Within the framework of the strong-coupling polaron theory the groundstate binding energy and the effective m s of the electron-Lo phonon system is retrieved as a function of the effective dimensiondity in a quantum-well confinement. The geometry we use is a threedimensional parabolic potential box, the harrier slopes of which C M he tuned so as to yield a unified bacterization interpolating between the bulk, the quasi-two-and onedimensional limits as well as the quantum-well box -e.

The g r o u n d state of the Frabli& polaron is retrieved as a function of the de-of confinement in a three-dimensiod quantum well with tunable barrier potentials. A unified overview of the binding energy interpolating between all possible confinement geometries is provided within the Lamework of the second-orda perturbation theory.

Abstract. In the limit of strong electron-phonon coupling, we provide a unified insight into the stability criterion for bipolaron formation in low-dimensionally confined media. The model that we use consists of a pair of electrons immersed in a reservoir of bulk LO phonons and confined within an anisotropic parabolic potential box, whose barrier slopes can be tuned arbitrarily from zero to infinity. Thus, encompassing the bulk and all low-dimensional geometric configurations of general interest, we obtain an explicit tracking of the critical ratio ηc of dielectric constants below which bipolarons can exist. PACS. 71.38.+i Polarons and electron-phonon interactions

Abstract. Within the framework of the Feynman path integral theory, we provide a unified insight into ground-state properties of the Fröhlich polaron in low-dimensionally confined media. The model that we adopt consists of an electron immersed in the field of bulk LO phonons and bounded within an anisotropic parabolic potential box, whose barrier slopes can be tuned so as to yield an explicit tracking of the Fröhlich interaction encompassing the bulk and all lowdimensional geometric configurations of general interest.

We consider the interaction of a confined electron with bulk polar-optical phonons in a cylindrical quantum well wire with infinite boundary potential. Expressions for the polaron self-energy and mass are derived within a variational scheme over reasonably broad ranges of the wire radius and the phonon-coupling strength. The formulation is based on the standard canonical transformation of the strong-coupling ansatz and consists of a variationally determined perturbative extension serving for the theory to interpolate in the overall range of the coupling constant. Contrary to the general trend that the electron-phonon interaction is inherently stronger in systems of lower dimensionality, our results indicate that, at weak coupling, the binding energy of the polaron can be smaller and its mass less inertial compared with the bulk case when the wire is made narrow.