Arbitrary Spin Orientations Research Articles

Generic gravito-magnetic clock effects

ABSTRACT General relativity predicts that two counter-orbiting clocks around a spinning mass differ in the time required to complete the same orbit. The difference in these two values for the orbital period is generally referred to as the gravito-magnetic (GM) clock effect. It has been proposed to measure the GM clock effect using atomic clocks carried by satellites in prograde and retrograde orbits around the Earth. The precision and stability required for satellites to accurately perform this measurement remains a challenge for current instrumentation. One of the most accurate clocks in the Universe is a millisecond pulsar, which emits periodic radio pulses with high stability. Timing of the pulsed signals from millisecond pulsars has proven to be very successful in testing predictions of general relativity and the GM clock effect is potentially measurable in binary systems. In this work, we derive the generic GM clock effect by considering a slowly spinning binary system on an elliptical orbit, with both arbitrary mass ratio and arbitrary spin orientations. The spin–orbit interaction introduces a perturbation to the orbit, causing the orbital plane to precess and nutate. We identify several different contributions to the clock effects: the choice of spin supplementary condition and the observer-dependent definition of a full revolution and ‘nearly identical’ orbits. We discuss the impact of these subtle definitions on the formula for GM clock effects and show that most of the existing formulae in the literature can be recovered under appropriate assumptions.

Signatures of a spinning supermassive black hole binary on the mas-scale jet of the quasar S5 1928+738 based on 25 yr of VLBI data

ABSTRACT In a previous work, we have identified the spin of the dominant black hole of a binary from its jet properties. Analysing Very Long Baseline Array (VLBA) observations of the quasar S5 1928+738, taken at 15-GHz during 43 epochs between 1995.96 and 2013.06, we showed that the inclination angle variation of the inner (<2 mas) jet symmetry axis naturally decomposes into a periodic and a monotonic contribution. The former emerges due to the Keplerian orbital evolution, while the latter is interpreted as the signature of the spin-orbit precession of the jet emitting black hole. In this paper, we revisit the analysis of the quasar S5 1928+738 by including new 15-GHz VLBA observations extending over 29 additional epochs, between 2013.34 and 2020.89. The extended data set confirms our previous findings which are further supported by the flux density variation of the jet. By applying an enhanced jet precession model that can handle arbitrary spin orientations κ with respect to the orbital angular momentum of a binary supermassive black hole system, we estimate the binary mass ratio as ν = 0.21 ± 0.04 for κ = 0 (i.e. when the spin direction is perpendicular to the orbital plane) and as ν = 0.32 ± 0.07 for κ = π/2 (i.e. when the spin lies in the orbital plane). We estimate more precisely the spin precession velocity, halving its uncertainty from $(-0.05\pm 0.02)$ to $(-0.04\pm 0.01)^{\circ }\, \mathrm{yr}^{-1}$.

NLO deflections for spinning particles and Kerr black holes

We employ the “KMOC” formalism of [1] to compute classical momentum deflections of spinning bodies with arbitrary spin orientations up to next-to-leading order (one loop). We do this in electrodynamics and gravity. The final result, valid for generic masses, is true for all spins at tree level and up to second (fourth) spin order for the electromagnetic (gravity) case at one loop. Furthermore, emphasis is given to the probe limit scenario where our results extend to all spin orders in the heavy source, even at next-to-leading order. We carry out our computations both using a unitarity based framework and Feynman diagrammatic approach which relies on scattering amplitudes computed on fixed backgrounds.

Arbitrarily spin-orientated and super-resolved focal spot.

In this Letter, we propose a facile approach for achieving a robust focal spot bearing both super-resolution and arbitrary spin orientation. Toward this aim, we meticulously devise a structured incident light consisting of three sorts of beams, which can be produced definitely by the superposition of a radially polarized beam and an azimuthally polarized beam. Based on the vectorial diffraction integral and spin density theory, such newly configurable beams are tightly focused and isotropically interfered in a 4π microscopic configuration to create three polarized field components perpendicular to each other beyond the diffraction limit, thus enabling us to yield a super-resolved focal spot possessing spatial spin axis. By further willfully adjusting the amplitude factors of the reconstituent fields, the photonic spin direction can be freely tunable. The demonstrated results in this Letter may hold great potential for the spin photonics.

Effect of an arbitrary spin orientation on the quadrupolar structure of an extended body in a Schwarzschild spacetime

The influence of an arbitrary spin orientation on the quadrupolar structure of an extended body moving in a Schwarzschild spacetime is investigated. The body dynamics is described by the Mathisson-Papapetrou-Dixon model, without any restriction on the motion or simplifying assumption on the associated spin vector and quadrupole tensor, generalizing previous works. The equations of motion are solved analytically in the limit of small values of the characteristic length scales associated with the spin and quadrupole variables with respect to the characteristic length of the background curvature. The solution provides all corrections to the circular geodesic on the equatorial plane taken as the reference trajectory due to both the dipolar and quadrupolar structures of the body as well as the conditions which the nonvanishing components of the quadrupole tensor must fulfill in order for the problem to be self-consistent.

Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling

We propose a way of including the next-to-leading (NLO) order spin-spin coupling into an effective-one-body (EOB) Hamiltonian. This work extends [S. Balmelli and P. Jetzer, Phys. Rev. D 87, 124036 (2013)], which is restricted to the case of equatorial orbits and aligned spins, to general orbits with arbitrary spin orientations. This is done applying appropriate canonical phase-space transformations to the NLO spin-spin Hamiltonian in Arnowitt-Deser-Misner (ADM) coordinates, and systematically adding "effectiv" quantities at NLO to all spin-squared terms appearing in the EOB Hamiltonian. As required by consistency, the introduced quantities reduce to zero in the test- mass limit. We expose the result both in a general gauge and in a gauge-fixed form. The last is chosen such as to minimize the number of new coefficients that have to be inserted into the effective spin squared. As a result, the 25 parameters that describe the ADM NLO spin-spin dynamics get condensed into only 12 EOB terms.

