Electron self-trapping on a nanocircle (Q2499758)

The paper aims to construct various eigenstates, and identify a ground state, in a model of a circular system of interacting monomers, each having its intrinsic electron degree of freedom. The Hamiltonian of the system couples the intrinsic electron field of monomers to three phonon degrees of freedom, which account for the deformation of the circle's shape: two of them take into regard displacements of the monomers inside the circle, and the third one deals with transverse displacements. To solve the Hamiltonian, an adiabatic approximation is employed, in which the Hamiltonian is reduced to its classical form, with cubic nonlinearity. Eigenstates of the latter are found by means of some approximations in an analytical form, and, in the general case, numerically. Also developed is the continuum approximation, that reduces to the stationary form of the cubic nonlinear Schrödinger equation. The Hamiltonian always has a delocalized state (plane wave), which is the ground state in the case of weak coupling. In the opposite case of strong coupling, self-trapped soliton-like states realize the energy minimum. These solitons feature strong localization of the electron (intrinsic) degree of freedom (on one or two sites of the circular lattice), and only weak localization of the deformation fields. The accordingly deformed shape of the circle is found.