Subdiffusion of nonlinear waves in quasiperiodic potentials

19 p.

Learning to perceive in the sensor motor approach: Piaget's theory of equilibration interpreted dynamically

Learning to perceive is faced with a classical paradox: if understanding is required for perception, how can we learn to perceive something new, something we do not yet understand? According to the sensorimotor approach, perception involves mastery of regular sensorimotor co-variations that depend on the agent and the environment, also known as the "laws" of sensorimotor contingencies (SMCs). In this sense, perception involves enacting relevant sensorimotor skills in each situation. It is important for this proposal that such skills can be learned and refined with experience and yet up to this date, the sensorimotor approach has had no explicit theory of perceptual learning. The situation is made more complex if we acknowledge the open-ended nature of human learning. In this paper we propose Piaget's theory of equilibration as a potential candidate to fulfill this role. This theory highlights the importance of intrinsic sensorimotor norms, in terms of the closure of sensorimotor schemes. It also explains how the equilibration of a sensorimotor organization faced with novelty or breakdowns proceeds by re-shaping pre-existing structures in coupling with dynamical regularities of the world. This way learning to perceive is guided by the equilibration of emerging forms of skillful coping with the world. We demonstrate the compatibility between Piaget's theory and the sensorimotor approach by providing a dynamical formalization of equilibration to give an explicit micro-genetic account of sensorimotor learning and, by extension, of how we learn to perceive. This allows us to draw important lessons in the form of general principles for open-ended sensorimotor learning, including the need for an intrinsic normative evaluation by the agent itself. We also explore implications of our micro-genetic account at the personal level.

One-dimensional potential for image-potential states on graphene

In the framework of dielectric theory, the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-potential states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by numerically solving the one-dimensional Schrodinger equation. The imagepotential state wave functions accumulate most of their probability outside the slab. We find that the random phase approximation (RPA) for the nonlocal dielectric function yields a superior description for the potential inside the slab, but a simple Fermi-Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters: the slab width and the electronic density. The theoretical calculations are compared with experimental results for the work function and image-potential states obtained by two-photon photoemission.