  We present a semianalytical theory for exciton transport in organic molecular
crystals interacting strongly with a single cavity mode. Based on the
Holstein-Tavis-Cummings model and the Kubo formula, we derive an exciton
mobility expression in the framework of a temperature-dependent variational
canonical transformation, which can cover a wide range of exciton-vibration
coupling, exciton-cavity coupling, and temperatures. A closed-form expression
for the coherent part of the total mobility is obtained in the zeroth order of
the exciton-vibration coupling, which demonstrates the significance of
vibrationally dressed dark excitons in the determination of the transport
mechanism. By performing numerical simulations on both the H- and J-aggregates,
we find that the exciton-cavity coupling has significant effects on the total
mobility: 1) At low temperatures, there exists an optimal exciton-cavity
coupling strength for the H-aggregate at which a maximal mobility is reached,
while the mobility in the J-aggregate decreases monotonically with increasing
exciton-cavity coupling; 2) At high temperatures, the mobility in both types of
aggregates get enhanced by the cavity. We illustrate the above-mentioned
low-temperature optimal mobility observed in the H-aggregate by using realistic
parameters at room temperature.
