The mobility of electrons in a quasi-one-dimensional channel on the surface of liquid helium is studied theoretically at temperatures lower than 1.5 K. The inBuence on the mobility due to the electron-ripplon interaction and to the electron scattering from helium atoms in the vapor phase is investigated. The nonmonotonic temperature dependence of the mobility below 0.5 K is attributed to the contribution coming from the matrix elements of the scattering operators between different subbands due to the confinement of the electron motion along the channel. It is shown that the results taking electron-electron correlations into account in the complete control approximation difFer significantly from the results in the usual one-electron approximation. This allows us to check the role of electron correlations in quasi-one-dimensional electron systems by comparing the theoretical temperature dependence of the mobility with the experimental data.

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The mobility of electrons localized over solid hydrogen is investigated theoretically using the Boltzmann equation. It is shown that the electron mobility for temperatures above 5 K is dominated by the interface roughness scattering of the hydrogen surface, which is described by the two-parameter model of Gaussian correlations. Prom detailed comparison between theory and experiment it is determined that the hydrogen surface has a roughness with the height of about 1 -2 atomic sizes and a lateral width in the mesoscopic scale (about 10 cm). The theoretical dependences of the mobility on the temperature obtained are in excellent agreement with the experimental high-temperature data available. However, for temperatures below 5 K, our results reproduce only qualitatively the overall temperature dependence of the mobility.