments. Each hydrogenoid
model predicts a discrete set of finitely measured neighbourhoods of orbits
with vanishing far-fields at the correct atomic magnitude and in quantitative
and qualitative agreement with experiment and quantum mechanics, i.e., the
spacings between consecutive discrete angular momenta agree with Planck's
constant within thirty-percent, while orbital frequencies agree with a
corresponding spectroscopic line within a few percent.Comment: Full re-write using same equations and back to original title
(version 18 compiled with the wrong figure 5). A few commas introduced and
all paragraphs broken into smaller ones whenever possibl
Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging
Lunar Laser Ranging (LLR) measurements are crucial for advanced exploration
of the laws of fundamental gravitational physics and geophysics. Current LLR
technology allows us to measure distances to the Moon with a precision
approaching 1 millimeter. As NASA pursues the vision of taking humans back to
the Moon, new, more precise laser ranging applications will be demanded,
including continuous tracking from more sites on Earth, placing new CCR arrays
on the Moon, and possibly installing other devices such as transponders, etc.
Successful achievement of this goal strongly demands further significant
improvement of the theoretical model of the orbital and rotational dynamics of
the Earth-Moon system. This model should inevitably be based on the theory of
general relativity, fully incorporate the relevant geophysical processes, lunar
librations, tides, and should rely upon the most recent standards and
recommendations of the IAU for data analysis. This paper discusses methods and
problems in developing such a mathematical model. The model will take into
account all the classical and relativistic effects in the orbital and
rotational motion of the Moon and Earth at the sub-centimeter level. The new
model will allow us to navigate a spacecraft precisely to a location on the
Moon. It will also greatly improve our understanding of the structure of the
lunar interior and the nature of the physical interaction at the core-mantle
interface layer. The new theory and upcoming millimeter LLR will give us the
means to perform one of the most precise fundamental tests of general
relativity in the solar system.Comment: 26 pages, submitted to Proc. of ASTROCON-IV conference (Princeton
Univ., NJ, 2007
Spectral Oscillations, Periodic Orbits, and Scaling
The eigenvalue density of a quantum-mechanical system exhibits oscillations,
determined by the closed orbits of the corresponding classical system; this
relationship is simple and strong for waves in billiards or on manifolds, but
becomes slightly muddy for a Schrodinger equation with a potential, where the
orbits depend on the energy. We discuss several variants of a way to restore
the simplicity by rescaling the coupling constant or the size of the orbit or
both. In each case the relation between the oscillation frequency and the
period of the orbit is inspected critically; in many cases it is observed that
a characteristic length of the orbit is a better indicator. When these matters
are properly understood, the periodic-orbit theory for generic quantum systems
recovers the clarity and simplicity that it always had for the wave equation in
a cavity. Finally, we comment on the alleged "paradox" that semiclassical
periodic-orbit theory is more effective in calculating low energy levels than
high ones.Comment: 19 pages, RevTeX4 with PicTeX. Minor improvements in content, new
references, typos correcte
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