Ultra-relativistic fermion scattering by slowly rotating gravitational sources

In this paper, we discuss the gravitational scattering of fermions in the gravitational field of a massive, slowly rotating source characterized by an arbitrary spin orientation. We derive the gravito-electromagnetic field of the source using the weak-field approximation of Einstein’s equations, which holds true when dealing with sources having a weak gravitational field and non-relativistic rotation. In such a gravitational background, we obtain the linearized fermion interaction Lagrangian. We then evaluate at the tree level the transition amplitude and the cross-section of the fermion scattering process in the ultra-relativistic limit (m ≪ E). We examine the dependence of the cross-section on the relative orientation between the source spin and the direction of the fermion flux and discuss the contributions deriving from the gravitoelectric and the gravitomagnetic parts of the background field of the source. Further insight into the underlying physics is gained by comparing the results with those obtained in the case of gravitational scattering of a massless scalar field. We also find evidence of non-null backscattering in the case of orthogonality between the direction of propagation of the fermion flux and the source spin.

Cherenkov radiation of a spinning particle

We consider the Cherenkov radiation of a neutral particle with magnetic moment, and the spin-dependent contribution to the Cherenkov radiation of a charged spinning particle. The corresponding radiation intensity is obtained for an arbitrary value of spin and for an arbitrary spin orientation with respect to velocity.

A fast ab initio approach to the simulation of spin dynamics

A spin dynamics simulation approach is proposed which is very much faster than a conventional ab initio spin dynamics code but which—nevertheless—exhibits ab initio or near-ab initio accuracy. In this approach the anewed ab initio calculation of the effective fields acting on the various spins in each time step of the spin dynamics algorithm which is required in the conventional ab initio codes and which makes them very costly is avoided. Instead, before starting the simulation, an analytical parametrization of the adiabatic energy hypersurface E for arbitrary spin orientations is obtained via the recently developed spin cluster expansion, and then the effective fields can be determined by simple derivatives. The new approach makes it possible to investigate the spin dynamics of technologically interesting spin nanostructures with strong atomic scale spin inhomogeneities like spin vortices.

Impurity states of two-dimensional magnetic electron–hole complexes on a spatially separated donor center

The barrier impurity states of two-dimensional electron–hole complexes are considered in the strong magnetic field limit. The energies of the lowest impurity states of the exciton, the 2e–h complex and the biexciton are calculated for the different projections of the total angular momentum M with arbitrary spin orientations. The stable impurity bound states of the exciton and the biexciton exist for the case of an impurity located near the barrier edge. The magnetic evaporation of such states is expected. The magnetic induced binding of the 2e–h complex by impurities in the barrier is predicted as the magnetic field increases. The energy of the exciton separation for the Se=0,M=0 barrier impurity bound state of the 2e–h complex can be 2 times larger than that of the delocalized trion.

Impurity states of two-dimensional magnetic electron–hole (e–h) complexes in a spatially separated e–h system

An interacting system of two-dimensional spatially separated electrons and holes containing charged impurity is considered in the strong magnetic field limit. The energies of the lowest impurity states of exciton, 2e–h complex and biexciton are calculated for the different projections of the total angular momentum M with arbitrary spin orientations. It is shown that on increasing the interlayer separation d the impurity states with higher momentum become more favorable. This progression leads to magnetic evaporation of impurity bound states of biexciton and 2e–h complex at large d. However, all impurity states of the 2e–h complex are unbound at d<0.8 r H . The spin-singlet–spin-triplet oscillations of the impurity-bound biexciton ground state are predicted as d increases from zero at fixed H.

Formal theory of neutron induced fission

General expression for differential cross section of neutron induced fission is derived with account of arbitrary spin orientation of colliding particles. A covariant description of angular dependence of fission cross section is proposed. Helicity representation for fission fragments is considered in details and limits of its validity are investigated. It is shown that this representation makes reliable basis for description of interference effects in total and differential cross sections of fission induced by slow neutrons. A relation between total fragment helicity K and A.Bohr quantum number K is discussed.

On the dynamics of electrons in the strong‐coupling Hubbard chain

AbstractThe dynamics of electrons is investigated in a Hubbard chain in the strong‐coupling limit. This problem may be figured as the motion of a double‐occupancy (consisting of one spin‐up and one spin‐down electron fixed at the same lattice site) on a linear chain, all other sites of which are occupied by single electrons of arbitrary spin orientation. The spectrum of this problem is derived exactly and from it the partition function is calculated. It agrees with the result derived by Beni and coworkers formerly with the aid of thermodynamic perturbation theory.

Scattering of Polarized Dirac Particles on Electrons

The cross section for electron-electron scattering in which the incident and target electrons have arbitrary spin orientations has been evaluated. For the special case in which the spin of the incident electron is polarized along the direction of motion, two different spin effects are obtained. The first of these effects is simply a dependence of the cross section on the relative spin orientation; the second effect corresponds to an up-down asymmetry in the cross section. Similar effects have been obtained for the scattering of polarized positrons on polarized electrons.The depolarization of electrons and muons in scattering on unpolarized electrons also has been considered. For electrons which lose an appreciable fraction of their initial energy in passing through matter, the depolarization is appreciable. If the fractional energy loss is small the depolarization is proportional to the fractional energy loss. For nonrelativistic muons the depolarization which occurs as they are brought to rest in matter is found to be negligible.