Uncertainty principle in a cavity at finite temperature

We employ a dressed state approach to perform a study on the behavior of the uncertainty principle for a system in a heated cavity. We find, in a small cavity for a given temperature, an oscillatory behavior of the momentum--coordinate product, $(\Delta\,p)\,(\Delta\,q)$, which attains periodically finite absolute minimum (maximum) values, no matter large is the elapsed time. This behavior is in a sharp contrast with what happens in free space, in which case, the product $(\Delta\,p)\,(\Delta\,q)$ tends asymptotically, for each temperature, to a constant value, independent of time.