5 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
Relativistic Coulomb Green's function in -dimensions
Using the operator method, the Green's functions of the Dirac and
Klein-Gordon equations in the Coulomb potential are derived for
the arbitrary space dimensionality . Nonrelativistic and quasiclassical
asymptotics of these Green's functions are considered in detail.Comment: 9 page
Virtual light-by-light scattering and the g factor of a bound electron
The contribution of the light-by-light diagram to the g factor of electron
and muon bound in Coulomb field is obtained. For electron in a ground state,
our results are in good agreement with the results of other authors obtained
numerically for large Z. For relatively small Z our results have essentially
higher accuracy as compared to the previous ones. For muonic atoms, the
contribution is obtained for the first time with the high accuracy in whole
region of Z.Comment: 10 pages, 3 figures, RevTe
Moving zero-gap Wannier-Mott excitons in graphene
We demonstrate the possibility of existence of indirect moving Wannier-Mott
excitons in graphene. Electron-hole binding is conditioned by the trigonal
warping of conic energy spectrum. The binding energies are found for the lowest
exciton states. These energies essentially depend on the value and direction of
exciton momentum and vanish when the exciton momentum tends to the conic
points. The ways to observe the exciton states are discussed. The opportunity
of experimental observation of zero-gap excitons by means of external electron
scattering is examined.Comment: 6 pages, 7 figure