Many-Body Expansion Dynamics of a Bose-Fermi Mixture Confined in an Optical Lattice

We unravel the correlated non-equilibrium dynamics of a mass balanced Bose-Fermi mixture in a one-dimensional optical lattice upon quenching an imposed harmonic trap from strong to weak confinement. Regarding the system's ground state, the competition between the inter and intraspecies interaction strength gives rise to the immiscible and miscible phases characterized by negligible and complete overlap of the constituting atomic clouds respectively. The resulting dynamical response depends strongly on the initial phase and consists of an expansion of each cloud and an interwell tunneling dynamics. For varying quench amplitude and referring to a fixed phase a multitude of response regimes is unveiled, being richer within the immiscible phase, which are described by distinct expansion strengths and tunneling channels.Comment: 13 pages, 7 figure

Design and Validation of Embedded Real-Time Applications

International audienceThe design and validation of embedded real-time applications is challenging, especially when legacy sub-systems are involved. To account for the uncertainty in system-development at early design stages we use statistical modelling and discrete event simulation to perform sensitivity analysis. These analysis results provide vital information about the system characteristics and indicate usage scenarios where the behaviour of the system differs significantly from the average case. Based on the simulation results and the initial system requirements a usage model for the application is being set up. The model represents the requirements in an unambiguous and traceably correct manner. For each possible path through the model, considering stimuli and their timing, a unique system reaction is defined. This way the requirements are clarified. The usage model allows the derivation of test cases that can be used in the design phase to validate the model and in the acceptance phase to test the final system. Through the combination of the simulation results and the usage modelling we are able to:•identify critical system conditions.•validate the system design w.r.t. the usage modelThe proposed methods are currently applied in both the design and validation of safety critical applications

The Pauli equation with complex boundary conditions

We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. A special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T.Comment: 16 pages, 4 figure

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

PT-symmetric models in curved manifolds

We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.Comment: 37 pages, PDFLaTeX with 11 figure

From multiple perspectives to shared understanding

The aim of this study was to explore how learners operating in a small group reach shared understanding as they work out joint research questions and build a theoretical framework and to identify the resources and tools they used in the process. The learners’ own interpretations of their group activities and learning were also taken into account. The data, consisting of group discussions and the documents produced by the group, were subjected to a qualitative content analysis. The group members employed a variety of resources and tools to exchange their individual perspectives and achieve shared understanding. Summaries of relevant literature laid a foundation for the group’s theoretical discussions. Reflective comparisons between their book knowledge and their personal experiences of online interaction and collaboration were frequent, suggesting that such juxtapositions may have enhanced their learning by intertwining the content to be mastered and the activities entailed by this particular content

Implementing concurrent-training and nutritional strategies in professional football: a complex challenge for coaches and practitioners

Purpose: To study concurrent-training (CT) and nutritional practices within a professional soccer team. Methods: Twenty-one professional football players competing in the English professional league participated in this study (mean ± standard deviations [M ± SD] 26 ± 4 years, stature 1.84 ± 0.1 m, body mass 83 ± 7 kg, VO2max; 58 ± 3 ml · kg−1 · min−1). A range of internal and external training metrics, the organisation of CT (training sequence, training rest period between bouts) and the nutritional intake around CT (timing, type and quantity) was collected for 10 weeks. Results: CT; n = 17 (endurance-training [ET] + resistance-training [RT]; n = 11; RT + ET; n = 6) rest period between bouts was not consistent and varied depending on the sequence of CT (RT + ET, 75 ± 48 min; ET + RT; 60 ± 5 min; P = 0.04). sRPE of football-specific ET was higher in RT + ET (RT + ET, 7 ± 1; ET + RT, 6 ± 1; P = 0.05). The timing of meals around training was influenced by the organisation of CT. Subsequently, CHO consumption before training session one was significantly less in RT + ET (CHO 0.10 ± 0.5 g · kg−1 vs. CHO 0.45 ± 0.2 g · kg−1). Conclusion: The present data demonstrate that the organisation of CT (i.e., exercise order and/or recovery time between bouts) and nutrition (i.e., timing of meal intake) can be unsystematic in the applied environment. The organisation of training and nutrition might influence the players’ ability to perform high-intensity actions in secondary training sessions and could potentially impact acute metabolic processes associated with muscle recovery and muscle adaptation

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics.Comment: version accepted for publication in J. Math. Phys.: criterion excluding basis property (Proposition 6) added, unbounded time-evolution discussed, new reference