827 research outputs found
On the total mean curvature of non-rigid surfaces
Using Green's theorem we reduce the variation of the total mean curvature of
a smooth surface in the Euclidean 3-space to a line integral of a special
vector field and obtain the following well-known theorem as an immediate
consequence: the total mean curvature of a closed smooth surface in the
Euclidean 3-space is stationary under an infinitesimal flex.Comment: 4 page
Neutron charge radius and the Dirac equation
We consider the Dirac equation for a finite-size neutron in an external
electric field. We explicitly incorporate Dirac-Pauli form factors into the
Dirac equation. After a non-relativistic reduction, the Darwin-Foldy term is
cancelled by a contribution from the Dirac form factor, so that the only
coefficient of the external field charge density is , i. e. the
root mean square radius associated with the electric Sachs form factor . Our
result is similar to a recent result of Isgur, and reconciles two apparently
conflicting viewpoints about the use of the Dirac equation for the description
of nucleons.Comment: 7 pages, no figures, to appear in Physical Review
Vortex matter in the charged Bose liquid at absolute zero
The Gross-Pitaevskii-type equation is solved for the charge Bose liquid in
the external magnetic field at zero temperature. There is a vortex lattice with
locally broken charge neutrality. The boson density is modulated in real space
and each vortex is charged. Remarkably, there is no upper critical field at
zero temperature, so the density of single flux-quantum vortices monotonously
increases with the magnetic field up to B=infinity and no indication of a phase
transition. The size of each vortex core decreases as about 1/sqrt(B) keeping
the system globally charge neutral. If bosons are composed of two fermions, a
phase transition to a spin-polarized Fermi liquid at some magnetic field larger
than the pair-breaking field is predicted.Comment: 4 pages, 4 figures, references update
Screening effects in the electron-optical phonon interaction
We show that recently reported unusual hardening of optical phonons
renormalized by the electron-phonon interaction is due to the neglect of
screening effects. When the electron-ion interaction is properly screened
optical phonons soften in three dimension. It is important that for
short-wavelength optical phonons screening is static while for long-wavelength
optical phonons screening is dynamic. In two-dimensional and one-dimensional
cases due to crossing of the nonperturbed optical mode with gapless plasmons
the spectrum of renormalized optical phonon-plasmon mode shows split momentum
dependence.Comment: 7 page
Hilbert space structure of covariant loop quantum gravity
We investigate the Hilbert space in the Lorentz covariant approach to loop
quantum gravity. We restrict ourselves to the space where all area operators
are simultaneously diagonalizable, assuming that it exists. In this sector
quantum states are realized by a generalization of spin network states based on
Lorentz Wilson lines projected on irreducible representations of an SO(3)
subgroup. The problem of infinite dimensionality of the unitary Lorentz
representations is absent due to this projection. Nevertheless, the projection
preserves the Lorentz covariance of the Wilson lines so that the symmetry is
not broken. Under certain conditions the states can be thought as functions on
a homogeneous space. We define the inner product as an integral over this
space. With respect to this inner product the spin networks form an orthonormal
basis in the investigated sector. We argue that it is the only relevant part of
a larger state space arising in the approach. The problem of the
noncommutativity of the Lorentz connection is solved by restriction to the
simple representations. The resulting structure shows similarities with the
spin foam approach.Comment: 20 pages, RevTE
M-Theory of Matrix Models
Small M-theories unify various models of a given family in the same way as
the M-theory unifies a variety of superstring models. We consider this idea in
application to the family of eigenvalue matrix models: their M-theory unifies
various branches of Hermitean matrix model (including Dijkgraaf-Vafa partition
functions) with Kontsevich tau-function. Moreover, the corresponding duality
relations look like direct analogues of instanton and meron decompositions,
familiar from Yang-Mills theory.Comment: 12 pages, contribution to the Proceedings of the Workshop "Classical
and Quantum Integrable Systems", Protvino, Russia, January, 200
Numerical Simulation of Multicomponent Ion Beam from Ion Sources
A program library for numerical simulation of a multicomponent charged particle beam from ion sources is presented. The library is aimed for simulation of high current, low energy multicomponent ion beam from ion source through beamline and realized under the Windows user interface for the IBM PC. It is used for simulation and optimization of beam dynamics and based on successive and consistent application of two methods: the momentum method of distribution function (RMS technique) and particle in cell method. The library has been used to simulate and optimize the transportation of tantalum ion beam from the laser ion source (CERN) and calcium ion beam from the ECR ion source (JINR, Dubna)
Instabilities for a relativistic electron beam interacting with a laser irradiated plasma
The effects of a radiation field (RF) on the unstable modes developed in
relativistic electron beam--plasma interaction are investigated assuming that
, where is the frequency of the RF and
is the plasma frequency. These unstable modes are parametrically
coupled to each other due to the RF and are a mix between two--stream and
parametric instabilities. The dispersion equations are derived by the
linearization of the kinetic equations for a beam--plasma system as well as the
Maxwell equations. In order to highlight the effect of the radiation field we
present a comparison of our analytical and numerical results obtained for
nonzero RF with those for vanishing RF. Assuming that the drift velocity
of the beam is parallel to the wave vector of the
excitations two particular transversal and parallel configurations of the
polarization vector of the RF with respect to are
considered in detail. It is shown that in both geometries resonant and
nonresonant couplings between different modes are possible. The largest growth
rates are expected at the transversal configuration when is
perpendicular to . In this case it is demonstrated that in general
the spectrum of the unstable modes in -- plane is split into two
distinct domains with long and short wavelengths, where the unstable modes are
mainly sensitive to the beam or the RF parameters, respectively. In parallel
configuration, , and at short wavelengths
the growth rates of the unstable modes are sensitive to both beam and RF
parameters remaining insensitive to the RF at long wavelengths.Comment: 23 pages, 5 figure
Profiles of inflated surfaces
We study the shape of inflated surfaces introduced in \cite{B1} and
\cite{P1}. More precisely, we analyze profiles of surfaces obtained by
inflating a convex polyhedron, or more generally an almost everywhere flat
surface, with a symmetry plane. We show that such profiles are in a
one-parameter family of curves which we describe explicitly as the solutions of
a certain differential equation.Comment: 13 pages, 2 figure
Selective addressing of high-rank atomic polarization moments
We describe a method of selective generation and study of polarization
moments of up to the highest rank possible for a quantum state with
total angular momentum . The technique is based on nonlinear magneto-optical
rotation with frequency-modulated light. Various polarization moments are
distinguished by the periodicity of light-polarization rotation induced by the
atoms during Larmor precession and exhibit distinct light-intensity and
frequency dependences. We apply the method to study polarization moments of
Rb atoms contained in a vapor cell with antirelaxation coating. Distinct
ultra-narrow (1-Hz wide) resonances, corresponding to different multipoles,
appear in the magnetic-field dependence of the optical rotation. The use of the
highest-multipole resonances has important applications in quantum and
nonlinear optics and in magnetometry.Comment: 5 pages, 6 figure
- …