Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz

The exactly solvable Lieb-Liniger model of interacting bosons in one-dimension has attracted renewed interest as current experiments with ultra-cold atoms begin to probe this regime. Here we numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss the novel features of the solutions, and how they deviate from the well-known string solutions [H. B. Thacker, Rev. Mod. Phys.\ \textbf{53}, 253 (1981)] at finite densities. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Finally we compare our results to those of exact diagonalization of the many-body Hamiltonian in a truncated basis. We also present excited state solutions and the excitation spectrum for the repulsive 1D Bose gas on a ring.Comment: 13 pages, 12 figure

Den "guten" Unterricht im Blick. Oder: Warum die Allgemeine Didaktik unersetzlich ist

Trotz interdisziplinärer Verschiebungen und bildungspolitischer Veränderungen, die die Position der Allgemeinen Didaktik immer wieder infrage stellen, wird im vorliegenden Beitrag dargelegt, dass sie die zentrale Disziplin der Lehrerinnen- und Lehrerbildung war, ist und auch in Zukunft sein kann. Entscheidend dafür ist zum einen eine Rückbesinnung auf bildungstheoretische Traditionen und zum anderen eine Neuorientierung in Richtung empirischer Bildungsforschung. Beide Perspektiven sind notwendig, um die Frage nach einem „guten“ Unterricht umfassend beleuchten zu können. Aufgrund ihres wissenschaftstheoretischen und wissenschaftsmethodischen Zugangs und Anspruchs bietet die Allgemeine Didaktik ein disziplinäres Alleinstellungsmerkmal für diese zukunftsweisende Herausforderung in der Lehrerinnen- und Lehrerbildung.&nbsp

Integral representations for correlation functions of the XXZ chain at finite temperature

We derive a novel multiple integral representation for a generating function of the \s^z-\s^z correlation functions of the spin-\2 XXZ chain at finite temperature and finite, longitudinal magnetic field. Our work combines algebraic Bethe ansatz techniques for the calculation of matrix elements with the quantum transfer matrix approach to thermodynamics.Comment: 33 pages, 2 figures, v2: 2 typos corrected, 1 figure adde

Analysis of the accuracy of ten algorithms for orientation estimation using inertial and magnetic sensing under optimal conditions: One size does not fit all

The orientation of a magneto and inertial measurement unit (MIMU) is estimated by means of sensor fusion algorithms (SFAs) thus enabling human motion tracking. However, despite several SFAs implementations proposed over the last decades, there is still a lack of consensus about the best performing SFAs and their accuracy. As suggested by recent literature, the filter parameters play a central role in determining the orientation errors. The aim of this work is to analyze the accuracy of ten SFAs while running under the best possible conditions (i.e., their parameter values are set using the orientation reference) in nine experimental scenarios including three rotation rates and three commercial products. The main finding is that parameter values must be specific for each SFA according to the experimental scenario to avoid errors comparable to those obtained when the de-fault parameter values are used. Overall, when optimally tuned, no statistically significant differ-ences are observed among the different SFAs in all tested experimental scenarios and the absolute errors are included between 3.8 deg and 7.1 deg. Increasing the rotation rate generally leads to a significant performance worsening. Errors are also influenced by the MIMU commercial model. SFA MATLAB implementations have been made available online

A Levenberg-Marquardt Algorithm for Sparse Identification of Dynamical Systems

Low complexity of a system model is essential for its use in real-time applications. However, sparse identification methods commonly have stringent requirements that exclude them from being applied in an industrial setting. In this article, we introduce a flexible method for the sparse identification of dynamical systems described by ordinary differential equations. Our method relieves many of the requirements imposed by other methods that relate to the structure of the model and the dataset, such as fixed sampling rates, full state measurements, and linearity of the model. The Levenberg-Marquardt algorithm is used to solve the identification problem. We show that the Levenberg-Marquardt algorithm can be written in a form that enables parallel computing, which greatly diminishes the time required to solve the identification problem. An efficient backward elimination strategy is presented to construct a lean system model.publishedVersio

Learning-based Robust Model Predictive Control for Sector-bounded Lur'e Systems

For dynamical systems with uncertainty, robust controllers can be designed by assuming that the uncertainty is bounded. The less we know about the uncertainty in the system, the more conservative the bound must be, which in turn may lead to reduced control performance. If measurements of the uncertain term are available, this data may be used to reduce the uncertainty in order to make bounds as tight as possible. In this paper, we consider a linear system with a sector-bounded uncertainty. We develop a model predictive control algorithm to control the system, and use a weighted Bayesian linear regression model to learn the least conservative sector condition using measurements collected in closed-loop. The resulting robust model predictive control algorithm therefore reduces the conservativeness of the controller, and provides probabilistic guarantees of asymptotic stability and constraint satisfaction. The efficacy of the proposed method is shown in simulation.publishedVersio