On quantum seas

The rules of quantum mechanics are simple and well understood, yet the collective behavior of large numbers of interacting constituents still hosts many mysteries. Even for models built from the simplest of quantum components, namely qubits or equivalently the spin-1/2 magnetic moment of fundamental particles, the collective behavior is hard to compute directly. Effective theories and approximate methods however capture universal properties which depend on the microscopic realization of the system only through a handful of phenomenological parameters. In this thesis we theoretically consider one-dimensional systems by combining exact methods with effective theory. Building on the new insights of nonlinear Luttinger liquid theory we consider spin chains and other systems with a boundary. Furthermore, we study out-of-equilibrium physics related to the famous Quantum Newton’s cradle experiment and adopt and extend effective field theory methods to such non-standard cases. We also present a detailed study of the Au/Ge(001) system of self-organised atomic chains formed by gold deposition on a germanium surface. Combining the detailed experimental investigations of collaborators at the University of Amsterdam and the University of Twente with theoretical reasoning we conclude that the experimental evidence conflicts earlier claims of the system hosting a Tomonaga-Luttinger liquid and the most likely explanation of all observations lies in a two-dimensional scenario with strong disorder and interaction effects.