Non-Equilibrium Random Matrix Theory : Transition Probabilities

In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large $N$ limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.Comment: REVTeX, 5 pages, 2 figure

Topological Polaritons in a Quantum Spin Hall Cavity

We study the topological structure of matter-light excitations, so called polaritons, in a quantum spin Hall insulator coupled to photonic cavity modes. We identify a topological invariant in the presence of time reversal (TR) symmetry, and demonstrate the existence of a TR-invariant topological phase. We find protected helical edge states with energies below the lower polariton branch and characteristic uncoupled excitonic states, both detectable by optical techniques. Applying a Zeeman field allows us to relate the topological index to the double coverage of the Bloch sphere by the polaritonic pseudospin.Comment: 5 pages + 4 pages supplemental material, 3 figure

Hierarchical Axion Inflation

We propose a new field theory mechanism for generating an effective trans-Planckian decay constant from sub-Planckian ones. Using the minimal two axions and a hierarchy between two axion decay constants is sufficient for realizing inflation through non-perturbative effects only and with minimal tuning. The inflationary motion is kept entirely within a sub-Planckian domain. We outline possible strategies of embedding the model in a string theory setup.Comment: REVTeX, 5 pages, 2 figures, added refs, changed the numerical parameter values of the stringy example, removed ED1's from the superpotentia

Financial engineering of western equities, derivatives and fixed income into Shariah compliant special purpose vehicles for Islamic investors

The evolution of Islamic finance has witnessed global expansion rooted in Shariah principles. SPVs serve as crucial mechanisms facilitating diverse, Shariah-compliant financial arrangements. To enhance profiles, expectations and diversity, Islamic investors seek entry into Western markets, employing innovative financial engineering tools as Equity Murabaha’s, Islamic Profit Rate Swaps, and various sukuk types (al-ijara, al-murabaha and al-wakalah). This study delves into the imperative strategy, Shariah alignment and the potential augmentation of prospects for Western Financial in Islamic Finance systems. It represents a conceptual academic exploration at the crossroads of Western Finance assimilation and integration into the Islamic Finance landscapes

Experimental realization of a momentum-space quantum walk

We report on a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. Each step of the walk consists of a coin toss (a microwave pulse) followed by a unitary shift operator (a resonant ratchet pulse). We carry out a comprehensive experimental study on the effects of various parameters, including the strength of the shift operation, coin parameters, noise, and initialization of the system on the behavior of the walk. The walk dynamics can be well controlled in our experiment; potential applications include atom interferometry and engineering asymmetric walks.Comment: 11 pages, 11 figure

Middle and elementary school students’ changes in self-determined motivation in a basketball unit taught using the Tactical Games Model

Studies examining student motivation levels suggest that this is a significant factor in students’ engagement in physical education and may be positively affected when teachers employ alternative pedagogical models such as game-centered approaches (GCAs). The aim of this study was to investigate changes in self-determined motivation of students as they participated in a GCA-basketball unit taught using the Tactical Games Model (TGM). Participants were 173 students (84 girls), 79 middle school (45 girls) and 94 (39 girls) elementary school students from four seventh and five fourth/fifth grade co-educational classes. Two teachers taught 32 (middle) and 33 (elementary) level one TGM basketball lessons. Need satisfaction and self-determined motivation data were collected using a previously validated instrument, while lesson context and teacher behavior data were recorded using systematic observation instruments. Repeated measures MANOVAs were employed to examine pre-posttest differences. Results revealed a significant main effect for time in need satisfaction for both middle (relatedness increased) and elementary school students (autonomy decreased) and a significant main effect in self-determined motivation for middle school students only (introjected regulation, external regulation, and amotivation all increased). Approximately 48%/42% (middle/elementary) of lesson time was game play, 22%/22% skill practice, 17%/17% management, and 13%/19% knowledge. The primary teacher behaviors used were instruction, management, specific observation, corrective feedback and modelling. Results indicate that it is important for future research to pay greater attention to the contextual factors associated with the application of the TGM, such as the students’ previous exposure to TGM lessons, and the teachers’ training and experience in utilizing the TGM. Indeed, results of the present study demonstrate that a longer-term commitment to the TGM is necessary to reduce controlling teacher behaviors, which will lead to positive changes in students’ need satisfaction and self-determined motivation. Future research is therefore needed to embrace this challenge to provide an increased evidence-base for GCAs such as the TGM

Estimation of gloss from rough surface parameters

Gloss is a quantity used in the optical industry to quantify and categorize materials according to how well they scatter light specularly. With the aid of phase perturbation theory, we derive an approximate expression for this quantity for a one-dimensional randomly rough surface. It is demonstrated that gloss depends in an exponential way on two dimensionless quantities that are associated with the surface randomness: the root-mean-square roughness times the perpendicular momentum transfer for the specular direction, and a correlation function dependent factor times a lateral momentum variable associated with the collection angle. Rigorous Monte Carlo simulations are used to access the quality of this approximation, and good agreement is observed over large regions of parameter space.Comment: 5 page