Zilch vortical effect for fermions

We consider the notion of zilch current that was recently discussed in the literature as an alternative helicity measure for photons. Developing this idea, we suggest the generalization of the zilch for the systems of fermions. We start with the definition of the photonic zilch current in chiral kinetic theory framework and work out field-theoretical definition of the fermionic zilch using the Wigner function formalism. This object has similar properties to the photonic zilch and is conserved in the non-interacting theory. We also show that, in full analogy with a case of photons, the fermionic zilch acquires a non-trivial contribution due to the medium rotation - zilch vortical effect (ZVE) for fermions. Combined with a previously studied ZVE for photons, these results form a wider set of chiral effects parameterized by the spin of the particles and the spin of the current. We briefly discuss the origin of the ZVE, its possible relation to the anomalies in the underlying microscopic theory and possible application for studying the spin polarization in chiral media.

Sharp Block–Sharkovsky Type Theorem for Multivalued Maps on the Circle and Its Application to Differential Equations and Inclusions

This is a final part of the series of our papers devoted to a multivalued version of the (Sharkovsky type) Block cycle coexistence theorem. It improves our last general result in the sense that its part related to the usual ordering of positive integers becomes a full analogy of the standard single-valued case, while the alternative part related to the Sharkovsky ordering of positive integers is an analogy of the multivalued case for interval maps, provided there exists a fixed point. That is why we call the obtained theorem here as “sharp”. This theorem is still applied via the associated Poincaré translation operators to differential equations and inclusions on the circle. All the deterministic results are also randomized in an advantageous way.

Uncertainty Principles on Weighted Spheres, Balls, and Simplexes

This paper studies the uncertainty principle for spherical h-harmonic expansions on the unit sphere of ℝ d associated with a weight function invariant under a general finite reflection group, which is in full analogy with the classical Heisenberg inequality. Our proof is motivated by a new decomposition of the Dunkl–Laplace–Beltrami operator on the weighted sphere.

Complexation parameters for the actinides(IV)-humic acid system: a search for consistency and application to laboratory and field observations

SummaryThe coherence of actinide(IV) complexation by humic substances (HS) is reviewed and new data are proposed. In a first attempt, the values of independent data from literature on Th(IV), U(IV), and Pu(IV) are collected, selected, and compiled. The data obtained follow the “classical” trend of increasing conditional formation “constants” with pH, led both by the increasing ionisation of HS and by the extensive hydrolysis of the tetravalent actinides. Even though a fair agreement is evident, the experimental uncertainties do not permit a full analogy between the actinides(IV) to be ascertained. In a second attempt, the experiments from which the original data are available were reinterpreted using only one hydrolysis constant set for U(IV) as an example, considering that all actinides(IV) have analogous humic complexation behaviour. Hence, the obtained evolution of conditional formation “constants” is much more coherent and the uncertainties do not permit to distinguish an actinide(IV) from one another. The obtained data are then applied to independent laboratory and