44 research outputs found
New quantum-mechanical phenomenon in a model of electron-electron interaction in graphene
A quantum mechanical model of two interacting electrons in graphene is
considered. We concentrate on the case of zero total momentum of the pair. We
show that the dynamics of the system is very unusual. Both stationary and
time-dependent problems are considered. It is shown that the complete set of
the wave functions with definite energy includes the new functions, previously
overlooked. The time evolution of the wave packet, corresponding to the
scattering problem setup, leads to the appearance of the localized state at
large time. The asymptotics of this state is found analytically. We obtain the
lower bound of the life time of this state, which is connected with the
breakdown of the continuous model on the lattice scale. The estimate of this
bound gives one a hope to observe the localized states in the experiment.Comment: 10 pages, 2 figure
Remarks on the spherical waves of the Dirac field on de Sitter spacetime
The Shishkin's solutions of the Dirac equation in spherical moving frames of
the de Sitter spacetime are investigated pointing out the set of commuting
operators whose eigenvalues determine the integration constants. It is shown
that these depend on the usual angular quantum numbers and, in addition, on the
value of the scalar momentum. With these elements a new result is obtained
finding the system of solutions normalized (in generalized sense) in the scale
of scalar momentum.Comment: 7 pages, no figure
Charge asymmetry in the differential cross section of high-energy e+e- photoproduction in the field of a heavy atom
First quasiclassical correction to the differential cross section of
high-energy electron-positron photoproduction in the electric field of a heavy
atom is obtained with the exact account of the field. This correction is
responsible for the charge asymmetry in this process. When the
transverse momentum of at least one of the produced particles is much larger
than the electron mass , the charge asymmetry can be as large as tens
percent. We also estimate the contribution to the charge
asymmetry coming from the Compton-type diagram. For heavy nuclei, this
contribution is negligible. For light nuclei, is noticeable
only when the angle between the momenta of electron and positron is of order of
( is the photon energy) while the transverse momenta of both
particles are much larger than .Comment: 19 pages, 7 figure
Angular distribution of high-energy photoproduction close to the end of spectrum
We consider the differential cross section of electron-positron pair
production by a high-energy photon in a strong Coulomb field close to the end
of the electron or positron spectrum. When the momentum transfer largely
exceeds the electron mass, the cross section is obtained analytically in a
compact form. Coulomb corrections essentially modify the cross section even for
moderate values of the nuclear charge number . In the same kinematical
region, the angular distribution for bound-free pair production,
bremsstrahlung, and photorecombination is also obtained.Comment: 12 pages, 4 figure
Spatial distributions in static heavy-light mesons: a comparison of quark models with lattice QCD
Lattice measurements of spatial distributions of the light quark bilinear
densities in static mesons allow to test directly and in detail the wave
functions of quark models. These distributions are gauge invariant quantities
directly related to the spatial distribution of wave functions. We make a
detailed comparison of the recent lattice QCD results with our own quark
models, formulated previously for quite different purposes. We find a striking
agreement not only between our two quark models, but also with the lattice QCD
data for the ground state in an important range of distances up to about 4/GeV.
Moreover the agreement extends to the L=1 states [j^P=(1/2)^+]. An explanation
of several particular features completely at odds with the non-relativistic
approximation is provided. A rather direct, somewhat unexpected and of course
approximate relation between wave functions of certain quark models and QCD has
been established.Comment: 40 pages, 5 figures (version published in PRD
Variational Two Fermion Wave Equations in QED: Muonium Like Systems
We consider a reformulation of QED in which covariant Green functions are
used to solve for the electromagnetic field in terms of the fermion fields. The
resulting modified Hamiltonian contains the photon propagator directly. A
simple Fock-state variational trial function is used to derive relativistic
two-fermion equations variationally from the expectation value of the
Hamiltonian of the field theory. The interaction kernel of the equation is
shown to be, in essence, the invariant M-matrix in lowest order. Solutions of
the two-body equations are presented for muonium like system for small coupling
strengths. The results compare well with the observed muonium spectrum, as well
as that for hydrogen and muonic hydrogen. Anomalous magnetic moment effects are
discussed
Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction
The spectral problem of the Dirac equation in an external quadratic vector
potential is considered using the methods of the perturbation theory. The
problem is singular and the perturbation series is asymptotic, so that the
methods for dealing with divergent series must be used. Among these, the
Distributional Borel Sum appears to be the most well suited tool to give
answers and to describe the spectral properties of the system. A detailed
investigation is made in one and in three space dimensions with a central
potential. We present numerical results for the Dirac equation in one space
dimension: these are obtained by determining the perturbation expansion and
using the Pad\'e approximants for calculating the distributional Borel
transform. A complete agreement is found with previous non-perturbative results
obtained by the numerical solution of the singular boundary value problem and
the determination of the density of the states from the continuous spectrum.Comment: 10 pages, 1 figur
Polarization of the electron and positron produced in combined Coulomb and strong laser fields
The process of production in the superposition of a Coulomb and a
strong laser field is considered. The pair production rate integrated over the
momentum and summed over the spin projections of one of the particles is
derived exactly in the parameters of the laser field and in the Born
approximation with respect to the Coulomb field. The case of a monochromatic
circularly polarized laser field is considered in detail. A very compact
analytical expression of the pair production rate and its dependence on the
polarization of one of the created particles is obtained in the quasiclassical
approximation for the experimentally relevant case of an undercritical laser
field. As a result, the polarization of the created electron (positron) is
derived.Comment: 16 pages, no figure
High-energy photoproduction cross section close to the end of spectrum
We consider the cross section of electron-positron pair production by a
high-energy photon in a strong Coulomb field close to the end of electron or
positron spectrum. We show that the cross section essentially differs from the
result obtained in the Born approximation as well as form the result which
takes into account the Coulomb corrections under assumption that both electron
and positron are ultrarelativistic. The cross section of bremsstrahlung in a
strong Coulomb field by a high-energy electron is also obtained in the region
where the final electron is not ultrarelativistic.Comment: 20 pages, 4 figure
Spinning particle in an external linearized gravitational wave field
We study the interaction of a scalar and a spinning particle with a coherent
linearized gravitational wave field treated as a classical spin two external
field. The spin degrees of freedom of the spinning particle are described by
skew-commuting variables. We derive the explicit expressions for the
eigenfunctions and the Green's functions of the theory. The discussion is exact
within the approximation of neglecting radiative corrections and we prove that
the result is completely determined by the semiclassical contribution.Comment: 11 page