Polaron effects in electron channels on a helium film

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 ($\alpha $), and lateral confinement ($\omega_{0}$). Analytical and numerical results are obtained for limiting cases of $T$, $\alpha $, and $\omega_{0}$. We found the surprising result that reducing the electron motion from 2D to quasi-1D makes the self-trapping transition more continuous.