Using Gutzwiller's semiclassical periodic-orbit theory, we demonstrate universal behavior of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in establishing the full correlator such that its Fourier transform, the spectral form factor, is determined for all times, below and above the Heisenberg time. We cover dynamics with and without time-reversal invariance (from the orthogonal and unitary symmetry classes). A key step in our reasoning is to sum the periodic-orbit expansion in terms of a matrix integral, like the one known from the sigma model of random matrix theory.
Abstract In recent years, the importance of mobile devices has increased for education in general and more specifically for science and mathematics education. In the classroom, approaches for teaching with mobile devices include using student-owned devices (“bring your own device”; BYOD approach) or using school-owned devices from central pools (POOL approach). While many studies point out features of mobile learning and BYOD that are conducive to learning, a research gap can be identified in the analysis of effects of mobile device access concepts on teaching–learning processes. Thus, this study aimed to empirically compare BYOD and POOL approaches in terms of learning performance and cognitive performance (subject knowledge development, cognitive load, concentration performance). Furthermore, the analyses included specific characteristics and preconditions (gender, socioeconomic status, fear of missing out, problematic smartphone use). A quasi-experimental study (two groups) was conducted in year 8 and 9 physics classes ( N = 339 students) in which smartphones are used for different purposes. The present data show no group differences between the BYOD and the POOL approach in the group of learners with respect to subject knowledge development, cognitive load, and concentration performance. However, individual findings in subsamples indicate that the POOL approach may be beneficial for certain learners (e.g., learners with low fear of missing out or learners tending toward problematic smartphone use). For school practice, these results indicate that organizational, economic, and ecological aspects appear to be the main factors in deciding about the mobile device access concept.
The field of Quantum Information Science and Technology (QIST) is booming. Due to this, many new educational courses and university programs are needed in order to prepare a workforce for the developing industry. Owing to its specialist nature, teaching approaches in this field can suffer with being disconnected from the substantial degree of science education research which aims to support the best approaches to teaching in STEM fields. In order to connect these two communities with a pragmatic and repeatable methodology, we have synthesised this educational research into a decision-tree based theoretical model for the transformation of QIST curricula, intended to provide a didactical perspective for practitioners. The QCTF consists of four steps: 1. choose a topic, 2. choose one or more targeted skills, 3. choose a learning goal and 4. choose a teaching approach that achieves this goal. We show how this can be done using an example curriculum and more specifically quantum teleportation as a basic concept of quantum communication within this curriculum. By approaching curriculum creation and transformation in this way, educational goals and outcomes are more clearly defined which is in the interest of the individual and the industry alike. The framework is intended to structure the narrative of QIST teaching, and with future testing and refinement it will form a basis for further research in the didactics of QIST.
In diesem Artikel wird ein Zugang zur Quantenphysik vorgestellt, der auf dem einfachsten moglichen Quantensystem basiert – dem Qubit. Dabei wird demonstriert, wie viele der zentralen Prinzipien der Quantenphysik – insbesondere das Uberlagerungsprinzip, das stochastische Verhalten, die Zustandsanderung bei Messungen, sowie die Heisenberg’sche Unscharferelation, mit Hilfe von Bildern und einfacher Mathematik den Schulern zuganglich gemacht werden konnen. Groser Wert wird dabei auf die Entwicklung von Visualisierungen gelegt, wobei neben den abstrakten Eigenschaften eines Qubits auch verschiedene physikalische Realisierungen des Qubits im Detail vorgestellt werden. Abschliesend werden noch Anwendungen der vorgestellten Prinzipien, insbesondere im Bereich der Quantenkryptographie, diskutiert.
What is the origin of quantum randomness? Why does the deterministic, unitary time development in Hilbert space (the ‘4π-realm’) lead to a probabilistic behaviour of observables in space-time (the ‘2π-realm’)? We propose a simple topological model for quantum randomness. Following Kauffmann, we elaborate the mathematical structures that follow from a distinction(A,B) using group theory and topology. Crucially, the 2:1-mapping from SL(2,C) to the Lorentz group SO(3,1) turns out to be responsible for the stochastic nature of observables in quantum physics, as this 2:1-mapping breaks down during interactions. Entanglement leads to a change of topology, such that a distinction between A and B becomes impossible. In this sense, entanglement is the counterpart of a distinction (A,B). While the mathematical formalism involved in our argument based on virtual Dehn twists and torus splitting is non-trivial, the resulting haptic model is so simple that we think it might be suitable for undergraduate courses and maybe even for High school classes.
