  We consider the energy transfer process between two identical atoms placed
inside a perfectly conducting cylindrical waveguide. We first introduce a
general analytical expression of the energy transfer amplitude in terms of the
electromagnetic Green's tensor; we then evaluate it in the case of a
cylindrical waveguide made of a perfect conductor, for which analytical forms
of the Green's tensor exist. We numerically analyse the energy transfer
amplitude when the radius of the waveguide is such that the transition
frequency of both atoms is below the lower cutoff frequency of the waveguide,
so that the resonant photon exchange is strongly suppressed. We consider both
cases of atomic dipoles parallel and orthogonal to the axis of the guide. In
both cases, we find that the energy transfer is modified by the presence of the
waveguide. In the near zone, that is when the atomic separation is smaller than
the atomic transition wavelength, the change, with respect to the free-space
case, is small for axial dipoles, while it is larger for radial dipoles; it
grows when the intermediate region between near and far zone is approached. In
the far zone, we find that the energy transfer amplitude is strongly suppressed
by the waveguide, becoming virtually zero. A physical interpretation of these
results is discussed. Finally, we discuss the resonance interaction energy and
force between two identical correlated atoms in the waveguide, one excited and
the other in the ground state, prepared in their symmetric or antisymmetric
superposition.
