We have investigated the effect of applying a dc source-drain voltage across a quasi-one-dimensional constriction formed at a GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterojunction. For conductances greater than 2${\mathit{e}}^2$/h, the measurements can be compared with the predictions of an adiabatic model proposed by Glazman and Khaetskii, in which the voltage is dropped symmetrically across the one-dimensional constriction. The source-drain voltage measurements are used to obtain the subband energies of the quasi-one-dimensional constriction. For conductances less than 2${\mathit{e}}^2$/h, the Glazman-Khaetskii model is no longer applicable and anomalous structure is observed.

• Received 22 July 1991

DOI:https://doi.org/10.1103/PhysRevB.44.13549