134,916 research outputs found
Cerenkov Emission by Neutral Particles in Gravitoelectro-magnetic Fields
It is shown that under the post-Newtonian approximation the Einstein
equations can be reduced to the standard Maxwell-type field equations in a
medium; in such a context the Cerenkov emission by a neutralparticle gives
large energy loss while the particle moves at faster than the phase speed of
waves in the medium.Comment: submit to GR
Posmon spectrosopy of quantum state on a circle
Developing the analysis of the distribution of the particle's
position-momentum dot product, the so-called \textit{posmom} \textbf{,} to quantum states on a circular circle on two-dimensional
Cartesian coordinates, we give its posmometry (introduced recently by Y. A.
Bernard and P. M. W. Gill, Posmom: The Unobserved Observable, J. Phys. Chem.
Lett. 1\textbf{(}2010\textbf{)}1254) for eigenstates of the free motion on the
circle, i.e., -axis component of the angular momentum. The posmom has two
parity symmetries, specifically, invariant under two operations and
representing mirror symmetry about and axis respectively. The
complete eigenfunction set of the posmom is then four-valued and consists of
four basic parts each of them is defined within a distinct quadrant of the
circle. The results are not only potentially experimentally testable, but also
reflect a fact that the embedding of the circle in two-dimensional flat
space is physically reasonable.Comment: 9 pages, 6 figure
Miura Map between Lattice KP and its Modification is Canonical
We consider the Miura map between the lattice KP hierarchy and the lattice
modified KP hierarchy and prove that the map is canonical not only between the
first Hamiltonian structures, but also between the second Hamiltonian
structures.Comment: 8 pages, LaTe
Geometric momentum for a particle constrained on a curved hypersurface
A strengthened canonical quantization scheme for the constrained motion on a
curved hypersurface is proposed with introduction of the second category of
fundamental commutation relations between Hamiltonian and positions/momenta,
whereas those between positions and moments are categorized into the first. As
an () dimensional hypersurface is embedded in an N dimensional
Euclidean space, we obtain the proper momentum that depends on the mean
curvature. For the surface is the spherical one, a long-standing problem on the
form of the geometric potential is resolved in a lucid and unambiguous manner,
which turns out to be identical to that given by the so-called confining
potential technique. In addition, a new dynamical group SO(N,1) symmetry for
the motion on the sphere is demonstrated.Comment: 5 pages, no figur
Painlev\'{e} Analysis and Exact Solutions of a Modified Boussinesq Equation
We consider a modified Boussinesq type equation. The Painlev\'{e} test of the
WTC method is performed for this equation and it shows that the equation has
weak Painlev\'{e} property. Some exact solutions are constructed.Comment: 7 pages, LaTeX fil
Generalized Centripetal Force Law and Quantization of Motion Constrained on 2D Surfaces
For a particle moves on a 2D surface f(x)=0 embedded in 3D Euclidean space,
the geometric momentum and potential are simultaneously admissible within the
Dirac canonical quantization scheme for constrained motion. In our approach,
not the full scheme but the symmetries indicated by classical brackets
[x,H]_{D} and [p,H]_{D} in addition to the fundamental ones [x,x]_{D},
[x,p]_{D} and [p,p]_{D} are utilized, where the subscript D stands for the
Dirac bracket. The generalized centripetal force law p=[p,H]_{D} for particle
on the 2D surface play the key role, and there is no simple relationship
between the force on a point of the surface and its curvatures of the point, in
sharp contrast to the motion on a curve.Comment: 11 pages, 1 figur
Distribution of xp in some molecular rotational states
Developing the analysis of the distribution of the so-called posmom xp to the
spherical harmonics that represents some molecular rotational states for such
as diatomic molecules and spherical cage molecules, we obtain posmometry
(introduced recently by Y. A. Bernard and P. M. W. Gill, Posmom: The Unobserved
Observable, J. Phys. Chem. Lett. 1(2010)1254) of the spherical harmonics and
demonstrate that it bears a striking resemblance to the momentum distributions
of the stationary states for a one-dimensional simple harmonic oscillator.Comment: 8 pages, 3 figure
Uncertainty of the Solar Neutrino Energy Spectrum
The solar neutrino spectrum measured by the Super-Kamiokande shows an excess
in high energy bins, which may be explained by vacuum oscillation solution or
neutrino effect. Here we reconsider an uncertainty of the data caused by
the tail of the energy resolution function. Events observed at energy higher
than 13.5 MeV are induced by the tail of the resolution. At Super-Kamiokande
precision level this uncertainty is no more than few percent within a Gaussian
tail. But a power-law decay tail at 3 results considerable excesses in
these bins, which may be another possible explanation of the anomaly in
708d(825d) data.Comment: 7 pages, proceeding latex file, Improvement of submitted version
(April 15) to proceeding of 17 International Workshop on Weak Interactions
and Neutrinos, South Africa, January 24-30, 1999. One figure added u
Breakdown of Ehrenfest theorem for free particle constrained on a hypersurface
There is a belief that the Ehrenfest theorem holds true universally. We
demonstrate that for a classically nonrelativistic particle constrained on an
() curved hypersurface embedded in flat space, the theorem
breaks down.Comment: 3 pages, no figur
Nonlinear Interactions of Gravitational Wave with Matter in Magnetic-type Maxwell-Vlasov Description
The interactions of gravitational waves with interstellar matter, dealing
with resonant wave-particle and wave-wave interactions, are considered on the
basis of magnetic-type Maxwell-Vlasov equations. It is found that the behavior
of the fields, involving the "gravitoelectromagnetic" or "GEM " fields, the
perturbed density field and self-generated gravitomagnetic field with low
frequency,can be described by the nonlinear coupling equations Eqs.
(6.10)-(6.12). Numerical results show that they may collapse. In other words,
due to self-condensing, a stronger GME fields could be produced; and they could
appear as the gravitational waves with high energy reaching on Earth. In this
case, Weber's results, perhaps, are acceptable.Comment: 13 figures, submit to Phys.Rev.
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