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1. Tensorization of the strong data processing inequality for quantum chi-square divergences

   https://doi.org/10.22331/q-2019-10-28-199  

   Cao, Yu; Lu, Jianfeng (October 2019, Quantum)

   It is well-known that any quantum channel E satisfies the data processing inequality (DPI), with respect to various divergences, e.g., quantum χ κ 2 divergences and quantum relative entropy. More specifically, the data processing inequality states that the divergence between two arbitrary quantum states ρ and σ does not increase under the action of any quantum channel E . For a fixed channel E and a state σ , the divergence between output states E ( ρ ) and E ( σ ) might be strictly smaller than the divergence between input states ρ and σ , which is characterized by the strong data processing inequality (SDPI). Among various input states ρ , the largest value of the rate of contraction is known as the SDPI constant. An important and widely studied property for classical channels is that SDPI constants tensorize. In this paper, we extend the tensorization property to the quantum regime: we establish the tensorization of SDPIs for the quantum χ κ 1 / 2 2 divergence for arbitrary quantum channels and also for a family of χ κ 2 divergences (with κ ≥ κ 1 / 2 ) for arbitrary quantum-classical channels. 

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2. SHARP – VIII. J0924+0219 lens mass distribution and time-delay prediction through adaptive-optics imaging

   https://doi.org/10.1093/mnras/stac1081  

   Chen, Geoff C-F; Fassnacht, Christopher D.; Suyu, Sherry H.; Koopmans, Léon V. E.; Lagattuta, David J.; McKean, John P.; Auger, Matt W.; Vegetti, Simona; Treu, Tommaso (April 2022, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT Strongly lensed quasars can provide measurements of the Hubble constant (H0) independent of any other methods. One of the key ingredients is exquisite high-resolution imaging data, such as Hubble Space Telescope (HST) imaging and adaptive-optics (AO) imaging from ground-based telescopes, which provide strong constraints on the mass distribution of the lensing galaxy. In this work, we expand on the previous analysis of three time-delay lenses with AO imaging (RX J1131−1231, HE 0435−1223, and PG 1115+080), and perform a joint analysis of J0924+0219 by using AO imaging from the Keck telescope, obtained as part of the Strong lensing at High Angular Resolution Program (SHARP) AO effort, with HST imaging to constrain the mass distribution of the lensing galaxy. Under the assumption of a flat Λ cold dark matter (ΛCDM) model with fixed Ωm = 0.3, we show that by marginalizing over two different kinds of mass models (power-law and composite models) and their transformed mass profiles via a mass-sheet transformation, we obtain $$\Delta t_{\rm BA}=6.89\substack{+0.8\\-0.7}\, h^{-1}\hat{\sigma }_{v}^{2}$$ d, $$\Delta t_{\rm CA}=10.7\substack{+1.6\\-1.2}\, h^{-1}\hat{\sigma }_{v}^{2}$$ d, and $$\Delta t_{\rm DA}=7.70\substack{+1.0\\-0.9}\, h^{-1}\hat{\sigma }_{v}^{2}$$ d, where $$h=H_{0}/100\,\rm km\, s^{-1}\, Mpc^{-1}$$ is the dimensionless Hubble constant and $$\hat{\sigma }_{v}=\sigma ^{\rm ob}_{v}/(280\,\rm km\, s^{-1})$$ is the scaled dimensionless velocity dispersion. Future measurements of time delays with 10 per cent uncertainty and velocity dispersion with 5 per cent uncertainty would yield a H0 constraint of ∼15 per cent precision. 

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3. Semiclassical resolvent bounds for short range L ∞ potentials with singularities at the origin

   https://doi.org/10.3233/ASY-231872  

   Shapiro, Jacob (February 2024, Asymptotic Analysis)

   We consider, for h , E > 0, resolvent estimates for the semiclassical Schrödinger operator − h 2 Δ + V − E. Near infinity, the potential takes the form V = V L + V S , where V L is a long range potential which is Lipschitz with respect to the radial variable, while V S = O ( | x | − 1 ( log | x | ) − ρ ) for some ρ > 1. Near the origin, | V | may behave like | x | − β , provided 0 ⩽ β < 2 ( 3 − 1 ). We find that, for any ρ ˜ > 1, there are C , h 0 > 0 such that we have a resolvent bound of the form exp ( C h − 2 ( log ( h − 1 ) ) 1 + ρ ˜ ) for all h ∈ ( 0 , h 0 ]. The h-dependence of the bound improves if V S decays at a faster rate toward infinity. 

