A Physically Meaningful Relativistic Description of the Spin State of an Electron

We introduced a new model to present the states of a two-state quantum system. The space is the complexified Minkowski space. The Lorentz group acts by the linear extension of its action on the four-vectors. We applied this model to represent the spin state of an electron or any relativistic spin 1/2 particle. The spin state of such particle is of the form U+iS, where U is the four-velocity of the particle in the lab frame, and S is the 4D spin in this frame. Under this description, the transition probability between two pure spin states ϱ1 and ϱ2 of particles moving with the same velocity are defined by use of Minkowski dot product as 12<ϱ2|ϱ1>. This transition probability is Lorentz invariant, coincide with the quantum mechanics prediction and thus agree with the experimental results testing quantum mechanics predictions based on Bell’s inequality. For a a particle of mass m and charge q with the spin state ϱ, the total momentum is mcϱ and the electromagnetic momentum is qϱ. This imply that the Landé g factor for such particles must be g=2. We obtain an evolution equation of the spin state in an electromagnetic field which defines correctly the anomalous Zeeman effect and the fine structure splitting.

Anomaly Non-renormalization in Interacting Weyl Semimetals

Weyl semimetals are 3D condensed matter systems characterized by a degenerate Fermi surface, consisting of a pair of ‘Weyl nodes’. Correspondingly, in the infrared limit, these systems behave effectively as Weyl fermions in $$3+1$$ 3 + 1 dimensions. We consider a class of interacting 3D lattice models for Weyl semimetals and prove that the quadratic response of the quasi-particle flow between the Weyl nodes is universal, that is, independent of the interaction strength and form. Universality is the counterpart of the Adler–Bardeen non-renormalization property of the chiral anomaly for the infrared emergent description, which is proved here in the presence of a lattice and at a non-perturbative level. Our proof relies on constructive bounds for the Euclidean ground state correlations combined with lattice Ward Identities, and it is valid arbitrarily close to the critical point where the Weyl points merge and the relativistic description breaks down.

BRAGINSKII EQUATIONS FOR HOT RELATIVISTIC PLASMAS: MIXED APPROACH

In the paper, the Braginskii equations for relativistic electrons in hot plasmas with slow macroscopic fluxes are derived. This consideration is suitable for description of the typical fusion plasma with the temperatures of about several tens of kiloelectronvolt, when the plasma rotation and the longitudinal currents should be taken into account. Contrary to other papers devoted to classical description of transport processes in fusion devices, as well as to fully relativistic description of the astrophysical objects, we propose the mixed approach with fully relativistic kinetics for the hot electrons and non-relativistic macroscopic fluxes. The obtained form of the Braginskii equations includes all important features of relativistic hydrodynamics, has the same form as the classical representation, which is currently implemented into modern transport codes, and can easily replace the latter.

Guidelines for Selecting Interlayer Spacers in Synthetic 2D-Based Antiferromagnets from First-Principles Simulations

Following the recent synthesis of graphene–based antiferromagnetic ultrathin heterostructures made of Co and Fe, we analyse the effect of the spacer between both ferromagnetic materials. Using density functional calculations, we carried out an exhaustive study of the geometric, electronic and magnetic properties for intercalated single Co MLs on top of Ir(111) coupled to monolayered Fe through n graphene layers (n = 1, 2, 3) or monolayered h-BN. Different local atomic arrangements have been considered to model the Moiré patterns expected in these heterostructures. The magnetic exchange interactions between both ferromagnets ( J C o − F e ) are computed from explicit calculations of parallel and anti-parallel Fe/Co inter–layer alignments, and discussed in the context of recent experiments. Our analysis confirms that the robust antiferromagnetic superexchange–coupling between Fe and Co layers is mediated by the graphene spacer through the hybridization of C’s p z orbitals with Fe and Co’s 3d states. The hybridization is substantially suppressed for multilayered graphene spacers, for which the magnetic coupling between ferromagnets is critically reduced, suggesting the need for ultrathin (monolayer) spacers in the design of synthetic graphene-based antiferromagnets. In the case of h–BN, p z orbitals also mediate d(Fe/Co) coupling. However, there is a larger contribution of local ferromagnetic interactions. Magnetic anisotropy energies were also calculated using a fully relativistic description, and show out–of–plane easy axis for all the configurations, with remarkable net values in the range from 1 to 4 meV.