3,967 research outputs found
Dynamics of Einstein - de Haas Effect: Application to Magnetic Cantilever
Local time-dependent theory of Einstein - de Haas effect is developed. We
begin with microscopicinteractions and derive dynamical equations that couple
elastic deformations with internal twists due to spins. The theory is applied
to the description of the motion of a magnetic cantilever caused by the
oscillation of the domain wall. Theoretical results are compared with a recent
experiment on Einstein - de Haas effect in a microcantilever.Comment: 7 PR pages, 5 figures, submitted to PR
The Maxwell Lagrangian in purely affine gravity
The purely affine Lagrangian for linear electrodynamics, that has the form of
the Maxwell Lagrangian in which the metric tensor is replaced by the
symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of
homothetic curvature, is dynamically equivalent to the Einstein-Maxwell
equations in the metric-affine and metric formulation. We show that this
equivalence is related to the invariance of the Maxwell Lagrangian under
conformal transformations of the metric tensor. We also apply to a purely
affine Lagrangian the Legendre transformation with respect to the tensor of
homothetic curvature to show that the corresponding Legendre term and the new
Hamiltonian density are related to the Maxwell-Palatini Lagrangian for the
electromagnetic field. Therefore the purely affine picture, in addition to
generating the gravitational Lagrangian that is linear in the curvature,
justifies why the electromagnetic Lagrangian is quadratic in the
electromagnetic field.Comment: 9 pages; published versio
Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation
It is shown that the energy of a mode of a classical chaotic field, following
the continuous exponential distribution as a classical random variable, can be
uniquely decomposed into a sum of its fractional part and of its integer part.
The integer part is a discrete random variable (we call it Planck variable)
whose distribution is just the Bose distribution yielding the Planck law of
black-body radiation. The fractional part is the dark part (we call is dark
variable) with a continuous distribution, which is, of course, not observed in
the experiments. It is proved that the Bose distribution is infinitely
divisible, and the irreducible decomposition of it is given. The Planck
variable can be decomposed into an infinite sum of independent binary random
variables representing the binary photons (more accurately photo-molecules or
photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons
follow the Fermi statistics. Consequently, the black-body radiation can be
viewed as a mixture of statistically and thermodynamically independent fermion
gases consisting of binary photons. The binary photons give a natural tool for
the dyadic expansion of arbitrary (but not coherent) ordinary photon
excitations. It is shown that the binary photons have wave-particle
fluctuations of fermions. These fluctuations combine to give the wave-particle
fluctuations of the original bosonic photons expressed by the Einstein
fluctuation formula.Comment: 29 page
New two-sided bound on the isotropic Lorentz-violating parameter of modified Maxwell theory
There is a unique Lorentz-violating modification of the Maxwell theory of
photons, which maintains gauge invariance, CPT, and renormalizability.
Restricting the modified-Maxwell theory to the isotropic sector and adding a
standard spin-one-half Dirac particle p^\pm with minimal coupling to the
nonstandard photon \widetilde{\gamma}, the resulting
modified-quantum-electrodynamics model involves a single dimensionless
"deformation parameter," \widetilde{\kappa}_{tr}. The exact tree-level decay
rates for two processes have been calculated: vacuum Cherenkov radiation p^\pm
\to p^\pm \widetilde{\gamma} for the case of positive \widetilde{\kappa}_{tr}
and photon decay \widetilde{\gamma} \to p^+ p^- for the case of negative
\widetilde{\kappa}_{tr}. From the inferred absence of these decays for a
particular high-quality ultrahigh-energy-cosmic-ray event detected at the
Pierre Auger Observatory and an excess of TeV gamma-ray events observed by the
High Energy Stereoscopic System telescopes, a two-sided bound on
\widetilde{\kappa}_{tr} is obtained, which improves by eight orders of
magnitude upon the best direct laboratory bound. The implications of this
result are briefly discussed.Comment: 18 pages, v5: published version in preprint styl
Einstein's fluctuation formula. A historical overview
A historical overview is given on the basic results which appeared by the
year 1926 concerning Einstein's fluctuation formula of black-body radiation, in
the context of light-quanta and wave-particle duality. On the basis of the
original publications (from Planck's derivation of the black-body spectrum and
Einstein's introduction of the photons up to the results of Born, Heisenberg
and Jordan on the quantization of a continuum) a comparative study is presented
on the first line of thoughts that led to the concept of quanta. The nature of
the particle-like fluctuations and the wave-like fluctuations are analysed by
using several approaches. With the help of the classical probability theory, it
is shown that the infinite divisibility of the Bose distribution leads to the
new concept of classical poissonian photo-multiplets or to the binary
photo-multiplets of fermionic character. As an application, Einstein's
fluctuation formula is derived as a sum of fermion type fluctuations of the
binary photo-multiplets.Comment: 34 page
Nonlocal Astroparticles in Einstein's Universe
Gravitational probes should maintain spatial flatness for
Einsten-Infeld-Hoffmann dynamics of relativistic matter-energy. The continuous
elementary source/particle in Einstein's gravitational theory is the r^{-4}
radial energy density rather than the delta-operator density in empty-space
gravitation. The space energy integral of such an infinite (astro)particle is
finite and determines its nonlocal gravitational charge for the
energy-to-energy attraction of other nonlocal (astro)particles. The non-empty
flat space of the undivided material Universe is charged continuously by the
world energy density of the global ensemble of overlapping radial particles.
