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L\'evy walks (LWs) are spatiotemporally coupled random-walk processesdescribing superdiffusive heat conduction in solids, propagation of light indisordered optical materials, motion of molecular motors in living cells, ormotion of animals, humans, robots, and viruses. We here investigate a keyfeature of LWs, their response to an external harmonic potential. In thisgeneric setting for confined motion we demonstrate that LWs equilibrateexponentially and may assume a bimodal stationary distribution. We also showthat the stationary distribution has a horizontal slope next to a reflectingboundary placed at the origin, in contrast to correlated superdiffusiveprocesses. Our results generalize LWs to confining forces and settle somelong-standing puzzles around LWs.

L\'evy walk dynamics in an external harmonic potential