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1. Characterizing the fundamental bending vibration of a linear polyatomic molecule for symmetry violation searches

   https://doi.org/10.1088/1367-2630/ace471  

   Jadbabaie, Arian; Takahashi, Yuiki; Pilgram, Nickolas H; Conn, Chandler J; Zeng, Yi; Zhang, Chi; Hutzler, Nicholas R (July 2023, New Journal of Physics)

   Abstract Polyatomic molecules have been identified as sensitive probes of charge-parity violating and parity violating physics beyond the Standard Model (BSM). For example, many linear triatomic molecules are both laser-coolable and have parity doublets in the ground electronic $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state arising from the bending vibration, both features that can greatly aid BSM searches. Understanding the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state is a crucial prerequisite to precision measurements with linear polyatomic molecules. Here, we characterize the fundamental bending vibration of ${}^{174}$YbOH using high-resolution optical spectroscopy on the nominally forbidden $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$ $\to \tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\left(000\right)$transition at 588 nm. We assign 39 transitions originating from the lowest rotational levels of the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state, and accurately model the state’s structure with an effective Hamiltonian using best-fit parameters. Additionally, we perform Stark and Zeeman spectroscopy on the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state and fit the molecule-frame dipole moment to $D_{\mathrm{m}\mathrm{o}\mathrm{l}}=2.16\left(1\right)$Dand the effective electrong-factor to $g_S=2.07\left(2\right)$. Further, we use an empirical model to explain observed anomalous line intensities in terms of interference from spin–orbit and vibronic perturbations in the excited $\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\left(000\right)$state. Our work is an essential step toward searches for BSM physics in YbOH and other linear polyatomic molecules. 

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2. The EDGE-CALIFA Survey: Spatially Resolved ¹³ CO(1–0) Observations and Variations in ¹² CO(1–0)/ ¹³ CO(1–0) in Nearby Galaxies on Kiloparsec Scales

   https://doi.org/10.3847/1538-4365/acd840  

   Cao, Yixian; Wong, Tony; Bolatto, Alberto D.; Leroy, Adam K.; Rosolowsky, Erik; Utomo, Dyas; Sánchez, Sebastián F.; Barrera-Ballesteros, Jorge K.; Levy, Rebecca C.; Colombo, Dario; et al (August 2023, The Astrophysical Journal Supplement Series)

   Abstract We present¹³CO(J= 1 → 0) observations for the EDGE-CALIFA survey, which is a mapping survey of 126 nearby galaxies at a typical spatial resolution of 1.5 kpc. Using detected¹²CO emission as a prior, we detect¹³CO in 41 galaxies via integrated line flux over the entire galaxy and in 30 galaxies via integrated line intensity in resolved synthesized beams. Incorporating our CO observations and optical IFU spectroscopy, we perform a systematic comparison between the line ratio ${\mathit{}}_{12/13}\equiv I{[}^{12}\mathrm{CO}(J=1\to 0)\left]/I{[}^{13}\mathrm{CO}\right(J=1\to 0\left)\right]$and the properties of the stars and ionized gas. Higher ${\mathit{}}_{12/13}$values are found in interacting galaxies compared to those in noninteracting galaxies. The global ${\mathit{}}_{12/13}$slightly increases with infrared colorF₆₀/F₁₀₀but appears insensitive to other host-galaxy properties such as morphology, stellar mass, or galaxy size. We also present azimuthally averaged ${\mathit{}}_{12/13}$profiles for our sample up to a galactocentric radius of 0.4r₂₅(∼6 kpc), taking into account the¹³CO nondetections by spectral stacking. The radial profiles of ${\mathit{}}_{12/13}$are quite flat across our sample. Within galactocentric distances of 0.2r₂₅, the azimuthally averaged ${\mathit{}}_{12/13}$increases with the star formation rate. However, Spearman rank correlation tests show the azimuthally averaged ${\mathit{}}_{12/13}$does not strongly correlate with any other gas or stellar properties in general, especially beyond 0.2r₂₅from the galaxy centers. Our findings suggest that in the complex environments in galaxy disks, ${\mathit{}}_{12/13}$is not a sensitive tracer for ISM properties. Dynamical disturbances, like galaxy interactions or the presence of a bar, also have an overall impact on ${\mathit{}}_{12/13}$, which further complicates the interpretations of ${\mathit{}}_{12/13}$variations. 

