Demand For Carbon Black Market Is Projected To Increase Its Market Share By Around 200 Bps Over The Forecast Period 2021-2031

The latest study done by Fact.MR, a market research and competitive intelligence provider, estimates the carbon black market to contribute significantly towards global chemical industry GVA. This is mainly attributed to the usage of the material in a wide range of applications such as printing inks, packaging, plastics, and paints and coatings.

The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain

Dynamical correlation functions contain important physical information on correlated spin models. Here a dynamical theory suitable suitable to the isotropic spin-1/2 Heisenberg chain in a longitudinal magnetic field is extended to anisotropy larger than one . The aim of this paper is the study of the line shape of the spin dynamical structure factor components +-, -+ and zz of the spin-1/2 Heisenberg-Ising chain in a longitudinal magnetic field near their sharp peaks. To reach that goal, the nature of the specific type of elementary magnetic configurations both unbound and associated with real Bethe-ansatz rapidities and bound and described by complex Bethe strings is clarified: They are singlet q-spin pairs of physical spins 1/2. We derive analytical expressions for the line shapes of dynamical structure factor components +-, -+ and zz valid in the vicinity of lines of sharp peaks. Those are mostly located at and just above lower thresholds of continua associated with both real-rapidity states with only unbound q-spin singlet pairs and states with real and complex rapidities populated by such unbound pairs and a single 2-string or a single 3-string. The latter contain 2 and 3 bound q-spin singlet pairs, respectively. Our results provide physically interesting and important information on the microscopic processes that determine the dynamical properties of the non-perturbative spin-1/2 Heisenberg-Ising chain in a longitudinal magnetic field.

Save up to 60% on Audio Damage’s synths and creative effects

Plugin Boutique has announced a Black Friday Sale on Audio Damage, offering discounts of up to 60% off on all of its audio plugins for a limited time. Since 2002, Audio Damage has been making tools for the creative musician, from experimental plugins for your DAW to top-of-the-line hardware sequencers. Making advanced music technology enjoyable and easy to use is our first and only goal.