Quantum mechanics is one of the pillars of modern physics, however rather difficult to teach at the introductory level due to the conceptual difficulties and the required advanced mathematics. Nevertheless, attempts to identify relevant features of quantum mechanics and to put forward concepts of how to teach it have been proposed.1–8 Here we present an approach to quantum physics based on the simplest quantum mechanical system—the quantum bit (qubit).1 Like its classical counterpart—the bit—a qubit corresponds to a two-level system, i.e., some system with a physical property that can admit two possible values. While typically a physical system has more than just one property or the property can admit more than just two values, in many situations most degrees of freedom can be considered to be fixed or frozen. Hence a variety of systems can be effectively described as a qubit. For instance, one may consider the spin of an electron or atom, with spin up and spin down as two possible values, and where other properties of the particle such as its mass or its position are fixed. Further examples include the polarization degree of freedom of a photon (horizontal and vertical polarization), two electronic degrees of freedom (i.e., two energy levels) of an atom, or the position of an atom in a double well potential (atom in left or right well). In all cases, only two states are relevant to describe the system.
In diesem Artikel wird der Zugang zur Quantenphysik uber das einfachst mogliche Modellsystem, das Qubit, erweitert zu der Kombination von zwei Qubits. Dabei tritt erstmals das fur die Quantenphysik zentrale Konzept der Verschrankung auf, welches nicht nur seltsame Eigenschaften der Quantenphysik illustriert, sondern auch der Schlussel zum Verstandnis von modernen Anwendungen der Quantenphysik ist. Ahnlich wie im Falle des einzelnen Qubits wird dabei versucht, die Grundprinzipien von Verschrankung und deren Anwendung mit Hilfe einfacher Mathematik und Bilder zu vermitteln, wobei Visualisierungen eine zentrale Rolle spielen. Die behandelten Themen umfassen verschrankte Zustande, Operationen und Messungen. Die moglichen physikalischen Realisierungen und Anwendungen, insbesondere im Bereich der Quanteninformation, werden hier kurz angesprochen, und in einer weiteren Publikation vertieft diskutiert.
In der Quantenoptik existieren Lehrangebote mit Einzelphotonenquellen, die zentrale Konzepte der Quantenphysik wie Verschrankung fur Lernende im Experiment erfahrbar machen sollen. Die theoretische Modellierung abstrakter Konzepte und deren Interpretation bei der Anwendung auf das reale Experiment stellen hierbei jedoch eine Herausforderung fur Lernende dar. Daher stellt sich bei quantenoptischen Experimenten aus didaktischer Sicht in besonderem Mase die Frage nach Gestaltungsprinzipien, die einen integrativen Umgang mit Reprasentationen auf verschiedenen Darstellungsebenen ermoglichen und die Handlungsebene einbeziehen. Im Projekt MiReQu soll erstmals geklart werden, ob und wie die Lucke zwischen experimenteller und abstrakter Modellebene durch integrativen Einsatz von Mixed Reality Lernumgebungen im Kontext von Praktikumsversuchen zu verschrankten Photonen verkleinert werden kann. Schwerpunkte bilden die Entwicklung passgenauer virtueller Erkenntnisinstrumente und die empirische Untersuchung von erweiterten Gestaltungsprinzipien des multimedialen Lernens.
Abstract Quantum technology is an emerging field of physics and engineering and important applications are expected in quantum computing, quantum sensing, quantum cryptography, quantum simulation, and quantum metrology. Thus the need for education in this field is increasing, while still remaining challenging. While the need for basic education in quantum physics is accepted in many countries, the possibilities still are limited. Concerning fundamental topics such as the superposition principle and complementarity, on the one hand, a large variety of simulations and animations are available. However, single-photon experiments are still beyond reach for any school, due to costs and technical difficulties. A promising approach seems to be a combination of cheap, easy-to-use and modular experimental kits for school which allow for wave optical experiments, in combination with quantum optical simulations. In the present article, we focus on the modularity and accessibility of an experimental kit based on 3D-printed ‘Optic Cubes’, which allow for a large variety of experiments in high school.
Parametric energy-level correlation describes the response of the energy-level statistics to an external parameter such as the magnetic field. Using semiclassical periodic-orbit theory for a chaotic system, we evaluate the parametric energy-level correlation depending on the magnetic field difference. The small-time expansion of the spectral form factor $K(\tau)$ is shown to be in agreement with the prediction of parameter dependent random-matrix theory to all orders in $\tau$.