Nonlocal gravitational/inertial energy-charges incorporate Machian relativism
quantitatively into Einstein's gravitation for self-contained SR-GR dynamics
without references on Newton's mass-to-mass attraction.Comment: 9 pages, typos and arguments adde
Magnetic Molecule on a Microcantilever: Quantum Magneto-mechanical Oscillations
We study the quantum dynamics of a system consisting of a magnetic molecule
placed on a microcantilever. The amplitude and frequencies of the coupled
magneto-mechanical oscillations are computed. Parameter-free theory shows that
the existing experimental techniques permit observation of the driven coupled
oscillations of the spin and the cantilever, as well as of the splitting of the
mechanical modes of the cantilever caused by spin tunneling.Comment: 4 pages, 3 figure
The Electrostatics of Einstein's Unified Field Theory
When sources are added at their right-hand sides, and g_{(ik)} is a priori
assumed to be the metric, the equations of Einstein's Hermitian theory of
relativity were shown to allow for an exact solution that describes the general
electrostatic field of n point charges. Moreover, the injunction of spherical
symmetry of g_{(ik)} in the infinitesimal neighbourhood of each of the charges
was proved to yield the equilibrium conditions of the n charges in keeping with
ordinary electrostatics. The tensor g_{(ik)}, however, cannot be the metric of
the theory, since it enters neither the eikonal equation nor the equation of
motion of uncharged test particles. A physically correct metric that rules both
the behaviour of wave fronts and of uncharged matter is the one indicated by
H\'ely. In the present paper it is shown how the electrostatic solution
predicts the structure of the n charged particles and their mutual positions of
electrostatic equilibrium when H\'ely's physically correct metric is adopted.Comment: 15 pages. Misprints corrected. To appear in General Relativity and
Gravitatio
Response of the Shockley surface state to an external electrical field: A density-functional theory study of Cu(111)
The response of the Cu(111) Shockley surface state to an external electrical
field is characterized by combining a density-functional theory calculation for
a slab geometry with an analysis of the Kohn-Sham wavefunctions. Our analysis
is facilitated by a decoupling of the Kohn-Sham states via a rotation in
Hilbert space. We find that the surface state displays isotropic dispersion,
quadratic until the Fermi wave vector but with a significant quartic
contribution beyond. We calculate the shift in energetic position and effective
mass of the surface state for an electrical field perpendicular to the Cu(111)
surface; the response is linear over a broad range of field strengths. We find
that charge transfer occurs beyond the outermost copper atoms and that
accumulation of electrons is responsible for a quarter of the screening of the
electrical field. This allows us to provide well-converged determinations of
the field-induced changes in the surface state for a moderate number of layers
in the slab geometry.Comment: 11 pages, 6 figures, 4 tables; accepted for publication by Phys. Rev.
B; changes from v1 in response to referee comments, esp. to Sections I and
V.B (inc. Table 4), with many added references, but no change in results or
conclusion
Gravitation, electromagnetism and the cosmological constant in purely affine gravity
The Eddington Lagrangian in the purely affine formulation of general
relativity generates the Einstein equations with the cosmological constant. The
Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, which
has the form of the Maxwell Lagrangian with the metric tensor replaced by the
symmetrized Ricci tensor, is dynamically equivalent to the Einstein-Maxwell
Lagrangian in the metric formulation. We show that the sum of the two affine
Lagrangians is dynamically inequivalent to the sum of the analogous Lagrangians
in the metric-affine/metric formulation. We also show that such a construction
is valid only for weak electromagnetic fields. Therefore the purely affine
formulation that combines gravitation, electromagnetism and the cosmological
constant cannot be a simple sum of terms corresponding to separate fields.
Consequently, this formulation of electromagnetism seems to be unphysical,
unlike the purely metric and metric-affine pictures, unless the electromagnetic
field couples to the cosmological constant.Comment: 14 pages, extended and combined with gr-qc/0701176; published versio
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