Boltzmann Collision Term

We derive the Boltzmann equation for scalar fields using the Schwinger-Keldysh formalism. The focus lies on the derivation of the collision term. We show that the relevant self-energy diagrams have a factorization property. The collision term assumes the Boltzmann-like form of scattering probability times statistical factors for those self-energy diagrams which correspond to tree level scattering processes. Our proof covers scattering processes with any number of external particles, which come from self-energy diagrams with any number of loops.Comment: 17 pages, 4 figure

Simulation-based Testing for Early Safety-Validation of Robot Systems

Industrial human-robot collaborative systems must be validated thoroughly with regard to safety. The sooner potential hazards for workers can be exposed, the less costly is the implementation of necessary changes. Due to the complexity of robot systems, safety flaws often stay hidden, especially at early design stages, when a physical implementation is not yet available for testing. Simulation-based testing is a possible way to identify hazards in an early stage. However, creating simulation conditions in which hazards become observable can be difficult. Brute-force or Monte-Carlo-approaches are often not viable for hazard identification, due to large search spaces. This work addresses this problem by using a human model and an optimization algorithm to generate high-risk human behavior in simulation, thereby exposing potential hazards. A proof of concept is shown in an application example where the method is used to find hazards in an industrial robot cell

Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting

In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing: given a matrix $X$ formed as the sum of an unknown diagonal matrix and an unknown low rank positive semidefinite matrix, decompose $X$ into these constituents. The second problem we consider is to determine the facial structure of the set of correlation matrices, a convex set also known as the elliptope. This convex body, and particularly its facial structure, plays a role in applications from combinatorial optimization to mathematical finance. The third problem is a basic geometric question: given points $v_1,v_2,...,v_n\in \R^k$ (where $n > k$) determine whether there is a centered ellipsoid passing \emph{exactly} through all of the points. We show that in a precise sense these three problems are equivalent. Furthermore we establish a simple sufficient condition on a subspace $U$ that ensures any positive semidefinite matrix $L$ with column space $U$ can be recovered from $D+L$ for any diagonal matrix $D$ using a convex optimization-based heuristic known as minimum trace factor analysis. This result leads to a new understanding of the structure of rank-deficient correlation matrices and a simple condition on a set of points that ensures there is a centered ellipsoid passing through them.Comment: 20 page

Kondo effect in a one dimensional d-wave superconductor

We derive a solvable resonant-level type model, to describe an impurity spin coupled to zero-energy bound states localized at the edge of a one dimensional d-wave superconductor. This results in a two-channel Kondo effect with a quite unusual low-temperature thermodynamics. For instance, the local impurity susceptibility yields a finite maximum at zero temperature (but no logarithmic-divergence) due to the splitting of the impurity in two Majorana fermions. Moreover, we make comparisons with the Kondo effect occurring in a two dimensional d-wave superconductor.Comment: 9 pages, final version; To be published in Europhysics Letter

Does a Brief Mindfulness Training Enhance Heartfulness in Students? Results of a Pilot Study

(1) Background: There is robust evidence that mindfulness trainings enhance mindfulness as operationalized in Western psychology, but evidence about their effect on aspects of heartfulness is sparse. This study seeks to test whether a brief mindfulness training enhances heart qualities, including self-compassion, gratitude, and the generation of feelings of happiness. (2) Methods: Eighteen students enrolled in a mindfulness training that was offered as part of an interdisciplinary class. The training consisted of five training sessions and four booster sessions of 45 minutes each over the course of nine weeks. Mindfulness was measured with the Five Facet Mindfulness Questionnaire-Short Form (FFMQ-SF) and self-compassion was measured with the Self-Compassion Scale Short Form (SCS-SF). In addition, two items were drawn from the Caring for Bliss Scale (CBS) measuring gratitude and the generation of feelings of happiness in the present moment. Assessments were conducted before the training (pre), after the training (post), and four weeks after the training (follow-up). (3) Results: Results showed that mindfulness, general self-compassion, and generating feelings of happiness increased from pre to post, whereas self-critical attitudes decreased and that these changes were maintained at follow-up. Gratitude increased from pre to post and then decreased from post to follow-up. (4) Conclusions: A brief mindfulness training seems to be beneficial for students to improve mindfulness and aspects of heartfulness, but further research is needed to investigate the effectiveness of the training relative to a cohort or active control group

Micro-SQUID technique for studying the temperature dependence of switching fields of single nanoparticles

An improved micro-SQUID technique is presented allowing us to measure the temperature dependence of the magnetisation switching fields of single nanoparticles well above the critical superconducting temperature of the SQUID. Our first measurements on 3 nm cobalt nanoparticle embedded in a niobium matrix are compared to the Neel Brown model describing the magnetisation reversal by thermal activation over a single anisotropy barrier.Comment: 3 pages, 4 figures; conference proceeding: 1st Joint European Magnetic Symposia (JEMS'01), Grenoble (France), 28th August - 1st September, 200

Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d+1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d+2 orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.Comment: 28 pages, to appear in J. Math. Phy

Stepwise Projection: Toward Brane Setups for Generic Orbifold Singularities

The construction of brane setups for the exceptional series E6,E7,E8 of SU(2) orbifolds remains an ever-haunting conundrum. Motivated by techniques in some works by Muto on non-Abelian SU(3) orbifolds, we here provide an algorithmic outlook, a method which we call stepwise projection, that may shed some light on this puzzle. We exemplify this method, consisting of transformation rules for obtaining complex quivers and brane setups from more elementary ones, to the cases of the D-series and E6 finite subgroups of SU(2). Furthermore, we demonstrate the generality of the stepwise procedure by appealing to Frobenius' theory of Induced Representations. Our algorithm suggests the existence of generalisations of the orientifold plane in string theory.Comment: 22 pages, 3 figure