Stern-Gerlach Force Research Articles

Spin-Gravity Coupling in a Rotating Universe

The coupling of intrinsic spin with the nonlinear gravitomagnetic fields of Gödel-type spacetimes is studied. We work with Gödel-type universes in order to show that the main features of spin-gravity coupling are independent of causality problems of the Gödel universe. The connection between the spin–gravitomagnetic field coupling and Mathisson’s spin-curvature force is demonstrated in the Gödel-type universe. That is, the gravitomagnetic Stern–Gerlach force due to the coupling of spin with the gravitomagnetic field reduces in the appropriate correspondence limit to the classical Mathisson spin-curvature force.

High-frequency magnetotransport in a viscous electron fluid under a Stern-Gerlach force

We apply a hydrodynamic theory to study transverse magnetosonic resonances in a viscous two-dimensional electron fluid under an in-plane Stern-Gerlach force (SGF), a perpendicular magnetic field with cyclotron frequency ${\ensuremath{\omega}}_{c}$, and an alternating electric field with frequency $\ensuremath{\omega}$. The SGF leads to a splitting in the dispersion curve of the transverse magnetosound wave and hinders the long-wavelength plasmonic excitation. The effective diagonal viscosity coefficient can be enhanced by about one order of magnitude due to the SGF. The variation of absorption power $Y$ with ${\ensuremath{\omega}}_{c}$ exhibits a viscoelastic (VE) resonance at ${\ensuremath{\omega}}_{c}=\ensuremath{\omega}/2$ and transverse magnetosound resonances. The SGF can raise the heights of all resonant peaks and leave the peak positions almost completely unchanged. The most substantial magnetosonic resonant peak, much weaker than the VE peak in the absence of SGF, can be tuned by the SGF to be well above the VE peak. Our results indicate that the SGF can be used to tune the VE resonance and transverse magnetosound resonances, which is relevant to the manipulation of photoresistance and photovoltaic effects in viscous electron fluids.

Motion of classical charged particles with magnetic moment in external plane-wave electromagnetic fields

We study the motion of a charged particle with magnetic moment in external electromagnetic fields utilizing covariant unification of Gilbertian and Amperian descriptions of particle magnetic dipole moment. Considering the case of a current loop, our approach is verified by comparing classical dynamics with the classical limit of relativistic quantum dynamics. We obtain motion of a charged particle in the presence of an external linearly polarized EM (laser) plane wave field incorporating the effect of spin dynamics. For specific laser-particle initial configurations, we determine that the Stern-Gerlach force can have a cumulative effect on the trajectory of charged particles.

Gravitomagnetic Stern-Gerlach Force.

A heuristic description of the spin-rotation-gravity coupling is presented and the implications of the corresponding gravitomagnetic Stern–Gerlach force are briefly mentioned. It is shown, within the framework of linearized general relativity, that the gravitomagnetic Stern–Gerlach force reduces in the appropriate correspondence limit to the classical Mathisson spin-curvature force.

Effect of Stern-Gerlach force on negative magnetoresistance and Hall resistance in spin-dependent viscous flow

In two-dimensional electron systems (2DES), a hydrodynamic regime with remarkable viscous effects is recognized when the sample width is small enough and momentum-conserving scattering is dominant. Based on hydrodynamic calculations for a 2DES, we obtain large effective viscosity coefficients, which lead to large negative magnetoresistance (MR) and Hall resistance due to the effect of an in-plane Stern-Gerlach force on the viscosity components. The spin-dependent viscous effect manifests itself via both longitudinal and Hall resistances. The negative MR and Hall resistance are markedly sensitive to the perpendicular magnetic field with amplitude around zero, which would be useful in MR sensors and magnetic recording devices.

Scaling laws for the depolarization time of relativistic particle beams in strong fields

The acceleration of polarized electrons and protons in strong laser and plasma fields is a very attractive option to obtain polarized beams in the GeV range. We investigate the feasibility of particle acceleration in strong fields without destroying an initial polarization, taking into account all relevant mechanisms that could cause polarization losses, i.e. the spin precession described by the T-BMT equation, the Sokolov-Ternov effect and the Stern-Gerlach force. Scaling laws for the (de-)polarization time caused by these effects reveal that the dominant polarization limiting effect is the rotation of the single particle spins around the local electromagnetic fields. We compare our findings to test-particle simulations for high energetic electrons moving in a homogeneous electric field. For high particle energies the observed depolarization times are in good agreement with the analytically estimated ones.

Relativistic dynamics of point magnetic moment

The covariant motion of a classical point particle with magnetic moment in the presence of (external) electromagnetic fields is revisited. We are interested in understanding extensions to the Lorentz force involving point particle magnetic moment (Stern–Gerlach force) and how the spin precession dynamics is modified for consistency. We introduce spin as a classical particle property inherent to Poincaré symmetry of space-time. We propose a covariant formulation of the magnetic force based on a ‘magnetic’ 4-potential and show how the point particle magnetic moment relates to the Amperian (current loop) and Gilbertian (magnetic monopole) descriptions. We show that covariant spin precession lacks a unique form and discuss the connection to g-2 anomaly. We consider the variational action principle and find that a consistent extension of the Lorentz force to include magnetic spin force is not straightforward. We look at non-covariant particle dynamics, and present a short introduction to the dynamics of (neutral) particles hit by a laser pulse of arbitrary shape.

