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1. Wigner non-negative states that verify the Wigner entropy conjecture

   https://doi.org/10.1103/PhysRevA.110.012228  

   Qian, Qipeng; Gagatsos, Christos N (July 2024, Physical Review A)

   We present further progress, in the form of analytical results, on the Wigner entropy conjecture set forth by Van Herstraeten and Cerf [Phys. Rev. A 104, 042211 (2021)] and Hertz et al. [J. Phys. A: Math. Theor. 50, 385301 (2017)]. Said conjecture asserts that the differential entropy defined for non-negative, yet physical, Wigner functions is minimized by pure Gaussian states while the minimum entropy is equal to 1 + ln π . We prove this conjecture for the qubits formed by Fock states |0⟩ and |1⟩ that correspond to non-negative Wigner functions. In particular, we derive an explicit form of the Wigner entropy for those states lying on the boundary of the set of Wigner non-negative qubits. We then consider general mixed states and derive a sufficient condition for the conjecture’s validity. Lastly, we elaborate on the states which are in accordance with our condition. 

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2. 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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3. 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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4. The Riemannian and symplectic geometry of the space of generalized Kähler structures

   https://doi.org/10.4171/CMH/585  

   Apostolov, Vestislav; Streets, Jeffrey; Ustinovskiy, Yury (February 2025, Commentarii Mathematici Helvetici)

   On a compact complex manifold(M, J)endowed with a holomorphic Poisson tensor \pi_{J}and a de Rham class\alpha\in H^{2}(M, \mathbb{R}), we study the space of generalized Kähler (GK) structures defined by a symplectic formF\in \alphaand whose holomorphic Poisson tensor is\pi_{J}. We define a notion of generalized Kähler class of such structures, and use the moment map framework of Boulanger (2019) and Goto (2020) to extend the Calabi program to GK geometry. We obtain generalizations of the Futaki–Mabuchi extremal vector field (1995) and the Calabi–Lichnerowicz–Matsushima result (1982, 1958, 1957) for the Lie algebra of the group of automorphisms of(M, J, \pi_{J}). We define a closed1-form on a GK class, which yields a generalization of the Mabuchi energy and thus a variational characterization of GK structures of constant scalar curvature. Next we introduce a formal Riemannian metric on a given GK class, generalizing the fundamental construction of Mabuchi–Semmes–Donaldson (1987, 1992, 1997) We show that this metric has nonpositive sectional curvature, and that the Mabuchi energy is convex along geodesics, leading to a conditional uniqueness result for constant scalar curvature GK structures. We finally examine the toric case, proving the uniqueness of extremal generalized Kähler structures and showing that their existence is obstructed by the uniform relative K-stability of the corresponding Delzant polytope. Using the resolution of the Yau–Tian–Donaldson conjecture in the toric case by Chen–Cheng (2021) and He (2019), we show in some settings that this condition suffices for existence and thus construct new examples. 

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5. Stereodynamics of cold HD and D2 collisions with He

   https://doi.org/10.1063/5.0250522  

   Mandal, Bikramaditya; Patkowski, Konrad; Jambrina, Pablo G; Aoiz, F Javier; Balakrishnan, Naduvalath (March 2025, The Journal of Chemical Physics)

   We present a comprehensive quantum mechanical study of stereodynamic control of HD + He and D2 + He collisions that have been probed experimentally by Perreault et al. [J. Phys. Chem. Lett. 13, 10912 (2022)] using Stark-induced adiabatic Raman passage (SARP) techniques. Our calculations utilize a highly accurate full-dimensional H2 + He interaction potential with diagonal Born–Oppenheimer correction appropriate for HD and D2 isotopomers. The results show that rotational quenching of HD from j = 2 → j′ = 0 in v = 2, j = 2 → j′ = 1 in v = 2 and v = 4, and j = 4 → j′ = 3 in v = 4 is dominated by an l = 1 shape resonance located between 0.1 and 1.0 cm−1. For collision energies less than 0.1 cm−1, isotropic scattering prevails. An l = 1 resonance centered around 0.02 cm−1 is also found to dominate the j = 2 → j′ = 0 and j = 4 → j′ = 2 transitions in v = 4 for He–D2 collisions consistent with our prior studies of Δj = −2 transition in He + D2(v = 2, j = 2) collisions. Our analysis does not support the hypothesis of Perreault et al. [J. Phys. Chem. Lett. 13, 10912 (2022)] that a strong l = 2 resonance controls the angular distribution for Δj = −2 transition for both systems. Despite improvements in the development of the potential energy surface, a good agreement with SARP experiments for v = 2 is achieved only when contributions from collision energies less than 1.0 cm−1 were excluded in the computation of velocity averaged differential rate coefficients for both systems. This could be due to some uncertainties in the velocity spread in the experiment that employs co-propagation of the collision partners and possibly, the neglect of transverse velocities in the simulation of the experiment. 

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