Kapitza resistance between electron and phonon gases in the 1d case

This study addresses the exact behavior of electrons and phonons in semi-infinite 1D systems with due allowance for the local interaction between them. The spectral functions of electrons and phonons in such a system have been derived and analyzed in an analytical form. The paper considers, in particular, the problems involved in the hardening and softening of phonon modes and renormalization of the electron-phonon interaction constant. The results obtained have been employed in calculation of the thermal resistance constant at the boundary separating the electron from the phonon systems and in an analysis of its dependence on the renormalized electron- phonon interaction constant. All the results were obtained in the adiabatic limit for several cases of special significance, such as a half-filled and an empty conduction band at temperatures both higher and lower than the characteristic phonon frequencies. Significantly, the problem was treated exactly for an arbitrary electron-phonon interaction constant, in both the weak and the strong limits. It has been demonstrated that thermal resistance decreases with increasing electron-phonon interaction coefficient and/or temperature; at large values of these parameters, thermal resistance at the boundary no longer depends on these quantities.