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1. Phase-factor spectra of turbulent phase screens

   https://doi.org/10.1364/JOSAA.429928  

   Muschinski, Andreas ( August 2021 , Journal of the Optical Society of America A)

   The optical phase$\mathrm{\varphi <\#comment/>}$is a key quantity in the physics of light propagating through a turbulent medium. In certain respects, however, the statistics of the phasefactor,$\mathrm{\psi <\#comment/>}=\exp <\#comment/>(i\mathrm{\varphi <\#comment/>})$, are more relevant than the statistics of the phase itself. Here, we present a theoretical analysis of the 2D phase-factor spectrum$F_{\mathrm{\psi <\#comment/>}}(\mathit{\kappa <\#comment/>})$of a random phase screen. We apply the theory to four types of phase screens, each characterized by a power-law phase structure function,$D_{\mathrm{\varphi <\#comment/>}}(r)=(r/r_c{)}^{\mathrm{\gamma <\#comment/>}}$(where$r_c$is the phase coherence length defined by$D_{\mathrm{\varphi <\#comment/>}}(r_c)=1{\mathrm{r}\mathrm{a}\mathrm{d}}^2$), and a probability density function$p_{\mathrm{\alpha <\#comment/>}}(\mathrm{\alpha <\#comment/>})$of the phase increments for a given spatial lag. We analyze phase screens with turbulent ($\mathrm{\gamma <\#comment/>}=5/3$) and quadratic ($\mathrm{\gamma <\#comment/>}=2$) phase structure functions and with normally distributed (i.e., Gaussian) versus Laplacian phase increments. We find that there is a pronounced bump in each of the four phase-factor spectra$F_{\mathrm{\psi <\#comment/>}}(\mathrm{\kappa <\#comment/>})$. The precise location and shape of the bump are different for the four phase-screen types, but in each case it occurs at$\mathrm{\kappa <\#comment/>}\sim <\#comment/>1/r_c$. The bump is unrelated to the well-known “Hill bump” and is not caused by diffraction effects. It is solely a characteristic of the refractive-index statistics represented by the respective phase screen. We show that the second-order$\mathrm{\psi <\#comment/>}$statistics (covariance function, structure function, and spectrum) characterize a random phase screen more completely than the second-order$\mathrm{\varphi <\#comment/>}$counterparts.

    

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2. Photoproduction of K+K− Pairs in Ultraperipheral Collisions

   https://doi.org/10.1103/PhysRevLett.132.222303  

   Acharya, S ; Adamová, D ; Aglieri_Rinella, G ; Agnello, M ; Agrawal, N ; Ahammed, Z ; Ahmad, S ; Ahn, S U ; Ahuja, I ; Akindinov, A ; et al ( May 2024 , Physical Review Letters)

   $K^{+}{K}^{-}$pairs may be produced in photonuclear collisions, either from the decays of photoproduced$\varphi (1020)$mesons or directly as nonresonant$K^{+}{K}^{-}$pairs. Measurements of$K^{+}{K}^{-}$photoproduction probe the couplings between the$\varphi (1020)$and charged kaons with photons and nuclear targets. The kaon-proton scattering occurs at energies far above those available elsewhere. We present the first measurement of coherent photoproduction of$K^{+}{K}^{-}$pairs on lead ions in ultraperipheral collisions using the ALICE detector, including the first investigation of direct$K^{+}{K}^{-}$production. There is significant$K^{+}{K}^{-}$production at low transverse momentum, consistent with coherent photoproduction on lead targets. In the mass range$1.1<M_{KK}<1.4\mathrm{GeV}/c^2$above the$\varphi (1020)$resonance, for rapidity$|y_{KK}|<0.8$and$p_{T,KK}<0.1\mathrm{GeV}/c$, the measured coherent photoproduction cross section is$\mathrm{d}\sigma /\mathrm{d}y=3.37\pm 0.61(\text{stat})\pm 0.15(\mathrm{syst})\mathrm{mb}$. The center-of-mass energy per nucleon of the photon-nucleus (Pb) system$W_{\gamma \mathrm{Pb},n}$ranges from 33 to 188 GeV, far higher than previous measurements on heavy-nucleus targets. The cross section is larger than expected for$\varphi (1020)$photoproduction alone. The mass spectrum is fit to a cocktail consisting of$\varphi (1020)$decays, direct$K^{+}{K}^{-}$photoproduction, and interference between the two. The confidence regions for the amplitude and relative phase angle for direct$K^{+}{K}^{-}$photoproduction are presented.

