• localization
• solitons
• kinks
• condensed matter theory
• classical physics

Localization is a central paradigm of modern condensed matter theory. Typically, it occurs when transport processes of a physical system are for some reasons suppressed. In this case the system can fail to smoothen out an initial macroscopic inhomogeneity in local densities of conserved quantities (e.g. in the energy density).

The best known and most studied phenomena of localization are those induced by disorder.
This category includes the Anderson localization, i.e. the localization of an electron moving in a lattice with random potentials on the lattice sites. In this thesis, I focus on a simple yet paradigmatic example of localization occurring in the classical world.
This is the localization of topological excitations, usually called kinks, in discrete classical models. In (1 + 1)-dimensional classical field theories, kinks are solitonic, particle-like excitations, whose topological nature is strictly related to the presence of multiple degenerate ground-states.

In discrete models kinks cannot move freely along the system, because of the lack of the continuous translational symmetry due to the lattice. Thus, in its motion the kink experiences an effective periodic potential, known as Peierls-Nabarro (PN) potential. Furthermore, the kink motion is coupled with the non-topological excitation modes of the system, the phonons. The combined effect of these phenomena is that a moving kink can lose energy through a process of phonon emission, by a sort of radiation damping, until it becomes trapped in the PN potential. In this thesis I study this kind of dynamical localization in the phi4 discrete model and in the classical Ising model.