Quantitative Density under Higher Rank Abelian Algebraic Toral Actions

We generalize Bourgain-Lindenstrauss-Michel-Venkatesh's recent one-dimensional quantitative density result to abelian algebraic actions on higher dimensional tori. Up to finite index, the group actions that we study are conjugate to the action of $U_K$, the group of units of some non-CM number field $K$, on a compact quotient of $K\otimes_{\mathbb Q}\mathbb R$. In such a setting, we investigate how fast the orbit of a generic point can become dense in the torus. This effectivizes a special case of a theorem of Berend; and is deduced from a parallel measure-theoretical statement which effectivizes a special case of a result by Katok-Spatzier. In addition, we specify two numerical invariants of the group action that determine the quantitative behavior, which have number-theoretical significance.Comment: 58 page

Resolving spin, valley, and moir\'e quasi-angular momentum of interlayer excitons in WSe2/WS2 heterostructures

Moir\'e superlattices provide a powerful way to engineer properties of electrons and excitons in two-dimensional van der Waals heterostructures. The moir\'e effect can be especially strong for interlayer excitons, where electrons and holes reside in different layers and can be addressed separately. In particular, it was recently proposed that the moir\'e superlattice potential not only localizes interlayer exciton states at different superlattice positions, but also hosts an emerging moir\'e quasi-angular momentum (QAM) that periodically switches the optical selection rules for interlayer excitons at different moir\'e sites. Here we report the observation of multiple interlayer exciton states coexisting in a WSe2/WS2 moir\'e superlattice and unambiguously determine their spin, valley, and moir\'e QAM through novel resonant optical pump-probe spectroscopy and photoluminescence excitation spectroscopy. We demonstrate that interlayer excitons localized at different moir\'e sites can exhibit opposite optical selection rules due to the spatially-varying moir\'e QAM. Our observation reveals new opportunities to engineer interlayer exciton states and valley physics with moir\'e superlattices for optoelectronic and valleytronic applications

Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture

In 2017 Tao proposed a variant Sarnak's M\"{o}bius disjointness conjecture with logarithmic averaging: For any zero entropy dynamical system $(X,T)$, $\frac{1}{\log N} \sum_{n=1} ^N \frac{f(T^n x) \mu (n)}{n}= o(1)$ for every $f\in \mathcal{C}(X)$ and every $x\in X$. We construct examples showing that this $o(1)$ can go to zero arbitrarily slowly. Nonetheless, all of our examples satisfy the conjecture.Comment: Preprint version, 12 pages. To appear in JMA

Constraining the Existence of Axion Clouds in M87* with Closure Trace Analyses

Black holes can amplify incoming bosonic waves via rotational superradiance, inducing bound states of ultralight bosons around them. This phenomenon has the potential to confine the parameter spaces of new bosons. Axions and axion-like particles (ALPs) are candidate beyond-standard-model particles that can form such clouds around supermassive black holes (SMBHs) and impact the polarization signal in a similar fashion to Faraday rotation via axion-photon coupling. Prior efforts have used polarized images from the Event Horizon Telescope (EHT) M87 2017 observations to limit the dimensionless axion-photon coupling to previously unexplored regions. However, with the novel calibration-insensitive quantities, closure traces and conjugate closure trace products, it is possible to constrain the existence of axion clouds while avoiding the dominant sources of systematic uncertainties, e.g., station gains and polarization leakages. We utilize a simple geometric model for the polarization map of M87* to fit the model parameters with both simulated and real data sets and reach a comparable level of constraint in the accuracy with which an axion cloud may be excluded in M87. Future applications of our approach include subsequent M87* and Sgr A* observations by EHT and next-generation EHT (ngEHT) are expected to produce stronger constraints across a wider range of axion and ALP masses. Because it does not require imaging, closure trace analyses may be applied to target AGN for which imaging is marginal, extending the number of SMBHs from which axion limits may be obtained significantly.Comment: 12 pages, 11 figures, 1 table, submitted to Ap