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1. The metastable Q ³ Δ ₂ state of ThO: a new resource for the ACME electron EDM search

   https://doi.org/10.1088/1367-2630/ab6a3a  

   Wu, X.; Han, Z.; Chow, J.; Ang, D. G.; Meisenhelder, C.; Panda, C. D.; West, E. P.; Gabrielse, G.; Doyle, J. M.; DeMille, D. (February 2020, New Journal of Physics)

   Abstract The best upper limit for the electron electric dipole moment was recently set by the ACME collaboration. This experiment measures an electron spin-precession in a cold beam of ThO molecules in their metastable $H{(}^3{\mathrm{\Delta }}_1)$state. Improvement in the statistical and systematic uncertainties is possible with more efficient use of molecules from the source and better magnetometry in the experiment, respectively. Here, we report measurements of several relevant properties of the long-lived $Q{(}^3{\mathrm{\Delta }}_2)$state of ThO, and show that this state is a very useful resource for both these purposes. TheQstate lifetime is long enough that its decay during the time of flight in the ACME beam experiment is negligible. The large electric dipole moment measured for theQstate, giving rise to a large linear Stark shift, is ideal for an electrostatic lens that increases the fraction of molecules detected downstream. The measured magnetic moment of theQstate is also large enough to be used as a sensitive co-magnetometer in ACME. Finally, we show that theQstate has a large transition dipole moment to the $C{(}^1{\mathrm{\Pi }}_1)$state, which allows for efficient population transfer between the ground state $X{(}^1{\mathrm{\Sigma }}^{+})$and theQstate via $X-C-Q$Stimulated Raman Adiabatic Passage (STIRAP). We demonstrate 90 % STIRAP transfer efficiency. In the course of these measurements, we also determine the magnetic moment ofCstate, the $X\to C$transition dipole moment, and branching ratios of decays from theCstate. 

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2. Products of primes in arithmetic progressions

   https://doi.org/10.1515/crelle-2023-0096  

   Matomäki, Kaisa; Teräväinen, Joni (January 2024, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract A conjecture of Erdős states that, for any large primeq, every reduced residue class $\left(\mathrm{mod}q\right)${(\operatorname{mod}q)}can be represented as a product $p_1{p}_2${p_{1}p_{2}}of two primes $p_1,p_2\le q${p_{1},p_{2}\leq q}. We establish a ternary version of this conjecture, showing that, for any sufficiently large cube-free integerq, every reduced residue class $\left(\mathrm{mod}q\right)${(\operatorname{mod}q)}can be written as $p_1{p}_2{p}_3${p_{1}p_{2}p_{3}}with $p_1,p_2,p_3\le q${p_{1},p_{2},p_{3}\leq q}primes. We also show that, for any $\epsilon >0${\varepsilon>0}and any sufficiently large integerq, at least $\left(\frac{2}{3}-\epsilon \right)\phi \left(q\right)${(\frac{2}{3}-\varepsilon)\varphi(q)}reduced residue classes $\left(\mathrm{mod}q\right)${(\operatorname{mod}q)}can be represented as a product $p_1{p}_2${p_{1}p_{2}}of two primes $p_1,p_2\le q${p_{1},p_{2}\leq q}.The problems naturally reduce to studying character sums. The main innovation in the paper is the establishment of a multiplicative dense model theorem for character sums over primes in the spirit of the transference principle. In order to deal with possible local obstructions we establish bounds for the logarithmic density of primes in certain unions of cosets of subgroups of ${\mathbb{Z}}_q^{\times }${\mathbb{Z}_{q}^{\times}}of small index and study in detail the exceptional case that there exists a quadratic character $\psi \left(\mathrm{mod}q\right)${\psi~{}(\operatorname{mod}\,q)}such that $\psi \left(p\right)=-1${\psi(p)=-1}for very many primes $p\le q${p\leq q}. 

