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1. Mid-IR spectroscopy of Er ³⁺ doped low-phonon CsCdCl ₃ and CsPbCl ₃ crystals

   https://doi.org/10.1364/JOSAB.470152  

   Brown, Ei_Ei; Fleischman, Zackery_D; McKay, Jason; Hommerich, Uwe; Kabir, Al_Amin; Riggins, Jazmine; Trivedi, Sudhir; Dubinskii, Mark (September 2022, Journal of the Optical Society of America B)

   The mid-IR spectroscopic properties of ${\mathrm{E}\mathrm{r}}^{3+}$doped low-phonon ${\mathrm{C}\mathrm{s}\mathrm{C}\mathrm{d}\mathrm{C}\mathrm{l}}_3$and ${\mathrm{C}\mathrm{s}\mathrm{P}\mathrm{b}\mathrm{C}\mathrm{l}}_3$crystals grown by the Bridgman technique have been investigated. Using optical excitations at $\sim <\#comment/>800\mathrm{n}\mathrm{m}$and $\sim <\#comment/>660\mathrm{n}\mathrm{m}$, both crystals exhibited IR emissions at $\sim <\#comment/>1.55$, $\sim <\#comment/>2.75$, $\sim <\#comment/>3.5$, and $\sim <\#comment/>4.5\text{µ<\#comment/>}\mathrm{m}$at room temperature. The mid-IR emission at 4.5 µm, originating from the ${}^4{\mathrm{I}}_{9/2}\to <\#comment/>{}^4{\mathrm{I}}_{11/2}$transition, showed a long emission lifetime of $\sim <\#comment/>11.6\mathrm{m}\mathrm{s}$for ${\mathrm{E}\mathrm{r}}^{3+}$doped ${\mathrm{C}\mathrm{s}\mathrm{C}\mathrm{d}\mathrm{C}\mathrm{l}}_3$, whereas ${\mathrm{E}\mathrm{r}}^{3+}$doped ${\mathrm{C}\mathrm{s}\mathrm{P}\mathrm{b}\mathrm{C}\mathrm{l}}_3$exhibited a shorter lifetime of $\sim <\#comment/>1.8\mathrm{m}\mathrm{s}$. The measured emission lifetimes of the ${}^4{\mathrm{I}}_{9/2}$state were nearly independent of the temperature, indicating a negligibly small nonradiative decay rate through multiphonon relaxation, as predicted by the energy-gap law for low-maximum-phonon energy hosts. The room temperature stimulated emission cross sections for the ${}^4{\mathrm{I}}_{9/2}\to <\#comment/>{}^4{\mathrm{I}}_{11/2}$transition in ${\mathrm{E}\mathrm{r}}^{3+}$doped ${\mathrm{C}\mathrm{s}\mathrm{C}\mathrm{d}\mathrm{C}\mathrm{l}}_3$and ${\mathrm{C}\mathrm{s}\mathrm{P}\mathrm{b}\mathrm{C}\mathrm{l}}_3$were determined to be $\sim <\#comment/>0.14\times <\#comment/>{10}^{-<\#comment/>20}{\mathrm{c}\mathrm{m}}^2$and $\sim <\#comment/>0.41\times <\#comment/>{10}^{-<\#comment/>20}{\mathrm{c}\mathrm{m}}^2$, respectively. The results of Judd–Ofelt analysis are presented and discussed. 

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2. Existence and stability for the travelling waves of the Benjamin equation

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

   Hakkaev, Sevdzhan; Stanislavova, Milena; Stefanov, Atanas G (January 2025, Nonlinearity)

   Abstract In the seminal work of Benjamin (1974Nonlinear Wave Motion(American Mathematical Society)), in the late 70s, he has derived the ubiquitous Benjamin model, which is a reduced model in the theory of water waves. Notably, it contains two parameters in its dispersion part and under some special circumstances, it turns into the celebrated KdV or the Benjamin–Ono equation, During the 90s, there was renewed interest in it. Benjamin (1992J. Fluid Mech.245401–11; 1996Phil. Trans. R. Soc.A3541775–806) studied the problem for existence of solitary waves, followed by works of Bona–Chen (1998Adv. Differ. Equ.351–84), Albert–Bona–Restrepo (1999SIAM J. Appl. Math.592139–61), Pava (1999J. Differ. Equ.152136–59), who have showed the existence of travelling waves, mostly by variational, but also bifurcation methods. Some results about the stability became available, but unfortunately, those were restricted to either small waves or Benjamin model, close to a distinguished (i.e. KdV or BO) limit. Quite recently, in 2024 (arXiv:2404.04711 [math.AP]), Abdallahet al, proved existence, orbital stability and uniqueness results for these waves, but only for large values of $\frac{c}{{\gamma }^2}\gg 1$. In this article, we present an alternative constrained maximization procedure for the construction of these waves, for the full range of the parameters, which allows us to ascertain their spectral stability. Moreover, we extend this construction to allL²subcritical cases (i.e. power nonlinearities $(|u{|}^{p-2}u{)}_x$, $2<p\text{⩽}6$). Finally, we propose a different procedure, based on a specific form of the Sobolev embedding inequality, which works for all powers $2<p<\mathrm{\infty }$, but produces some unstable waves, for largep. Some open questions and a conjecture regarding this last result are proposed for further investigation. 

