A Langevin canonical framework for a chiral two--level system coupled to a bath of harmonic oscillators is developed within a coupling scheme different to the well known spin-boson model. Thermal equilibrium values are reached at asymptotic times by
solving the corresponding set of non--linear coupled equations in a Markovian regime. In particular, phase difference thermal values (or, equivalently, the so--called coherence factor) and heat capacity through energy fluctuations are obtained and discussed in terms of tunneling rates and asymmetries.
The trajectories of a qubit dynamics over the two-sphere are shown to be geodesics of certain Riemannian or physically-sound Lorentzian manifolds, both in the non-dissipative and dissipative formalisms, when using action-angle variables. Several aspe
cts of the geometry and topology of these manifolds (qubit manifolds) have been studied for some special physical cases.
A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative fea
tures, such as reduction of the asymmetry with increased incidence energy as well as asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to soft corrugated potentials. Analytic expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.
