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According to the Bogoliubov theory the low energy behaviour of the Bose gas at zero temperature can be described by non-interacting bosonic quasiparticles called phonons. In this work the damping rate of phonons at low momenta, the so-called Beliaev damping, is explained and computed with simple arguments involving the Fermi Golden Rule and Bogoliubov's quasiparticles., Comment: 27 pages, 2 figures, revised version

The continuous advancements in ultrafast lasers, characterized by high pulse energy, great average power, and ultrashort pulse duration, have opened up new frontiers and applications in various fields such as high-energy-density science. In this study, we investigated the implementation of non-Hermitian nonlinear parametric amplification by introducing anti-parity-time (anti-PT) symmetry to three-wave interaction processes. By exploring the parameter space defined by the coupling coefficient, phase mismatch, and absorption, we categorized the behavior of the non-Hermitian optical parametric system into four distinct quadrants, representing unbroken/broken anti-PT symmetry and amplification/attenuation, and amplification-attenuation boundaries and exceptional lines can be observed in such parametric space. Through simulations of the dynamical behavior of the interacting waves, we demonstrated the rich evolutions of the signal and idler waves in systems belonging to the respective quadrants and near exceptional points, revealed by the unique performance of eigenmodes. Our findings provide insights into the evaluation of energy flow direction in optical parametric amplification engineering by the directly linked parameter space, which contribute to a deeper understanding of photonics and laser science, potentially leading to new applications in these fields., Comment: 12 pages; 4 figures

An asymptotic formula is proved for the expected $T$-functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere in $\mathbb{R}^n$ according to an arbitrary positive continuous density. As an application, the approximation of the sphere by random polytopes in terms of $L_p$ surface area differences is discussed., Comment: 20 pages

This study is a continuation of the combined experimental and numerical investigation [1] of the flow of the eutectic GaInSn alloy inside a cylindrical vessel exposed to a constant electrical current. The emerging electrovortex flow driven by the interaction of the current, which is applied through a tapered electrode, with its own magnetic field might have both detrimental and advantageous effects in liquid metal batteries. While the former work [1] was mainly concerned with time-averaged results, this paper focuses on the transient behaviour of the electrovortex flow which becomes most relevant under the influence of an external axial field. The additional Lorentz force generated by the interaction of the imposed current with the vertical component of the geomagnetic field bz drives the ordinary electrovortex jet flow into a swirling motion. Velocity distributions and motion characteristics, such as spiral streamlines and shortened and irregularly swinging jet regions, are investigated. The mechanism is analysed in detail for bz = 25.5 {\mu}T. The maximum angular velocity of the rotating jet is basically linearly dependent on bz, at least for the values studied here. A good agreement between the transient simulation and the experimental result is shown.

The detection of extended TeV $\gamma$-ray emission (dubbed "TeV halos") from Geminga and Monogem pulsars by HAWC collaboration implies that the halo-like morphologies around middle-aged pulsars may be common. The $\gamma$-rays above 10 TeV are thought to arise from inverse Compton (IC) scattering of relativistic electrons/positrons in the pulsar halos off cosmic microwave background photons. In the meanwhile, these electrons and positrons can produce X-ray synchrotron emission in the interstellar magnetic field, resulting in a diffuse emission in the X-ray band (namely X-ray halos). Here, we study the prospect of detecting X-ray halos with eROSITA from 10 middle-aged pulsars with characteristic age larger than tens of thousands of years in the ATNF pulsar catalog. Assuming a benchmark value (i.e., $B = 3 \rm \, \mu G$) for the magnetic field, most of the X-ray halos are found to be bright enough to be detectable by eROSITA in the energy range of 0.5-2 keV during its four-year all-sky survey. Among these pulsar halos, three are supposed to produce X-ray fluxes above the eROSITA sensitivity of the first all-sky survey. Given the good angular resolution and the large field of view, eROSITA is expected to be able to measure the spatial distribution of the X-ray halos from sub-pc scale up to tens of pc scale. The intensity profiles of the X-ray halos are very useful to constrain the magnetic field and the energy-dependence of the diffusion coefficient in the pulsar halos., Comment: 9 pages, 5 figures, 1 table, submitted to MNRAS

The linear transform-based tensor nuclear norm (TNN) methods have recently obtained promising results for tensor completion. The main idea of this type of methods is exploiting the low-rank structure of frontal slices of the targeted tensor under the linear transform along the third mode. However, the low-rankness of frontal slices is not significant under linear transforms family. To better pursue the low-rank approximation, we propose a nonlinear transform-based TNN (NTTNN). More concretely, the proposed nonlinear transform is a composite transform consisting of the linear semi-orthogonal transform along the third mode and the element-wise nonlinear transform on frontal slices of the tensor under the linear semi-orthogonal transform, which are indispensable and complementary in the composite transform to fully exploit the underlying low-rankness. Based on the suggested low-rankness metric, i.e., NTTNN, we propose a low-rank tensor completion (LRTC) model. To tackle the resulting nonlinear and nonconvex optimization model, we elaborately design the proximal alternating minimization (PAM) algorithm and establish the theoretical convergence guarantee of the PAM algorithm. Extensive experimental results on hyperspectral images, multispectral images, and videos show that the our method outperforms linear transform-based state-of-the-art LRTC methods qualitatively and quantitatively., Comment: Nonlinear transform, tensor nuclear norm, proximal alternating minimization, tensor completion