  We consider heat transport across a harmonic chain of charged particles, with
transverse degrees of freedom, in the presence of a uniform magnetic field. For
an open chain connected to heat baths at the two ends we obtain the
nonequilibrium Green's function expression for the heat current. This
expression involves two different Green's functions which can be identified as
corresponding respectively to scattering processes within or between the two
transverse waves. The presence of the magnetic field leads to two phonon bands
of the isolated system and we show that the net transmission can be written as
a sum of two distinct terms attributable to the two bands. Exact expressions
are obtained for the current in the thermodynamic limit, for the the cases of
free and fixed boundary conditions. In this limit, we find that at small
frequency $\omega$, the effective transmission has the frequency-dependence
$\omega^{3/2}$ and $\omega^{1/2}$ for fixed and free boundary conditions
respectively. This is in contrast to the zero magnetic field case where the
transmission has the dependence $\omega^2$ and $\omega^0$ for the two boundary
conditions respectively, and can be understood as arising from the quadratic
low frequency phonon dispersion.
