Multi-dimensional metric approximation by primitive points

We refine metrical statements in the style of the Khintchine-Groshev Theorem by requiring certain coprimality constraints on the coordinates of the integer solutions

Quantum key distribution session with 16-dimensional photonic states

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.Comment: 8 pages, 3 figure

On invariant measures of the Euclidean algorithm

We study the ergodic properties of the additive Euclidean algorithm $f$ defined in $\mathbb{R}^2_+$. A natural extension of $f$ is obtained using the action of ${\it SL}(2, \mathbb{Z})$ on a subset of ${\it SL}(2, \mathbb{R})$. We prove that, while $f$ is an ergodic transformation with an infinite invariant measure equivalent to the Lebesgue measure, the invariant measure is not unique up to scalar multiples, and in fact there is a continuous family of such measures

Sendrá el tenor de sólidos solubles totales de los frutos de cucumis melo influenciado por carlavirus?

Melão; Cucumis melo; Insetos; Mosca-Branca; Bemisia tabaci; Teor de sólido

Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin–Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211–237) at low Strouhal number ( St ) and non-zero azimuthal wavenumbers ( m ). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency–wavenumber space where each dominates, finding lift-up to be dominant as St/m→0 . Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core

Spin and Charge Josephson effects between non-uniform superconductors with coexisting helimagnetic order

We consider the spin and charge Josephson current between two non-uniform Fulde-Ferrel-Larkin-Ovchinnikov superconductors with helimagnetic order. We demonstrate that the presence of the helimagnetic phase generates a spin Josephson effect and leads to additional contributions to both single-particle and Josephson charge current. It is shown that for such systems the AC effect differs more radically from the DC effect than in the case of a BCS superconductor with helimagnetic order considered earlier in the literature [M. L. Kuli\'c and I. M. Kuli\'c, Phys. Rev. B {\bf 63}, 104503 (2001)] where a spin Josephson current has also been found. In our system the most interesting effect occurs in the presence of an external magnetic field and in absence of voltage, where we show that the charge Josephson current can be tuned to zero while the spin Josephson current is non-vanishing. This provides a well controlled mechanism to generate a spin supercurrent in absence of charge currents.Comment: final versio