The rain stick, a simple model for the dynamics of particles passing obstacles in a gravitational field

The problem of a light particle travelling through a field of obstacles or very massive particles in equilibrium pervades multiple fields in modern physics. We analyse such a problem by considering a toy rain-stick model, the mechanical analogue of the Drude model, for the motion of non-interacting electrons through a medium. We study the differences and similarities between a rain-stick model and the Drude model. Interestingly, we find that, when the only potential is gravitational, the system behaves very differently. Rather than finding a mechanical analogue to Ohm's law, a different law is recovered. We further analyse the multi-particle case, and find the conditions under which the linear Ohm's law might be restored. This might yield important tools to physicists’ arsenal, namely, the ability to look at bulk behaviour without the need for the microscopic model. Author summary: The rain stick is a musical instrument, that at least on its face is a mechanical analogue to the classical Drude model. This model can and is used extensively to describe a directional interaction between two mediums, such as gaseous jets and other relatively localized interactions. Remarkably, we find the ’Ohm's law’ analogue is essentially different, provided the thermal velocity is tightly coupled to the potential. This result might yield another tool in the physicist's tool-box.