Using the Feynman path-integral formalism we study the polaron effects in
quantum wires above a liquid helium film. The electron interacts with
two-dimensional (2D) surface phonons, i.e. ripplons, and is confined in one
dimension (1D) by an harmonic potential. The obtained results are valid for
arbitrary temperature (T), electron-phonon coupling strength (α), and
lateral confinement (ω0). Analytical and numerical results are
obtained for limiting cases of T, α, and ω0. We found the
surprising result that reducing the electron motion from 2D to quasi-1D makes
the self-trapping transition more continuous.Comment: 6 pages, 7 figures, submitted to Phys. Rev.