  Thermal atomic vibrations in amorphous solids can be distinguished by whether
they propagate as elastic waves or do not propagate due to lack of atomic
periodicity. In a-Si, prior works concluded that non-propagating waves are the
dominant contributors to heat transport, while propagating waves are restricted
to frequencies less than a few THz and are scattered by anharmonicity. Here, we
present a lattice and molecular dynamics analysis of vibrations in a-Si that
supports a qualitatively different picture in which propagating elastic waves
dominate the thermal conduction and are scattered by elastic fluctuations
rather than anharmonicity. We explicitly demonstrate the propagating nature of
vibration with frequency approaching 10 THz using a triggered wave
computational experiment. Our work suggests that most heat is carried by
propagating elastic waves in a-Si and demonstrates a route to achieve extreme
thermal properties in amorphous materials by manipulating elastic fluctuations.
