Magneto-optical and Magneto-electric Effects of Topological Insulators in Quantizing Magnetic Fields

We develop a theory of the magneto-optical and magneto-electric properties of a topological insulator thin film in the presence of a quantizing external magnetic field. We find that low-frequency magneto-optical properties depend only on the sum of top and bottom surface Dirac-cone filling factors $\nu_{\mathrm{T}}$ and $\nu_{\mathrm{B}}$, whereas the low-frequency magneto-electric response depends only on the difference. The Faraday rotation is quantized in integer multiples of the fine structure constant and the Kerr effect exhibits a $\pi/2$ rotation. Strongly enhanced cyclotron-resonance features appear at higher frequencies that are sensitive to the filling factors of both surfaces. When the product of the bulk conductivity and the film thickness in $e^2/h$ units is small compared to $\alpha$, magneto-optical properties are only weakly dependent on accidental doping in the interior of the film.Comment: 4 page

Giant Magneto-optical Kerr Effect and Universal Faraday Effect in Thin-film Topological Insulators

Topological insulators can exhibit strong magnetoelectric effects when their time-reversal symmetry is broken. In this Letter we consider the magneto-optical Kerr and Faraday effects of a topological insulator thin film weakly exchange-coupled to a ferromagnet. We find that its Faraday rotation has a universal value at low-frequencies, $\theta_{\mathrm{F}} = \mathrm{tan}^{-1}\,\alpha$ where $\alpha$ is the vacuum fine structure constant, and that it has a giant Kerr rotation $\theta_{\mathrm{K}} = \pi/2$. These properties follow from a delicate interplay between thin-film cavity confinement and the surface Hall conductivity of a topological insulator's helical quasiparticles.Comment: 5 pages, 4 figure

Where does Volatility and Return Come From? The Case of Asian ETFs

We analyze return and volatility of Asian iShares traded in the U.S. The difference in trading schedules between the U.S. and Asia offers a unique market setting that allows us to distinguish various return and volatility sources. We find Asian ETFs have higher overnight volatility than daytime volatility, explained by public information released during each local market’s trading session. Local Asian markets also play an important role in determining each Asian ETF return. Nonetheless, returns for these funds are highly correlated with U.S. markets, indicative of the effects of investor sentiment and location of trade. Finally, returns in the U.S. market Granger-cause returns in all six Asian markets analyzed.International ETF; iShares; returns; variance; diversification

Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces

We develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces with respect to the 2-Wasserstein distance. We also discuss the overdamped limit to a nonlocal equation used in the modelling of granular media with respect to the 2-Wasserstein distance, and provide rigorous proofs for particular examples in one spatial dimension

An analytical framework for a consensus-based global optimization method

In this paper we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the convergence to the global minimizer for a large class of functions. Theoretical results on consensus estimates are then illustrated by numerical simulations where variants of the method including nonlinear diffusion are introduced