Interimpurity transfer in condensed media: Breakdown of coherent tunneling and conditions for the creation of localized states

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Abstract
This paper deals with the problem of interimpurity transport of quasiparticles (electron, exciton, etc.) in condensed media. A realistic situation is simulated by the simple two-level model interacting with an environment whose influence is described by a set of harmonic oscillators. The model is general enough to include most of the situations of interest by a convenient choice of parameters. A variational approach is developed which enables one to formulate the set of evolution equations for the variables describing the essential system properties in practically the whole parameter space, which consists of the coupling constant and the adiabaticity parameter (representing the ratio of the interimpurity-transfer integral to the phonon bandwidth). It was found that the parameter space (plane of the coupling constant vs adiabaticity parameter) is divided into two regions with quite distinct physical properties. In the first one the dynamics is dominated by the quantum nature of the phonon subsystem and the localization transition is achieved through the reduction of the effective transfer integral. In the second, the so-called symmetry-breaking region, the classical nature of the phonon field prevails. Therefore, the dynamics and localization are described by the discrete nonlinear Schrödinger equation. The symmetry breaking itself is induced by nature of the phonon field, which, in the strong coupling limit, behaves classically. The results are presented in such a form that it allows for the precise determination of the system behavior for any set of realistic system parameters, enabling comparison with previous results.