Interacting quantum walk on a graph

We introduce an elementary quantum system consisting of a set of spins on a graph and a particle hopping between its nodes. The quantum state is build sequentially, applying a unitary transformation that couples neighboring spins and, at a node, the local spin with the particle. We observe the relaxation of the system towards a stationary paramagnetic or ferromagnetic state, and demonstrate that it is related to eigenvectors thermalization and random matrix statistics. The relation between these macroscopic properties and interaction generated entanglement is discussed.Comment: 15 pages, 11 figures (v2 extended version

Skyrmion collapse

We investigate the topological change of a Belavin-Polyakov skyrmion under the action of a spin-polarized current. The dynamics is described by the Schr\"odinger equation for the electrons carrying the current coupled to the Landau-Lifshitz equation for the evolution of the magnetic texture in a square lattice. We show that the addition of an exchange dissipation term, tends to smooth the transition from the skyrmion state to the ferromagnetic state. We demonstrate that this topological change, in the continuum dissipationless limit, can be described as a self-similar finite-time singularity by which the skyrmion core collapses.Comment: 9 pages, 6 figures; v2. discussion added (the title of the published version is "Skyrmion to ferromagnetic state transition: A description of the topological change as a finite-time singularity in the skyrmion dynamics"

Edge states in a two-dimensional quantum walk with disorder

We investigate the effect of spatial disorder on the edge states localized at the interface between two topologically different regions. Rotation disorder can localize the quantum walk if it is strong enough to change the topology, otherwise the edge state is protected. Nonlinear spatial disorder, dependent on the walker's state, attracts the walk to the interface even for very large coupling, preserving the ballistic transport characteristic of the clean regime.Comment: extended new version; 10 pages, 10 figure

Topological changes of two-dimensional magnetic textures

We investigate the interaction of magnetic vortices and skyrmions with a spin-polarized current. In a square lattice, fixed classical spins and quantum itinerant electrons, evolve according to the coupled Landau-Lifshitz and Schr\"odinger equations. Changes in the topology occur at microscopic time and length scales, and are shown to be triggered by the nucleation of a nontrivial electron-spin structure at the vortex core.Comment: See supplementary material (high resolution figures and movies) https://drive.google.com/folderview?id=0By4j_RJ9SKLpQ2R5UklXLURvbEE&usp=sharing --- v2: Extended versio