Multi-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States

We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral equation for N-coupled channels and show that, unlike to the case of the radial inverse scattering problem, the information on the bound state energies and asymptotic normalization constants can be inferred from the reflection coefficient matrix alone. Thus, given this matrix, the Marchenko inverse scattering procedure can provide us with a unique multi-channel potential. The relationship to supersymmetric partner potentials as well as possible applications are discussed. The integral equation has been implemented numerically and applied to several schematic examples showing the characteristic features of multi-channel systems. A possible application of the formalism to technological problems is briefly discussed.Comment: 19 pages, 5 figure

Combining brain-computer interfaces and assistive technologies: state-of-the-art and challenges

In recent years, new research has brought the field of EEG-based Brain-Computer Interfacing (BCI) out of its infancy and into a phase of relative maturity through many demonstrated prototypes such as brain-controlled wheelchairs, keyboards, and computer games. With this proof-of-concept phase in the past, the time is now ripe to focus on the development of practical BCI technologies that can be brought out of the lab and into real-world applications. In particular, we focus on the prospect of improving the lives of countless disabled individuals through a combination of BCI technology with existing assistive technologies (AT). In pursuit of more practical BCIs for use outside of the lab, in this paper, we identify four application areas where disabled individuals could greatly benefit from advancements in BCI technology, namely,“Communication and Control”, “Motor Substitution”, “Entertainment”, and “Motor Recovery”. We review the current state of the art and possible future developments, while discussing the main research issues in these four areas. In particular, we expect the most progress in the development of technologies such as hybrid BCI architectures, user-machine adaptation algorithms, the exploitation of users’ mental states for BCI reliability and confidence measures, the incorporation of principles in human-computer interaction (HCI) to improve BCI usability, and the development of novel BCI technology including better EEG devices

Detecting unambiguously non-Abelian geometric phases with trapped ions

We propose for the first time an experimentally feasible scheme to disclose the noncommutative effects induced by a light-induced non-Abelian gauge structure with trapped ions. Under an appropriate configuration, a true non-Abelian gauge potential naturally arises in connection with the geometric phase associated with two degenerated dark states in a four-state atomic system interacting with three pulsed laser fields. We show that the population in atomic state at the end of a composed path formed by two closed loops $C_1$ and $C_2$ in the parameter space can be significantly different from the composed counter-ordered path. This population difference is directly induced by the noncommutative feature of non-Abelian geometric phases and can be detected unambiguously with current technology.Comment: 6 page

Effects of P300-based BCI use on reported presence in a virtual environment

Brain-computer interfaces (BCIs) are becoming more and more popular as an input device for virtual worlds and computer games. Depending on their function, a major drawback is the mental workload associated with their use and there is significant effort and training required to effectively control them. In this paper, we present two studies assessing how mental workload of a P300-based BCI affects participants" reported sense of presence in a virtual environment (VE). In the first study, we employ a BCI exploiting the P300 event-related potential (ERP) that allows control of over 200 items in a virtual apartment. In the second study, the BCI is replaced by a gaze-based selection method coupled with wand navigation. In both studies, overall performance is measured and individual presence scores are assessed by means of a short questionnaire. The results suggest that there is no immediate benefit for visualizing events in the VE triggered by the BCI and that no learning about the layout of the virtual space takes place. In order to alleviate this, we propose that future P300-based BCIs in VR are set up so as require users to make some inference about the virtual space so that they become aware of it,which is likely to lead to higher reported presence

Relevance of pseudospin symmetry in proton-nucleus scattering

The manifestation of pseudospin-symmetry in proton-nucleus scattering is discussed. Constraints on the pseudospin-symmetry violating scattering amplitude are given which require as input cross section and polarization data, but no measurements of the spin rotation function. Application of these constraints to p-58Ni and p-208Pb scattering data in the laboratory energy range of 200 MeV to 800 MeV, reveals a significant violation of the symmetry at lower energies and a weak one at higher energies. Using a schematic model within the Dirac phenomenology, the role of the Coulomb potential in proton-nucleus scattering with regard to pseudospin symmetry is studied. Our results indicate that the existence of pseudospin-symmetry in proton-nucleus scattering is questionable in the whole energy region considered and that the violation of this symmetry stems from the long range nature of the Coulomb interaction.Comment: 22 pages including 9 figures, correction of 1 reference, revision of abstract and major modification of chapter 4, Fig. 6, and Fig. 7; addition of Fig. 8 and Fig.

Violation of pseudospin symmetry in nucleon-nucleus scattering: exact relations

An exact determination of the size of the pseudospin symmetry violating part of the nucleon-nucleus scattering amplitude from scattering observables is presented. The approximation recently used by Ginocchio turns out to underestimate the violation of pseudospin symmetry. Nevertheless the conclusion of a modestly broken pseudospin symmetry in proton-208Pb scattering at EL=800MeV remains valid.Comment: 8 pages, 2 figure