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Multiple scattering occurs when a disturbance encounters more than one scatterer, or revisits scatterers after earlier deflections. Each object is driven by both the original incident wave and fields produced by other objects. Solving the coupled responses therefore differs from adding independent single-scattering intensities.

When wave phases remain correlated, alternative paths must be added as complex amplitudes before squaring, retaining their interference. If suitable randomization makes those cross terms negligible, transport may instead be approximated by a sequence of random deflections; the relevant mean free path compares the typical distance between encounters with sample size. A thick cloudy sample can transmit diffuse light even when its direct beam is weak. Under appropriate coherent conditions, repeated wave scattering also produces weak localization or Anderson localization, which cannot be inferred from independent path probabilities alone.

In quasi-one-dimensional quantum transport, transverse confinement makes discrete subbands while motion along a quantum wire remains continuous. Only occupied propagating subbands conduct. For elastic scattering between equilibrated reservoirs, the Landauer formula isThe sum explicitly counts spin. A perfectly transmitting spin-degenerate subband gives $2e^2/h$ at low temperature; a quantum point contact shows steps as a gate opens additional subbands. The one-dimensional density of states cancels the carrier velocity in the current, giving a conductance quantum rather than a material-dependent velocity factor. Finite two-terminal contact resistance remains even without internal scattering.

Transport is ballistic transport for length $L\ll \ell$, where $\ell$ is the mean free path. In a multichannel wire with $\ell \ll L$ below its localization length, scattering reduces transmission and gives approximately Ohmic behaviour. If the phase coherence length exceeds the sample length, amplitudes interfere; weak localization and sample-dependent universal conductance fluctuations can appear. At greater lengths, generic coherent disordered wires undergo Anderson localization, with localization length of order the channel number times $\ell$, up to symmetry-dependent factors. Thermal averaging and dephasing smear the quantum features.

Strong interactions require more than independent-electron transmission. A clean single-channel interacting wire is described at low energy by a Luttinger liquid, with collective modes and possible spin-charge separation; impurities can generate temperature-dependent power laws. Ideal contacts to noninteracting leads can still fix the two-terminal conductance of a clean wire, so it must not automatically be multiplied by a bulk Luttinger parameter.