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3. Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems

   https://doi.org/10.1088/1361-6544/ac50bb  

   Chen, Qinbo; de la Llave, Rafael (March 2022, Nonlinearity)

   Abstract The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the followinga prioriunstable Hamiltonian system with a time-periodic perturbation ${\mathcal{H}}_{\epsilon }\left(p,q,I,\phi ,t\right)=h\left(I\right)+\sum _{i=1}^n\pm \left(\frac{1}{2}{p}_i^2+V_i\left(q_i\right)\right)+\epsilon H_1\left(p,q,I,\phi ,t\right),$where $\left(p,q\right)\in {\mathbb{R}}^n\times {\mathbb{T}}^n$, $\left(I,\phi \right)\in {\mathbb{R}}^d\times {\mathbb{T}}^d$withn,d⩾ 1,V_iare Morse potentials, andɛis a small non-zero parameter. The unperturbed Hamiltonian is not necessarily convex, and the induced inner dynamics does not need to satisfy a twist condition. Using geometric methods we prove that Arnold diffusion occurs for generic analytic perturbationsH₁. Indeed, the set of admissibleH₁isC^ωdense andC³open (a fortiori,C^ωopen). Our perturbative technique for the genericity is valid in theC^ktopology for allk∈ [3, ∞) ∪ {∞,ω}. 

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4. The Evolving Effect of Cosmic Web Environment on Galaxy Quenching

   https://doi.org/10.3847/1538-4357/acd11c  

   Hasan, Farhanul; Burchett, Joseph N.; Abeyta, Alyssa; Hellinger, Douglas; Mandelker, Nir; Primack, Joel R.; Faber, S. M.; Koo, David C.; Elek, Oskar; Nagai, Daisuke (June 2023, The Astrophysical Journal)

   Abstract We investigate how cosmic web structures affect galaxy quenching in the IllustrisTNG (TNG100) cosmological simulations by reconstructing the cosmic web within each snapshot using the DisPerSE framework. We measure the comoving distance from each galaxy with stellar mass $\log \left(M_{*}/M_{\odot }\right)\ge 8$to the nearest node (d_node) and the nearest filament spine (d_fil) to study the dependence of both the median specific star formation rate (〈sSFR〉) and the median gas fraction (〈f_gas〉) on these distances. We find that the 〈sSFR〉 of galaxies is only dependent on the cosmic web environment atz< 2, with the dependence increasing with time. Atz≤ 0.5, $8\le \log \left(M_{*}/M_{\odot }\right)<9$galaxies are quenched atd_node≲ 1 Mpc, and have significantly suppressed star formation atd_fil≲ 1 Mpc, trends driven mostly by satellite galaxies. Atz≤ 1, in contrast to the monotonic drop in 〈sSFR〉 of $\log \left(M_{*}/M_{\odot }\right)<10$galaxies with decreasingd_nodeandd_fil, $\log \left(M_{*}/M_{\odot }\right)\ge 10$galaxies—both centrals and satellites—experience an upturn in 〈sSFR〉 atd_node≲ 0.2 Mpc. Much of this cosmic web dependence of star formation activity can be explained by an evolution in 〈f_gas〉. Our results suggest that in the past ∼10 Gyr, low-mass satellites are quenched by rapid gas stripping in dense environments near nodes and gradual gas starvation in intermediate-density environments near filaments. At earlier times, cosmic web structures efficiently channeled cold gas into most galaxies. State-of-the-art ongoing spectroscopic surveys such as the Sloan Digital Sky Survey and DESI, as well as those planned with the Subaru Prime Focus Spectrograph, JWST, and Roman, are required to test our predictions against observations. 

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5. Degenerate parabolic p -Laplacian equations: Existence, uniqueness, and asymptotic behavior of solutions

   https://doi.org/10.1515/acv-2024-0060  

   Cruz-Uribe, David; Moen, Kabe; Shao, Yuanzhen (April 2025, Advances in Calculus of Variations)

   Abstract In this paper we study the degenerate parabolicp-Laplacian, ${\partial }_{t}u-v^{-1}\mathrm{div}\left({\left|\sqrt{Q}\nabla u\right|}^{p-2}Q\nabla u\right)=0${\partial_{t}u-v^{-1}\operatorname{div}(|\sqrt{Q}\nabla u|^{p-2}Q\nabla u)=0},where the degeneracy is controlled by a matrixQand a weightv.With mild integrability assumptions onQandv, we prove theexistence and uniqueness of solutions on any interval $[0,T]${[0,T]}. If we further assumethe existence of a degenerate Sobolev inequality with gain, thedegeneracy again controlled byvandQ, then we can prove bothfinite time extinction and ultracontractive bounds. Moreover, weshow that there is equivalence between the existence ofultracontractive bounds and the weighted Sobolev inequality. 

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