  Here, we study a minimal model, the three-level V system coupled to two heat
baths, and investigate the role of quantum coherences in heat transport in both
the transient regime and in the nonequilibrium steady-state. In our model,
energy is exchanged between the baths through two parallel pathways, which can
be made distinct through the nondegeneracy of excited levels (energy splitting
$\Delta$) and a control parameter $\alpha$, which adjusts the strength of one
of the arms. Using a nonsecular quantum master equation of Redfield form, we
succeed in deriving closed-form expressions for the quantum coherences and the
heat current in the steady state limit for closely degenerate excited levels.
By including three ingredients in our analysis: nonequilibrium baths,
nondegeneracy of levels, and asymmetry of pathways, we show that quantum
coherences are generated and sustained in the V model in the steady-state limit
if three conditions, conjoining thermal and coherent effects are simultaneously
met: (i) The two baths are held at different temperatures. (ii) Bath-induced
pathways do not interfere destructively. (iii) Thermal rates do not mingle with
the control parameter $\alpha$ to destroy interferences through an effective
local equilibrium condition. We find that coherences are maximized when the
heat current is suppressed. On the other hand, the secular Redfield quantum
master equation is shown to fail in a broad range of parameters. Although we
mainly focus on analytical results in the steady state limit, numerical
simulations reveal that the transient behavior of coherences contrasts the
steady-state limit, suggesting that different mechanisms are at play in these
two regimes. Enhancing either the lifetime of transient coherences or their
magnitude at steady state thus requires the control and optimization of
different physical parameters.
