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1. Hunter Self-Similar Implosion Profiles for the Gravitational Euler–Poisson System

   https://doi.org/10.1007/s00220-024-05132-1  

   Sandine, Ely ( October 2024 , Communications in Mathematical Physics)

   Our result is a construction of infinitely many radial self-similar implosion profiles for the gravitational Euler–Poisson system. The problem can be expressed as solving a system of non-autonomous non-linear ODEs. The first rigorous existence result for a non-trivial solution to these ODEs is due to Guo et al. (Commun Math Phys 386(3):1551–1601, 2021), in which they construct a solution found numerically by Larson (Mon Not R Astron Soc 145(3):271–295, 1969) and Penston (Mon Not R Astron Soc 144(4):425–448, 1969) independently. The solutions we construct belong to a different regime and correspond to a strict subset of the family of profiles discovered numerically by Hunter (Astrophys J 218:834, 1977). Our proof adapts a technique developed by Collot et al. (Mem Am Math Soc 260(1255):v+97, 2019), in which they study blowup for a family of energy-supercritical focusing semilinear heat equations. In our case, the quasilinearity presents complications, most severely near the sonic point where the system degenerates.

    

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2. Global Gradient Estimate for a Divergence Problem and Its Application to the Homogenization of a Magnetic Suspension

   Dang, T ( April 2022 , Association for Women in Mathematics series)

   Español, M (Ed.)

   "This paper generalizes the results obtained by the authors in Dang et al. (SIAM J. Appl. Math. 81(6):2547--2568, 2021) concerning the homogenization of a non-dilute suspension of magnetic particles in a viscous flow. More specifically, in this paper, a restrictive assumption on the coefficients of the coupled equation, made in Dang et al. (SIAM J. Appl. Math. 81(6):2547--2568, 2021), that significantly narrowed the applicability of the homogenization results obtained is relaxed and a new regularity of the solution of the fine-scale problem is proven. In particular, we obtain a global L∞-bound for the gradient of the solution of the scalar equation −divax∕$\epsilon$∇$\phi$$\epsilon$(x)=f(x){\$}{\$}- {\backslash}operatorname {\{}{\{}{\backslash}mathrm {\{}div{\}}{\}}{\}} {\backslash}left [ {\backslash}mathbf {\{}a{\}} {\backslash}left ( x/{\backslash}varepsilon {\backslash}right ){\backslash}nabla {\backslash}varphi ^{\{}{\backslash}varepsilon {\}}(x) {\backslash}right ] = f(x){\$}{\$}, uniform with respect to microstructure scale parameter $\epsilon${\thinspace}≪{\thinspace}1 in a small interval (0, $\epsilon$0), where the coefficient a is only piecewise H{\"o}lder continuous. Thenceforth, this regularity is used in the derivation of the effective response of the given suspension discussed in Dang et al. (SIAM J. Appl. Math. 81(6):2547--2568, 2021)." 

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3. Imaging topology of Hofstadter ribbons

   https://doi.org/10.1088/1367-2630/ab165b  

   Genkina, Dina ; Aycock, Lauren M. ; Lu, Hsin-I ; Lu, Mingwu ; Pineiro, Alina M. ; Spielman, I. B. ( May 2019 , New Journal of Physics)

   Physical systems with non-trivial topological order find direct applications in metrology (Klitzinget al1980Phys.Rev. Lett.45494–7) and promise future applications in quantum computing (Freedman 2001Found. Comput. Math.1183–204; Kitaev 2003Ann. Phys.3032–30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system’s topology (Laughlin 1981Phys. Rev.B235632–33). At magnetic fields beyond the reach of current condensed matter experiment, around${\mathrm{10}}^{\mathrm{4}}$T, this conductance remains precisely quantized with values based on the topological order (Thoulesset al1982Phys. Rev. Lett.49405–8). Hitherto, quantized conductance has only been measured in extended 2D systems. Here, we experimentally studied narrow 2D ribbons, just 3 or 5 sites wide along one direction, using ultracold neutral atoms where such large magnetic fields can be engineered (Jaksch and Zoller 2003New J. Phys.556; Miyakeet al2013Phys. Rev. Lett.111185302; Aidelsburgeret al2013Phys. Rev. Lett.111185301; Celiet al2014Phys. Rev. Lett.112043001; Stuhlet al2015Science3491514; Manciniet al2015Science3491510; Anet al2017Sci. Adv.3). We microscopically imaged the transverse spatial motion underlying the quantized Hall effect. Our measurements identify the topological Chern numbers with typical uncertainty of$\mathrm{5}\%$, and show that although band topology is only properly defined in infinite systems, its signatures are striking even in nearly vanishingly thin systems.

    

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4. Electron vacancy-level dependent hybrid photoionization of the F − @ C60+ molecule: a novel effect

   https://doi.org/10.1088/1361-6455/ac4ff3  

   Ali, Esam ; O’Brien, Taylor ; Dennis, Andrew ; El-Amine Madjet, Mohamed ; Manson, Steven T ; Chakraborty, Himadri S ( February 2022 , Journal of Physics B: Atomic, Molecular and Optical Physics)

   Abstract Our previous studies (Shields et al 2020 J. Phys. B: At. Mol. Opt. Phys. 53 125101; Shields et al 2020 Euro. Phys. J. D 74 191) have predicted that the atom-fullerene hybrid photoionization properties for X = Cl, Br and I endohedrally confined in C 60 are different before and after an electron transfers from C 60 to the halogen. It was further found as a rule that the ionization dynamics is insensitive to the C 60 level the electron originates from to produce X − @ C 60 + . In the current study, we report an exception to this rule in F@C 60 . It is found that when the electron vacancy is situated in the C 60 level that participates in the hybridization in F − @ C 60 + , the mixing becomes dramatically large leading to strong modifications in the photoionization of the hybrid levels. This novel effect is fundamentally based on a level-crossing phenomenon driven by the electron transfer in F@C 60 . But when the vacancy is at any other pure level of C 60 , the level-invariance is retained showing weak hybridization. Even though this case of F@C 60 is an exception in the halogen@C 60 series, the phenomenon can be more general and can occur with compounds of other atoms caged in a variety of fullerenes. Possible experimental studies are suggested to benchmark the present results. 

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5. An optical tweezer array of ground-state polar molecules

   https://doi.org/10.1088/2058-9565/ac676c  

   Zhang, Jessie T ; Picard, Lewis R ; Cairncross, William B ; Wang, Kenneth ; Yu, Yichao ; Fang, Fang ; Ni, Kang-Kuen ( May 2022 , Quantum Science and Technology)

   Abstract Fully internal and motional state controlled and individually manipulable polar molecules are desirable for many quantum science applications leveraging the rich state space and intrinsic interactions of molecules. While prior efforts at assembling molecules from their constituent atoms individually trapped in optical tweezers achieved such a goal for exactly one molecule (Zhang J T et al 2020 Phys. Rev. Lett. 124 253401; Cairncross W B et al 2021 Phys. Rev. Lett. 126 123402; He X et al 2020 Science 370 331–5), here we extend the technique to an array of five molecules, unlocking the ability to study molecular interactions. We detail the technical challenges and solutions inherent in scaling this system up. With parallel preparation and control of multiple molecules in hand, this platform now serves as a starting point to harness the vast resources and long-range dipolar interactions of molecules. 

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