  L\'evy walks (LWs) are spatiotemporally coupled random-walk processes
describing superdiffusive heat conduction in solids, propagation of light in
disordered optical materials, motion of molecular motors in living cells, or
motion of animals, humans, robots, and viruses. We here investigate a key
feature of LWs, their response to an external harmonic potential. In this
generic setting for confined motion we demonstrate that LWs equilibrate
exponentially and may assume a bimodal stationary distribution. We also show
that the stationary distribution has a horizontal slope next to a reflecting
boundary placed at the origin, in contrast to correlated superdiffusive
processes. Our results generalize LWs to confining forces and settle some
long-standing puzzles around LWs.
