Focusing on three-pion states with maximal isospin (π^+π^+π^+), we present the first nonperturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.A chiral bobber is a localized three-dimensional magnetization configuration, terminated by a singularity. Chiral bobbers coexist with magnetic skyrmions in chiral magnets, lending themselves to new types of skyrmion-complementary bits of information. However, the on-demand creation of bobbers, as well as their direct observation remained elusive. Here, we introduce a new mechanism for creating a stable chiral bobber lattice state via the proximity of two skyrmion species with comparable size. This effect is experimentally demonstrated in a Cu_2OSeO_3/[Ta/CoFeB/MgO]_4 heterostructure in which an exotic bobber lattice state emerges in the phase diagram of Cu_2OSeO_3. To unambiguously reveal the existence of the chiral bobber lattice state, we have developed a novel characterization technique, magnetic truncation rod analysis, which is based on resonant elastic x-ray scattering.We compare two optical clocks based on the ^2S_1/2(F=0)→^2D_3/2(F=2) electric quadrupole (E2) and the ^2S_1/2(F=0)→^2F_7/2(F=3) electric octupole (E3) transition of ^171Yb^+ and measure the frequency ratio ν_E3/ν_E2=0.932829404530965376(32), improving upon previous measurements by an order of magnitude. Using two caesium fountain clocks, we find ν_E3=642121496772645.10(8)  Hz, the most accurate determination of an optical transition frequency to date. Repeated measurements of both quantities over several years are analyzed for potential violations of local position invariance. We improve by factors of about 20 and 2 the limits for fractional temporal variations of the fine structure constant α to 1.0(1.1)×10^-18/yr and of the proton-to-electron mass ratio μ to -8(36)×10^-18/yr. Using the annual variation of the Sun's gravitational potential at Earth Φ, we improve limits for a potential coupling of both constants to gravity, (c^2/α)(dα/dΦ)=14(11)×10^-9 and (c^2/μ)(dμ/dΦ)=7(45)×10^-8.Deep inelastic scattering of e^± off protons is sensitive to contributions from "dark photon" exchange. Using HERA data fit to HERA's parton distribution functions (PDFs), we obtain the model-independent bound ε≲0.02 on the kinetic mixing between hypercharge and the dark photon for dark photon masses ≲10  GeV. This slightly improves on the bound obtained from electroweak precision observables. For higher masses, the limit weakens monotonically; ε≲1 for a dark photon mass of 5 TeV. Utilizing PDF sum rules, we demonstrate that the effects of the dark photon cannot be (trivially) absorbed into refit PDFs and, in fact, lead to non-Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (Bjorken x_B-independent) scaling violations that could provide a smoking gun in data. The proposed e^±p collider operating at sqrt[s]=1.3  TeV (Large Hadron Electron Collider) is anticipated to accumulate 10^3 times the luminosity of HERA, providing substantial improvements in probing the effects of a dark photon sensitivity to ε well below that probed by electroweak precision data is possible throughout virtually the entire dark photon mass range, as well as being able to probe to much higher dark photon masses, up to 100 TeV.It was recently shown that a scalar field suitably coupled to the Gauss-Bonnet invariant G can undergo a spin-induced linear tachyonic instability near a Kerr black hole. This instability appears only once the dimensionless spin j is sufficiently large, that is, j≳0.5. A tachyonic instability is the hallmark of spontaneous scalarization. Focusing, for illustrative purposes, on a class of theories that do exhibit this instability, we show that stationary, rotating black hole solutions do indeed have scalar hair once the spin-induced instability threshold is exceeded, while black holes that lie below the threshold are described by the Kerr solution. Our results provide strong support for spin-induced black hole scalarization.High-quality long-distance entanglement is essential for both quantum communication and scalable quantum networks. Entanglement purification is to distill high-quality entanglement from low-quality entanglement in a noisy environment and it plays a key role in quantum repeaters. The previous significant entanglement purification experiments require two pairs of low-quality entangled states and were demonstrated in tabletop. Here we propose and report a high-efficiency and long-distance entanglement purification using only one pair of hyperentangled state. We also demonstrate its practical application in entanglement-based quantum key distribution (QKD). One pair of polarization spatial-mode hyperentanglement was distributed over 11 km multicore fiber (noisy channel). After purification, the fidelity of polarization entanglement arises from 0.771 to 0.887 and the effective key rate in entanglement-based QKD increases from 0 to 0.332.  https://www.selleckchem.com/products/mptp-hydrochloride.html  The values of Clauser-Horne-Shimony-Holt inequality of polarization entanglement arises from 1.829 to 2.128. Moreover, by using one pair of hyperentanglement and deterministic controlled-NOT gates, the total purification efficiency can be estimated as 6.6×10^3 times than the experiment using two pairs of entangled states with spontaneous parametric down-conversion sources. Our results offer the potential to be implemented as part of a full quantum repeater and large-scale quantum network.Ice nucleation is a phenomenon that, despite the relevant implications for life, atmospheric sciences, and technological applications, is far from being completely understood, especially under extreme thermodynamic conditions. In this work we present a computational investigation of the homogeneous ice nucleation at negative pressures. By means of the seeding technique we estimate the size of the ice critical nucleus N_c for the TIP4P/Ice water model. This is done along the isotherms 230, 240, and 250 K, from positive to negative pressures until reaching the liquid-gas kinetic stability limit (where cavitation cannot be avoided). We find that N_c is nonmonotonic upon depressurization, reaching a minimum at negative pressures in the doubly metastable region of water. According to classical nucleation theory we establish the nucleation rate J and the surface tension γ, revealing a retracing behavior of both when the liquid-gas kinetic stability limit is approached. We also predict a reentrant behavior of the homogeneous nucleation line.