  In a 2DEG confined to two coaxial tubes the `tube degree of freedom' can be
described in terms of pseudospin-1/2 dynamics. The presence of tunneling
between the two tubes leads to a collective oscillation known as pseudospin
resonance. We employ perturbation theory to examine the dependence of the
frequency of this mode with respect to a coaxial magnetic field for the case of
small intertube distances. Coulomb interaction leads to a shift of the
resonance frequency and to a finite lifetime of the pseudospin excitations. The
presence of the coaxial magnetic field gives rise to pronounced peaks in the
shift of the resonance frequency. For large magnetic fields this shift vanishes
due to the effects of Zeeman splitting. Finally, an expression for the
linewidth of the resonance is derived. Numerical analysis of this expression
suggests that the linewidth strongly depends on the coaxial magnetic field,
which leads to several peaks of the linewidth as well as regions where damping
is almost completely suppressed.
