In mesoscopic physics, ballistic conduction (ballistic transport) is the unimpeded flow (or transport) of charge carriers (usually electrons), or energy-carrying particles, over relatively long distances in a material. In general, the resistivity of a material exists because an electron, while moving inside a medium, is scattered by impurities, defects, thermal fluctuations of ions in a crystalline solid, or, generally, by any freely-moving atom/molecule composing a gas or liquid. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds.

The mean free path of a particle can be described as the average length that the particle can travel freely, i.e., before a collision, which could change its momentum. The mean free path can be increased by reducing the number of impurities in a crystal or by lowering its temperature. Ballistic transport is observed when the mean free path of the particle is (much) longer than the dimension of the medium through which the particle travels. The particle alters its motion only upon collision with the walls. In the case of a wire suspended in air/vacuum the surface of the wire plays the role of the box reflecting the electrons and preventing them from exiting toward the empty space/open air. This is because there is an energy to be paid to extract the electron from the medium (work function).

Ballistic conduction is typically observed in quasi-1D structures, such as carbon nanotubes or silicon nanowires, because of extreme size quantization effects in these materials. Ballistic conduction is not limited to electrons (or holes) but can also apply to phonons. It is theoretically possible for ballistic conduction to be extended to other quasi-particles, but this has not been experimentally verified. For a specific example, ballistic transport can be observed in a metal nanowire: due to the small size of the wire (nanometer-scale or 10⁻⁹ meters scale) and the mean free path which can be longer than that in a metal.

Ballistic conduction differs from superconductivity due to 1) a finite, non-zero resistance and 2) the absence of the Meissner effect in the material. The presence of resistance implies that the heat is dissipated in the leads outside of the "ballistic" conductor, where inelastic scattering effects can take place.

In general, carriers will exhibit ballistic conduction when ${\displaystyle L\leq \lambda _{\rm {MFP}}}$ where ${\displaystyle L}$ is the length of the active part of the device (e.g., a channel in a MOSFET). ${\displaystyle \lambda _{\rm {MFP}}}$ is the mean free path for the carrier which can be given by Matthiessen's rule, written here for electrons:

where

In terms of scattering mechanisms, optical phonon emission normally dominates, depending on the material and transport conditions. There are also other scattering mechanisms which apply to different carriers that are not considered here (e.g. remote interface phonon scattering, Umklapp scattering). To get these characteristic scattering rates, one would need to derive a Hamiltonian and solve Fermi's golden rule for the system in question.

In 1957, Rolf Landauer proposed that conduction in a 1D system could be viewed as a transmission problem. For the 1D graphene nanoribbon field effect transistor (GNR-FET) on the right (where the channel is assumed to be ballistic), the current from A to B, given by the Boltzmann transport equation, is