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1. Quantum group intertwiner space from quantum curved tetrahedron

   https://doi.org/10.1088/1361-6382/ad5f71  

   Han, Muxin; Hsiao, Chen-Hung; Pan, Qiaoyin (July 2024, Classical and Quantum Gravity)

   In this paper, we develop a quantum theory of homogeneously curved tetrahedron geometry, by applying the combinatorial quantization to the phase space of tetrahedron shapes defined in Haggard et al (2016 Ann. Henri Poincaré 17 2001–48). Our method is based on the relation between this phase space and the moduli space of SU(2) flat connections on a 4-punctured sphere. The quantization results in the physical Hilbert space as the solution of the quantum closure constraint, which quantizes the classical closure condition $M_4{M}_3{M}_2{M}_1=1$, $M_{\nu }\in \mathrm{SU}\left(2\right)$, for the homogeneously curved tetrahedron. The quantum group $U_q\left(\mathfrak{su}\right(2\left)\right)$emerges as the gauge symmetry of a quantum tetrahedron. The physical Hilbert space of the quantum tetrahedron coincides with the Hilbert space of 4-valent intertwiners of $U_q\left(\mathfrak{su}\right(2\left)\right)$. In addition, we define the area operators quantizing the face areas of the tetrahedron and compute the spectrum. The resulting spectrum is consistent with the usual Loop-Quantum-Gravity area spectrum in the large spin regime but is different for small spins. This work closely relates to 3+1 dimensional Loop Quantum Gravity in presence of cosmological constant and provides a justification for the emergence of quantum group in the theory. 

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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. Perturbative second-order optical susceptibility of bulk materials: a symmetry-enforced return to non-orthogonal localized basis sets

   https://doi.org/10.1088/1361-648X/ae35fa  

   Huamán, Angiolo; Enrique_Rosas-Hernandez, Luis; Barraza-Lopez, Salvador (January 2026, Journal of Physics: Condensed Matter)

   Abstract The second-order optical susceptibility of semiconductors ${\chi }_{ijk}^{\left(2\right)}(-2\omega ;\omega ,\omega )$finds application in metrology, spectroscopy, telecommunications, material characterization, and quantum information. Pioneering calculations of ${\chi }_{ijk}^{\left(2\right)}(-2\omega ;\omega ,\omega )$utilized non-orthogonal Gaussian orbitals centered at atoms. That formulation transitioned into plane-wave-based algorithms as time went by. As of late, nevertheless, multiple tools for calculating optical susceptibilities have recast the problem using Wannier (i.e.localized) orbitals, making a comeback onto frameworks based on localized basis sets. Here, we present an approach for calculating ${\chi }_{ijk}^{\left(2\right)}(-2\omega ;\omega ,\omega )$reliant on numerical pseudo-atomic orbitals (PAOs) within perturbation theory in the velocity gauge. Its salient feature is a calculation of ‘Slater–Koster-like’ two-center integrals of the momentum operator in between PAOs identified by symmetry. The approach was successfully tested on paradigmatic cubic silicon carbide (3C-SiC) and gallium arsenide, for which linear responses are contributed as well. 

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4. Bounds on eigenfunctions of quantum cat maps

   https://doi.org/10.1088/1402-4896/ad0331  

   Kim, Elena; Koirala, Robert (October 2023, Physica Scripta)

   Abstract We studyℓ^∞norms ofℓ²-normalized eigenfunctions of quantum cat maps. For maps with short quantum periods (constructed by Bonechi and de Biévre in F Bonechi and S De Bièvre (2000,Communications in Mathematical Physics,211, 659–686)) we show that there exists a sequence of eigenfunctionsuwith $\parallel u{\parallel }_{\infty }\gtrsim {\left(\log N\right)}^{-1/2}$. For general eigenfunctions we show the upper bound $\parallel u{\parallel }_{\infty }\lesssim {\left(\log N\right)}^{-1/2}$. Here the semiclassical parameter is $h={\left(2\pi N\right)}^{-1}$. Our upper bound is analogous to the one proved by Bérard in P Bérard (1977,Mathematische Zeitschrift,155, 249-276) for compact Riemannian manifolds without conjugate points. 

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5. 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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