Spin-one-half particles in strong electromagnetic fields: Spin effects and radiation reaction

Various classical models of electrons including their spin degrees of freedom are commonly applied to describe the electron dynamics in strong electromagnetic fields. We demonstrate that different models can lead to different or even contradicting predictions regarding how the spin degree of freedom modifies the electron's orbital motion when the electron moves in strong electromagnetic fields. This discrepancy is rooted in the model-specific energy dependency of the spin-induced Stern-Gerlach force acting on the electron. The Frenkel model and the classical Foldy-Wouthuysen model are compared exemplarily in the nonrelativistic and the relativistic limits in order to identify parameter regimes where these classical models make different predictions. This allows for experimental tests of these models. In ultrastrong laser setups in parameter regimes where effects of the Stern-Gerlach force become relevant, radiation-reaction effects are also expected to set in. We incorporate the radiation reaction classically via the Landau-Lifshitz equation and demonstrate that although radiation-reaction effects can have a significant effect on the electron trajectory, the Frenkel model and the classical Foldy-Wouthuysen model remain distinguishable also if radiation-reaction effects are taken into account. Our calculations are also suitable to verify the Landau-Lifshitz equation for the radiation reaction of electrons and other spin-1/2 particles.

Identifying the Stern-Gerlach force of classical electron dynamics.

Different classical theories are commonly applied in various branches of physics to describe the relativistic dynamics of electrons by coupled equations for the orbital motion and spin precession. Exemplarily, we benchmark the Frenkel model and the classical Foldy-Wouthuysen model with spin-dependent forces (Stern-Gerlach forces) to the quantum dynamics as predicted by the Dirac equation. Both classical theories can lead to different or even contradicting predictions how the Stern-Gerlach forces modify the electron’s orbital motion, when the electron moves in strong electromagnetic field configurations of emerging high-intensity laser facilities. In this way, one may evaluate the validity and identify the limits of these classical theories via a comparison with possible experiments to provide a proper description of spin-induced dynamics. Our results indicate that the Foldy-Wouthuysen model is qualitatively in better agreement with the Dirac theory than the widely used Frenkel model.

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the “wave spin”. Both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern–Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler–Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and lead to equations for the wave spin, which happens to be an (N2−1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N=2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann–Michel–Telegdi equations with added Stern–Gerlach force.

Covariant hamiltonian spin dynamics in curved space–time

The dynamics of spinning particles in curved space–time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space–time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern–Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.

Vorticity, gyroscopic precession, and spin-curvature force

In investigating the relationship between vorticity and gyroscopic precession, we calculate the vorticity vector in Godel, Kerr, Lewis, Schwarzschild, and Minkowski metrics and find that the vorticity vector of the specific observers is the angular velocity of the gyroscopic precession. Furthermore, when space-time torsion is included, the vorticity and spin-curvature force change sign. This result is very similar to the behavior of the positive and negative helicities of quantum spin in the Stern-Gerlach force. It implies that the inclusion of torsion will lead to an analogous property of quantum spin even in classical treatment.

Semiclassical limit for Dirac particles interacting with a gravitational field

The behavior of a spin-$1/2$ particle in a weak static gravitational field is considered. The Dirac Hamiltonian is diagonalized by the Foldy-Wouthuysen transformation providing also the simple form for the momentum and spin polarization operators. The operator equations of momentum and spin motion are derived for a first time. Their semiclassical limit is analyzed. The dipole spin-gravity coupling in the previously found (another) Hamiltonian does not lead to any observable effects. The general agreement between the quantum and classical approaches is established, contrary to several recent claims. The expression for the gravitational Stern-Gerlach force is derived. The helicity evolution in the gravitational field and corresponding accelerated frame coincides, being the manifestation of the equivalence principle.

Convective instabilities in spin-polarized gases

We study some peculiarities of spin polarized quantum gases hydrodynamics and proposed experiments in which, in a sense, the Pauli principle can be macroscopically observed. For example, we discuss in this context the original features of the Rayleigh-Bénard situation. A new magnetic convective instability (due to Stern-Gerlach force) is presented. A (very) brief survey of the interest of these quantum systems with regard to specific problems of non-linear hydrodynamics (pattern selection, bifurcations) is given.

Convective instabilities in spin-polarized gases

We study some peculiarities of spin polarized quantum gases hydrodynamics and propose experiments in which, in a sense, the Pauli principle can be macroscopically observed. For example, we discuss in this context the original features of the Rayleigh-Bénard situation. A new magnetic convective instability (due to Stern-Gerlach force) is presented. A (very) brief survey of the interest of these quantum systems with regard to specific problems of non-linear hydrodynamics (pattern selection, bifurcations) is given.

Asymptotic solution of the Dirac equation and the inertial mass of an electron

The asymptotic ($h\ensuremath{\rightarrow}0$) limit of Dirac's single-electron theory is discussed with the magnetic field strength formally regarded as a quantity of order $\frac{1}{h}$. The main new result is that the phase function for the asymptotic series is to be calculated from the relativistic Hamilton-Jacobi equation with the orientation energy of the magnetic moment added to the electron's rest mass. This is the mechanism by means of which Hamilton's equations contain the Stern-Gerlach force when the phase function is interpreted as a classical generating function. An attempt is made to clarify the physical significance of this result.

Critical Examination of a Proposed Charged-Particle Stern–Gerlach Experiment

It has been proposed by Enga and Bloom that combined electric and magnetic helical quadrupole fields may be used to perform a Stern–Gerlach experiment on charged particles. A detailed investigation shows that the longitudinal Lorentz force due to coupling of the transverse velocity of the particles to the transverse magnetic field produces an additional focusing effect which masks the Stern–Gerlach force in large regions of initial phase space. Consideration of uncompensated magnetic fields, produced by small random variations in conductor dimensions and location, shows that the tolerances required to preserve spin separation in the useful range of initial conditions are several orders of magnitude higher than can be achieved at this time.