| Strongly interacting quasiparticle-boson systems form an important part of condensed matter physics. Among the various approximation schemes used in the literature to study such systems, the family of schemes falling under the semiclassical approximation has received a lot of interest. We examine the validity of some of these schemes through a comparison between their predictions and exact numerical calculations of certain observables in small systems. We identify their domain of validity and find it to be rather limited. In addition we also examine the validity of an approach, introduced in the context of exciton transport in molecular crystals, known as the memory function approach; this memory approach is shown to work remarkably well. Applications to various interesting systems and experiments, highlighting the comparison between the memory function approach, the exact solution, and the semiclassical approach are displayed, with the result that the memory function approach is found to be almost always better than the semiclassical approximation. We present arguments and models that help bridge the two approaches.; A semiclassical analysis of the thermal stability of nonlinear localized structures such as Davydov solitons is undertaken. Extensions of previous work to extended systems confirm earlier results about the dual nature of temperature. Curious behaviour is identified at low temperatures.; The interplay between initial phases and nonlinearity in small quantum systems is studied. The surprising and counter-intuitive conclusion presented is that with a proper choice of initial phases, an initially delocalized state is more likely to become self-trapped than an initially localized one. The effect of complex initial phases is studied, and an analogy between the quantum nonlinear dimer and a linear nondegenerate dimer is made in order to understand essential self-trapping effects.; Two miscellaneous results are also presented. The first steps towards a fully quantum-mechanical rotational polaron, previously introduced semiclassically, are taken through the study of a quantum-mechanical rotational oscillator. Also, a surprising connection between dynamic localization in crystals and trapping in two-level atoms is presented. |
