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} $\mathbf{x}\mathbf{p}$\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., $z$-axis component of the angular momentum. The posmom has two parity symmetries, specifically, invariant under two operations $m_{x}$ and $m_{y}$ representing mirror symmetry about $x$ and $y$ 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 $S^{1}$ in two-dimensional flat space $R^{2}$ 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 $N-1$ ($N\geq2$) 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 $hep$ 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 $\sigma$ 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 $N-1$ ($N\geq 2$) curved hypersurface embedded in $N$ 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.