10,339 research outputs found
Relativistic effects on information measures for hydrogen-like atoms
Position and momentum information measures are evaluated for the ground state
of the \emph{relativistic} hydrogen-like atoms. Consequences of the fact that
the radial momentum operator is not self-adjoint are explicitly studied,
exhibiting fundamental shortcomings of the conventional uncertainty measures in
terms of the radial position and momentum variances. The Shannon and R\'enyi
entropies, the Fisher information measure, as well as several related
information measures, are considered as viable alternatives. Detailed results
on the onset of relativistic effects for low nuclear charges, and on the
extreme relativistic limit, are presented. The relativistic position density
decays exponentially at large , but is singular at the origin.
Correspondingly, the momentum density decays as an inverse power of . Both
features yield divergent R\'enyi entropies away from a finite vicinity of the
Shannon entropy. While the position space information measures can be evaluated
analytically for both the nonrelativistic and the relativistic hydrogen atom,
this is not the case for the relativistic momentum space. Some of the results
allow interesting insight into the significance of recently evaluated
Dirac-Fock vs. Hartree-Fock complexity measures for many-electron neutral
atoms.Comment: Accepted for publication in the Journal of Computational and Applied
Mathematic
Fundamental Physical Constants: Looking from Different Angles
We consider fundamental physical constants which are among a few of the most
important pieces of information we have learned about Nature after its
intensive centuries-long studies. We discuss their multifunctional role in
modern physics including problems related to the art of measurement, natural
and practical units, origin of the constants, their possible calculability and
variability etc
Interference of Clocks: A Quantum Twin Paradox
The phase of matter waves depends on proper time and is therefore susceptible
to special-relativistic (kinematic) and gravitational time dilation (redshift).
Hence, it is conceivable that atom interferometers measure general-relativistic
time-dilation effects. In contrast to this intuition, we show that light-pulse
interferometers without internal transitions are not sensitive to gravitational
time dilation, whereas they can constitute a quantum version of the
special-relativistic twin paradox. We propose an interferometer geometry
isolating the effect that can be used for quantum-clock interferometry.Comment: 9 Pages, 2 Figure
History of Spin and Statistics
These lectures were given in the framework of the ``Dixi\`eme s\'eminaire
rhodanien de physique'' entitled ``Le spin en physique'', given at Villa
Gualino, Turin, March 2002. We have shown how the difficulties of
interpretation of atomic spectra led to the Pauli exclusion principle and to
the notion of spin, and then described the following steps: the Pauli spin with
22 matrices after the birth of "new" quantum mechanics, the Dirac
equation and the magnetic moment of the electron, the spins and magnetic
moments of other particles, proton, neutron and hyperons. Finally, we show the
crucial role of statistics in the stability of the world.Comment: latex file, 7 figures, 3 table
Testing the Equivalence Principle by Lamb shift Energies
The Einstein Equivalence Principle has as one of its implications that the
non-gravitational laws of physics are those of special relativity in any local
freely-falling frame. We consider possible tests of this hypothesis for systems
whose energies are due to radiative corrections, i.e. which arise purely as a
consequence of quantum field theoretic loop effects. Specifically, we evaluate
the Lamb shift transition (as given by the energy splitting between the
and atomic states) within the context of violations of
local position invariance and local Lorentz invariance, as described by the formalism. We compute the associated red shift and time dilation
parameters, and discuss how (high-precision) measurements of these quantities
could provide new information on the validity of the equivalence principle.Comment: 40 pages, latex, epsf, 1 figure, final version which appears in
Physical Review
Spin effects probed by Rayleigh X-ray scattering off hydrogenic ions
We study the polarization characteristics of x-ray photons scattered by
hydrogenic atoms, based on the Dirac equation and second-order perturbation
theory. The relativistic states used in calculations are obtained using the
finite basis set method and expressed in terms of B-splines and B-polynomials.
We derive general analytical expressions for the polarization-dependent total
cross sections, which are applicable to any atom and ion, and evaluate them
separately for linear and circular polarization of photons. In particular,
detailed calculations are performed for the integrated Stokes parameters of the
scattered light for hydrogen as well as hydrogenlike neon and argon. Analyzing
such integrated Stokes parameters, special attention is given to the
electron-photon spin-spin interaction, which mostly stems from the
magnetic-dipole contribution of the electron-photon interaction. Subsequently,
we find an energy window for the selected targets in which such spin-spin
interactions can be probed.Comment: 8 pages,ures 4 fig, To be appeared in Radiat. Phys. Chem. arXiv admin
note: text overlap with arXiv:1208.308
The Structure of Light Nuclei and Its Effect on Precise Atomic Measurements
This review consists of three parts: (a) what every atomic physicist needs to
know about the physics of light nuclei; (b) what nuclear physicists can do for
atomic physics; (c) what atomic physicists can do for nuclear physics. A brief
qualitative overview of the nuclear force and calculational techniques for
light nuclei will be presented, with an emphasis on debunking myths and on
recent progress in the field. Nuclear quantities that affect precise atomic
measurements will be discussed, together with their current theoretical and
experimental status. The final topic will be a discussion of those atomic
measurements that would be useful to nuclear physics, and nuclear calculations
that would improve our understanding of existing atomic data.Comment: 24 pages, latex, 6 figures, svmult.cls required -- index at back To
appear in "Precision Physics of Simple Atomic Systems," ed. by S.
Karshenboim, (Springer-Verlag, Berlin, in preparation
Local Relativistic Exact Decoupling
We present a systematic hierarchy of approximations for {\it local}
exact-decoupling of four-component quantum chemical Hamiltonians based on the
Dirac equation. Our ansatz reaches beyond the trivial local approximation that
is based on a unitary transformation of only the atomic block-diagonal part of
the Hamiltonian. Systematically, off-diagonal Hamiltonian matrix blocks can be
subjected to a unitary transformation to yield relativistically corrected
matrix elements. The full hierarchy is investigated with respect to the
accuracy reached for the electronic energy and molecular properties on a
balanced test molecule set that comprises molecules with heavy elements in
different bonding situations. Our atomic (local) assembly of the unitary
transformation needed for exact decoupling provides an excellent local
approximation for any relativistic exact-decoupling approach. Its order-
scaling can be further reduced to linear scaling by employing the
neighboring-atomic-blocks approximation. Therefore, it is an efficient
relativistic method perfectly well suited for relativistic calculations on
large molecules. If a large molecule contains many light atoms (typically
hydrogen atoms), the computational costs can be further reduced by employing a
well-defined non-relativistic approximation for these light atoms without
significant loss of accuracy
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