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3. Global existence and singularity formation for the generalized Constantin–Lax–Majda equation with dissipation: the real line vs. periodic domains

   https://doi.org/10.1088/1361-6544/ad140c  

   Ambrose, David M; Lushnikov, Pavel M; Siegel, Michael; Silantyev, Denis A (December 2023, Nonlinearity)

   Abstract The question of global existence versus finite-time singularity formation is considered for the generalized Constantin–Lax–Majda equation with dissipation $-{\mathrm{\Lambda }}^{\sigma }$, where $\widehat{{\mathrm{\Lambda }}^{\sigma }}=|k{|}^{\sigma }$, both for the problem on the circle $x\in [-\pi ,\pi ]$and the real line. In the periodic geometry, two complementary approaches are used to prove global-in-time existence of solutions for $\sigma \text{⩾}1$and all real values of an advection parameterawhen the data is small. We also derive new analytical solutions in both geometries whena = 0, and on the real line when $a=1/2$, for various values ofσ. These solutions exhibit self-similar finite-time singularity formation, and the similarity exponents and conditions for singularity formation are fully characterized. We revisit an analytical solution on the real line due to Schochet fora = 0 andσ = 2, and reinterpret it terms of self-similar finite-time collapse. The analytical solutions on the real line allow finite-time singularity formation for arbitrarily small data, even for values ofσthat are greater than or equal to one, thereby illustrating a critical difference between the problems on the real line and the circle. The analysis is complemented by accurate numerical simulations, which are able to track the formation and motion of singularities in the complex plane. The computations validate and build upon the analytical theory. 

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4. Deep multi-task mining Calabi–Yau four-folds

   https://doi.org/10.1088/2632-2153/ac37f7  

   Erbin, Harold; Finotello, Riccardo; Schneider, Robin; Tamaazousti, Mohamed (November 2021, Machine Learning: Science and Technology)

   Abstract We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi–Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi–Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for $h^{(1,1)}$and 97% for $h^{(2,1)}$(100% for both), 81% (96%) for $h^{(3,1)}$, and 49% (83%) for $h^{(2,2)}$. Assuming that the Euler number is known, as it is easy to compute, and taking into account the linear constraint arising from index computations, we get 100% total accuracy. 

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5. Computation of the expectation value of the spin operator ${\hat{S}}^2$ for the spin-flip Bethe–Salpeter equation

   https://doi.org/10.1088/2516-1075/ad48ed  

   Barker, B A; Seshappan, A; Strubbe, D A (May 2024, Electronic Structure)

   Abstract Spin-flip (SF) methods applied to excited-state approaches like the Bethe–Salpeter equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are generally not eigenstates of the spin operator ${\hat{S}}^2$. Even for simple cases where the excitation vector is expected to be, for example, a triplet state, the value of $⟨{\hat{S}}^2⟩$may be found to differ from 2.00; this difference is called ‘spin contamination’. The expectation values $⟨{\hat{S}}^2⟩$must be computed for each excitation vector, to assist with the characterization of the particular excitation and to determine the amount of spin contamination of the state. Our aim is to provide for the first time in the SF methods literature a comprehensive resource on the derivation of the formulas for $⟨{\hat{S}}^2⟩$as well as its computational implementation. After a brief discussion of the theory of the SF Bethe–Salpeter equation (BSE) and some examples further illustrating the need for calculating $⟨{\hat{S}}^2⟩$, we present the derivation for the general equation for computing $⟨{\hat{S}}^2⟩$with the eigenvectors from an SF-BSE calculation, how it is implemented in a Python script, and timing information on how this calculation scales with the size of the SF-BSE Hamiltonian. 

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