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3. First Determination of the Spin-Parity of ${\mathrm{\Xi }}_c(3055{)}^{+,0}$ Baryons

   https://doi.org/10.1103/PhysRevLett.134.081901  

   Aaij, R; Abdelmotteleb, A_S W; Abellan_Beteta, C; Abudinén, F; Ackernley, T; Adefisoye, A A; Adeva, B; Adinolfi, M; Adlarson, P; Agapopoulou, C; et al (February 2025, Physical Review Letters)

   The ${\mathrm{\Xi }}_b^{0(-)}\to {\mathrm{\Xi }}_c\left(3055{)}^{+\left(0\right)}\right(\to D^{+\left(0\right)}\mathrm{\Lambda }){\pi }^{-}$decay chains are observed, and the spin-parity of ${\mathrm{\Xi }}_c(3055{)}^{+\left(0\right)}$baryons is determined for the first time. The measurement is performed using proton-proton collision data at a center-of-mass energy of $\sqrt{s}=13\mathrm{TeV}$, corresponding to an integrated luminosity of $5.4{\mathrm{fb}}^{-1}$, recorded by the LHCb experiment between 2016 and 2018. The spin-parity of the ${\mathrm{\Xi }}_c(3055{)}^{+\left(0\right)}$baryons is determined to be $3/2^{+}$with a significance of more than $6.5\sigma$( $3.5\sigma$) compared to all other tested hypotheses. The up-down asymmetries of the ${\mathrm{\Xi }}_b^{0(-)}\to {\mathrm{\Xi }}_c(3055{)}^{+\left(0\right)}{\pi }^{-}$transitions are measured to be $-0.92\pm 0.10\pm 0.05$( $-0.92\pm 0.16\pm 0.22$), consistent with maximal parity violation, where the first uncertainty is statistical and the second is systematic. These results support the hypothesis that the ${\mathrm{\Xi }}_c(3055{)}^{+\left(0\right)}$baryons correspond to the first $D$-wave $\lambda$-mode excitation of the ${\mathrm{\Xi }}_c$flavor triplet. © 2025 CERN, for the LHCb Collaboration2025CERN 

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4. Ordinary modules for vertex algebras of 𝔬𝔰𝔭 _1|2𝑛

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

   Creutzig, Thomas; Genra, Naoki; Linshaw, Andrew (August 2024, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We show that the affine vertex superalgebra $V^k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$V^{k}(\mathfrak{osp}_{1|2n})at generic level 𝑘 embeds in the equivariant 𝒲-algebra of $\mathfrak{s}{\mathfrak{p}}_{2n}$\mathfrak{sp}_{2n}times $4n$4nfree fermions.This has two corollaries:(1) it provides a new proof that, for generic 𝑘, the coset $\mathrm{Com}(V^k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right),V^k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right))$\operatorname{Com}(V^{k}(\mathfrak{sp}_{2n}),V^{k}(\mathfrak{osp}_{1|2n}))is isomorphic to ${\mathcal{W}}^{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$\mathcal{W}^{\ell}(\mathfrak{sp}_{2n})for $\mathrm{\ell }=-\left(n+1\right)+\left(k+n+1\right)/\left(2k+2n+1\right)$\ell=-(n+1)+(k+n+1)/(2k+2n+1), and(2) we obtain the decomposition of ordinary $V^k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$V^{k}(\mathfrak{osp}_{1|2n})-modules into $V^k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)\otimes {\mathcal{W}}^{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$V^{k}(\mathfrak{sp}_{2n})\otimes\mathcal{W}^{\ell}(\mathfrak{sp}_{2n})-modules.Next, if 𝑘 is an admissible level and ℓ is a non-degenerate admissible level for $\mathfrak{s}{\mathfrak{p}}_{2n}$\mathfrak{sp}_{2n}, we show that the simple algebra $L_k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$L_{k}(\mathfrak{osp}_{1|2n})is an extension of the simple subalgebra $L_k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)\otimes {\mathcal{W}}_{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$L_{k}(\mathfrak{sp}_{2n})\otimes{\mathcal{W}}_{\ell}(\mathfrak{sp}_{2n}).Using the theory of vertex superalgebra extensions, we prove that the category of ordinary $L_k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$L_{k}(\mathfrak{osp}_{1|2n})-modules is a semisimple, rigid vertex tensor supercategory with only finitely many inequivalent simple objects.It is equivalent to a certain subcategory of ${\mathcal{W}}_{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$\mathcal{W}_{\ell}(\mathfrak{sp}_{2n})-modules.A similar result also holds for the category of Ramond twisted modules.Due to a recent theorem of Robert McRae, we get as a corollary that categories of ordinary $L_k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$L_{k}(\mathfrak{sp}_{2n})-modules are rigid. 

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5. 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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