The First Eigenvalue of the Dirac Operator on Quaternionic Kaehler Manifolds

In a previous paper we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kaehler manifolds. In the present article we show that the only manifolds in the limit case, i.e. the only manifolds where the lower bound is attained as an eigenvalue, are the quaternionic projective spaces. We use the equivalent formulation in terms of the quaternionic Killing equation and show that a nontrivial solution defines a parallel spinor on the associated hyperkaehler manifold.Comment: 19 pages, LaTeX2e, fullpage styl

Personality, personality disorders, and the process of change.

The present paper elaborates a process perspective of change in psychotherapy for personality disorders (PDs). Firstly, the paper reviews the literature of mechanisms of change in treatments of PD, with the main focus on emotional processing and socio-cognitive processing. Secondly, it proposes an illustrative case-series analysis of eight cases, drawn from a mediation analysis conducted within the context of a randomized controlled trial for borderline personality disorder (BPD). As such, cases with good and poor outcomes are compared, as are cases with poor and good intake features and cases with poor and good process markers across treatment. The results illustrate possible pathways to healthy change over the course of four months of treatment, and possible pathways of the absence of change. These results are discussed with regard to three main research perspectives: the combination of qualitative and quantitative methodology in psychotherapy research may be applied to case study research, a neurobehavioral perspective on change may incorporate the individualized experience in the laboratory and therapist responsiveness to patient characteristics may be a core feature of fostering change. Clinical or methodological significance of this article: The present paper illustrates individual pathways to change in personality disorders. It illustrates how coping capacities influence the process of psychotherapy and outcome in personality disorders. It demonstrates the relevance of individualizing treatments for personality disorders. It demonstrates several integrative features of psychotherapy research, in particular the use of neurobehavioral paradigms and the integration of single-case research within randomized controlled trials

Mechanisms of Change in Treatments of Personality Disorders: Introduction to the Special Section.

The present introduction to the Special Section on Mechanisms of Change in Treatments of Personality Disorders explains the value of research focusing on processes of change in psychotherapy by referring to a variety of methodologies. Whereas outcome for these treatments has been repeatedly demonstrated, it remains an open question what the core psychobiological features of change are. Taking a radically empirical perspective, this introduction focuses on patient and therapeutic relationship variables, such as emotional and socio-cognitive processing. The six empirical articles of the Special Section are introduced, as are the three discussions of the Special Section

Spin and rotational symmetries in unrestricted Hartree Fock states of quantum dots

Ground state energies are obtained using the unrestricted Hartree Fock method for up to four interacting electrons parabolically confined in a quantum dot subject to a magnetic field. Restoring spin and rotational symmetries we recover Hund first rule. With increasing magnetic field, crossovers between ground states with different quantum numbers are found for fixed electron number that are not reproduced by the unrestricted Hartree Fock approximation. These are consistent with the ones obtained with more refined techniques. We confirm the presence of a spin blockade due to a spin mismatch in the ground states of three and four electrons.Comment: 16 Pages, 2 figures, accepted for publication on New Journal of Physic

On the "Causality Paradox" of Time-Dependent Density Functional Theory

I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in real time, but also leads to a new expression for the causal exchange-correlation kernel in terms of Berry curvature. Furthermore, I show that all the results that were previously derived from symmetries of the action functional remain valid in the present formulation. Finally, I develop a model functional theory which explicitly demonstrates the workings of the new formulation.Comment: 21 page