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4. On the properties and implications of collapse-driven MHD turbulence

   https://doi.org/10.1093/mnras/stae1085  

   Vázquez-Semadeni, Enrique; Hu, Yue; Xu, Siyao; Guerrero-Gamboa, Rubén; Lazarian, Alex (April 2024, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We investigate the driving of MHD turbulence by gravitational contraction using simulations of an initially spherical, isothermal, magnetically supercritical molecular cloud core with transonic and trans-Alfvénic turbulence. We perform a Helmholtz decomposition of the velocity field, and investigate the evolution of its solenoidal and compressible parts, as well as of the velocity component along the gravitational acceleration vector, a proxy for the infall component of the velocity field. We find that (1) In spite of being supercritical, the core first contracts to a sheet perpendicular to the mean magnetic field, and the sheet itself collapses. (2) The solenoidal component of the turbulence remains at roughly its initial level throughout the simulation, while the compressible component increases continuously, implying that turbulence does not dissipate towards the centre of the core. (3) The distribution of simulation cells in the B–ρ plane occupies a wide triangular region at low densities, bounded below by the expected trend for fast MHD waves (B ∝ ρ, applicable for high-local Alfvénic Mach number MA) and above by the trend expected for slow waves (B ∼ constant, applicable for low local MA). At high densities, the distribution follows a single trend $$B \propto \rho ^{\gamma _{\rm eff}}$$, with 1/2 < γeff < 2/3, as expected for gravitational compression. (4) The mass-to-magnetic flux ratio λ increases with radius r due to the different scalings of the mass and magnetic flux with r. At a fixed radius, λ increases with time due to the accretion of material along field lines. (5) The solenoidal energy fraction is much smaller than the total turbulent component, indicating that the collapse drives the turbulence mainly compressibly, even in directions orthogonal to that of the collapse. 

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5. Spatially Variable Advection Correction of Doppler Radial Velocity Data

   https://doi.org/10.1175/JAS-D-20-0048.1  

   Shapiro, Alan; Gebauer, Joshua G.; Dahl, Nathan A.; Bodine, David J.; Mahre, Andrew; Potvin, Corey K. (January 2021, Journal of the Atmospheric Sciences)

   null (Ed.)

   Abstract Techniques to mitigate analysis errors arising from the nonsimultaneity of data collections typically use advection-correction procedures based on the hypothesis (frozen turbulence) that the analyzed field can be represented as a pattern of unchanging form in horizontal translation. It is more difficult to advection correct the radial velocity than the reflectivity because even if the vector velocity field satisfies this hypothesis, its radial component does not—but that component does satisfy a second-derivative condition. We treat the advection correction of the radial velocity ( υ r ) as a variational problem in which errors in that second-derivative condition are minimized subject to smoothness constraints on spatially variable pattern-translation components ( U , V ). The Euler–Lagrange equations are derived, and an iterative trajectory-based solution is developed in which U , V , and υ r are analyzed together. The analysis code is first verified using analytical data, and then tested using Atmospheric Imaging Radar (AIR) data from a band of heavy rainfall on 4 September 2018 near El Reno, Oklahoma, and a decaying tornado on 27 May 2015 near Canadian, Texas. In both cases, the analyzed υ r field has smaller root-mean-square errors and larger correlation coefficients than in analyses based on persistence, linear time interpolation, or advection correction using constant U and V . As some experimentation is needed to obtain appropriate parameter values, the procedure is more suitable for non-real-time applications than use in an operational setting. In particular, the degree of spatial variability in U and V , and the associated errors in the analyzed υ r field are strongly dependent on a smoothness parameter. 

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