  Future of silicon-based microelectronics relies on solving the heat
dissipation problem. A solution may lie in a nanoscale phenomenon known as
ballistic heat conduction, which implies heat conduction without heating the
conductor. But, attempts to demonstrate this phenomenon experimentally are
controversial and scarce whereas its mechanism in confined nanostructures is
yet to be fully understood. Here, we experimentally demonstrate quasi-ballistic
heat conduction in silicon nanowires (NWs). We show that the ballisticity is
strongest in short NWs at low temperatures but weakens as the NW length or
temperature is increased. Yet, even at room temperature, quasi-ballistic heat
conduction remains visible in short NWs. To better understand this phenomenon,
we probe directionality and lengths of phonon flights. Our experiments and
simulations show that the quasi-ballistic phonon transport in NWs is the L\'evy
walk with short flights between the NW boundaries and long ballistic leaps
along the NW.