   © 2024 CERN, for the ALICE Collaboration2024CERN 

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3. 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)

   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${\mathcal{H}}_{\epsilon }(p,q,I,\phi ,t)=h(I)+\sum _{i=1}^n\pm \left(\frac{1}{2}{p}_i^2+V_i(q_i)\right)+\epsilon H_1(p,q,I,\phi ,t),$where$(p,q)\in {\mathbb{R}}^n\times {\mathbb{T}}^n$,$(I,\phi )\in {\mathbb{R}}^d\times {\mathbb{T}}^d$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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4. Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks

   https://doi.org/10.3847/1538-4357/ad1f69  

   Tran, Aaron ; Sironi, Lorenzo ( April 2024 , The Astrophysical Journal)

   We measure the thermal electron energization in 1D and 2D particle-in-cell simulations of quasi-perpendicular, low-beta (β_p= 0.25) collisionless ion–electron shocks with mass ratiom_i/m_e= 200, fast Mach number${\mathcal{M}}_{\mathrm{ms}}=1$–4, and upstream magnetic field angleθ_Bn= 55°–85° from the shock normal$\hat{\mathit{n}}$. It is known that shock electron heating is described by an ambipolar,B-parallel electric potential jump, Δϕ_∥, that scales roughly linearly with the electron temperature jump. Our simulations have$\mathrm{\Delta }{\varphi }_{\parallel }/(0.5m_{\mathrm{i}}{u_{\mathrm{sh}}}^2)\sim 0.1$–0.2 in units of the pre-shock ions’ bulk kinetic energy, in agreement with prior measurements and simulations. Different ways to measureϕ_∥, including the use of de Hoffmann–Teller frame fields, agree to tens-of-percent accuracy. Neglecting off-diagonal electron pressure tensor terms can lead to a systematic underestimate ofϕ_∥in our low-β_pshocks. We further focus on twoθ_Bn= 65° shocks: a${\mathcal{M}}_{\mathrm{s}}=4$(${\mathcal{M}}_{\mathrm{A}}=1.8$) case with a long, 30d_iprecursor of whistler waves along$\hat{\mathit{n}}$, and a${\mathcal{M}}_{\mathrm{s}}=7$(${\mathcal{M}}_{\mathrm{A}}=3.2$) case with a shorter, 5d_iprecursor of whistlers oblique to both$\hat{\mathit{n}}$andB;d_iis the ion skin depth. Within the precursors,ϕ_∥has a secular rise toward the shock along multiple whistler wavelengths and also has localized spikes within magnetic troughs. In a 1D simulation of the${\mathcal{M}}_{\mathrm{s}}=4$,θ_Bn= 65° case,ϕ_∥shows a weak dependence on the electron plasma-to-cyclotron frequency ratioω_pe/Ω_ce, andϕ_∥decreases by a factor of 2 asm_i/m_eis raised to the true proton–electron value of 1836.

    

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5. Jacobian determinants for nonlinear gradient of planar ∞-harmonic functions and applications

   https://doi.org/10.1515/crelle-2024-0016  

   Dong, Hongjie ; Peng, Fa ; Zhang, Yi Ru-Ya ; Zhou, Yuan ( April 2024 , Journal für die reine und angewandte Mathematik (Crelles Journal))

   We introduce a distributional Jacobian determinant$detD{V}_{\beta }(Dv)$\det DV_{\beta}(Dv)in dimension two for the nonlinear complex gradient$V_{\beta }(Dv)={|Dv|}^{\beta }(v_{x_1},-v_{x_2})$V_{\beta}(Dv)=\lvert Dv\rvert^{\beta}(v_{x_{1}},-v_{x_{2}})for any$\beta >-1$\beta>-1, whenever$v\in W_{\mathrm{loc}}^{1,2}$v\in W^{1\smash{,}2}_{\mathrm{loc}}and$\beta {|Dv|}^{1+\beta }\in W_{\mathrm{loc}}^{1,2}$\beta\lvert Dv\rvert^{1+\beta}\in W^{1\smash{,}2}_{\mathrm{loc}}.This is new when$\beta \ne 0$\beta\neq 0.Given any planar ∞-harmonic function 𝑢, we show that such distributional Jacobian determinant$detD{V}_{\beta }(Du)$\det DV_{\beta}(Du)is a nonnegative Radon measure with some quantitative local lower and upper bounds.We also give the following two applications.

   Applying this result with$\beta =0$\beta=0, we develop an approach to build up a Liouville theorem, which improves that of Savin.Precisely, if 𝑢 is an ∞-harmonic function in the whole${\mathbb{R}}^2$\mathbb{R}^{2}with$\underset{R\to \mathrm{\infty }}{lim\; inf}\underset{c\in \mathbb{R}}{inf}\frac{1}{R}{⨍}_{B(0,R)}|u(x)-c|\mathit{d}x<\mathrm{\infty },$\liminf_{R\to\infty}\inf_{c\in\mathbb{R}}\frac{1}{R}\barint_{B(0,R)}\lvert u(x)-c\rvert\,dx<\infty,then$u=b+a\cdot x$u=b+a\cdot xfor some$b\in \mathbb{R}$b\in\mathbb{R}and$a\in {\mathbb{R}}^2$a\in\mathbb{R}^{2}.

   Denoting by$u_p$u_{p}the 𝑝-harmonic function having the same nonconstant boundary condition as 𝑢, we show that$detD{V}_{\beta }(D{u}_p)\to detD{V}_{\beta }(Du)$\det DV_{\beta}(Du_{p})\to\det DV_{\beta}(Du)as$p\to \mathrm{\infty }$p\to\inftyin the weak-⋆ sense in the space of Radon measure.Recall that$V_{\beta }(D{u}_p)$V_{\beta}(Du_{p})is always quasiregular mappings, but$V_{\beta }(Du)$V_{\beta}(Du)is not in general.

    

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