Semiclassical dynamics of electron wave packet states with phase vortices

We consider semiclassical higher-order wave packet solutions of the Schr?dinger equation with phase vortices. The vortex line is aligned with the propagation direction, and the wave packet carries a well-defined orbital angular momentum (OAM) variant Planck's over 2pil (l is the vortex strength) along its main linear momentum. The probability current coils around the momentum in such OAM states of electrons. In an electric field, these states evolve like massless particles with spin l. The magnetic-monopole Berry curvature appears in momentum space, which results in a spin-orbit-type interaction and a Berry/Magnus transverse force acting on the wave packet. This brings about the OAM Hall effect. In a magnetic field, there is a Zeeman interaction, which, can lead to more complicated dynamics.     

The effect of inertia on the Dirac electron,the spin Hall current and the momentum space Berry curvature

We have studied the spin dependent force and the associated momentum space Berry curvature in an accelerating system. The results are derived by taking into consideration the non-relativistic limit of a generally covariant Dirac equation with an electromagnetic field present, where the methodology of the Foldy–Wouthuysen transformation is applied to achieve the non-relativistic limit. Spin currents appear due to the combined action of the external electric field, the crystal field and the induced inertial electric field via the total effective spin–orbit interaction. In an accelerating frame, the crucial role of momentum space Berry curvature in the spin dynamics has also been addressed from the perspective of spin Hall conductivity. For time dependent acceleration, the expression for the spin polarization has been derived.     

Berry phase in a nonisolated system

We investigate the effect of the environment on a Berry phase measurement involving a spin-half. We model the spin + environment using a biased spin-boson Hamiltonian with a time-dependent magnetic field. We find that, contrary to naive expectations, the Berry phase acquired by the spin can be observed, but only on time scales which are neither too short nor very long. However this Berry phase is not the same as for the isolated spin-half. It does not have a simple geometric interpretation in terms of the adiabatic evolution of either bare spin states or the dressed spin resonances. This result is crucial for proposed Berry phase measurements in superconducting nanocircuits.     

Equation of Motion of a Spinning Test Particle in Gravitational Field

Based on the coupfing between the spin of a particle and gravitoelectromagnetic field, the equation of motion of a spinning test particle in gravitational field is deduced. From this equation of motion, it is found that the motion of a spinning particle deviates from the geodesic trajectory, and this deviation originates from the coupling between the spin of the particle and gravitoelectromagnetic field, which is also the origin of Lense-Thirring effects. In post-Newtonian approximations, this equation gives the same results as those of Mathisson-Papapetrou equation. Effect of the deviation of geodesic trajectory is detectable.     

Berry effect in unmagnetized inhomogeneous cold plasmas

The propagation of electromagnetic waves in an unmagnetized weakly inhomogeneous cold plasma is examined. We show that the inhomogeneity induces a gauge connection term in wave equation, which gives rise to Berry effects in the dynamics of polarized rays in the post geometric optics approximation. The polarization plane of a plane polarized ray rotates as a result of the geometric Berry phase, which is the Rytov rotation. Also, the Berry curvature causes the optical Hall effect, according to which, rays of left/right circular polarization deflect oppositely to produce a spin current directed across the direction of propagation.     

Semiclassical diagonalization of quantum Hamiltonian and equations of motion with Berry phase corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article presents a general diagonalization method at order ħ for a large class of quantum Hamiltonians directly inducing Berry phase corrections. As a consequence, Berry phase terms on both coordinates and momentum operators naturally arise during the diagonalization procedure. This leads to new equations of motion for a wide class of semiclassical system. As physical applications we consider here a Dirac particle in an electromagnetic or static gravitational field, and the propagation of a Bloch electrons in an external electromagnetic field.     

Torsion-induced spin precession

We investigate the motion of a spinning test particle in a spatially-flat FRW-type space-time in the framework of the Einstein–Cartan theory. The space-time has a torsion arising from a spinning fluid filling the space-time. We show that, for spinning particles with non-zero transverse spin components, the torsion induces a precession of the particle spin around the direction of the spin of the fluid. We also show that a charged spinning particle moving in a torsion-less spatially-flat FRW space-time in the presence of a uniform magnetic field undergoes a precession of a different character.     

Transition of Bery Phase and Pancharatnam Phase and Phase Change

Berry Phase and time-dependent Pancharatnam phase are investigated for nuclear spin polarization in a liquid by a rotation magnetic field, where two-state mixture effect is exactly included in the geometric phases. We find that when the system of nuclear spin polarization is in the unpolarized state, the transitive phenomena of both Berry phase and Pancharatnam phase are taken place. For the polarized system, in contrast, such a transition is not taken place. It is obvious that the transitions of geometric phase correspond to the phase change of physical system.     

Quantization of spin direction for solitary waves in a uniform magnetic field

It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data) and have nonzero spin (nonzero intrinsic angular momentum in the center of momentum frame). In this paper we consider vector-valued solitary wave solutions to a nonlinear Klein-Gordon equation and investigate the behavior of these spinning solitary waves under the influence of an externally imposed uniform magnetic field. We find that the only stationary spinning solitary wave solutions have spin parallel or anti-parallel to the magnetic field direction.     

Topological quenching of spin tunneling in Fe8-tacn molecules

A Berry phase in the path integral for spin gives rise to an interference effect in the tunneling of a biaxially symmetric spin Hamiltonian. As the magnetic field applied along a hard axis is varied, the tunnel splitting between the two lowest energy states oscillates, with field values where it is completely quenched. This Hamiltonian is realized in Fe₈-tacn molecules, where these oscillations have just now been seen and provide, in fact, strong evidence for tunneling below 0.36 K in the first place.     

Berry phase for a spin 1/2 particle in a classical fluctuating field

The effect of fluctuations in the classical control parameters on the Berry phase of a spin 1/2 interacting with an adiabatically cyclically varying magnetic field is analyzed. It is explicitly shown that in the adiabatic limit dephasing is due to fluctuations of the dynamical phase.     

Exact quantum mechanical description of the motion of spin-1/2 particles and of spin motion in a uniform magnetic field

The Dirac-Pauli equation is used to obtain the exact equation of spin motion for spin-1/2 particles with an anomalous magnetic moment in a constant and uniform magnetic field. Exact formulas are established for the angular velocity of the revolution of such particles along circular orbits and the rotation of the particle spin with respect to momentum. Finally, a quantum mechanical equation for the motion of the particles in a strong magnetic field is derived. Zh. éksp. Teor. Fiz. 114, 448–457 (August 1998)     

Lienard-Wiechert potentials and synchrotron radiation from a relativistic spinning particle in pseudoclassical theory

For a relativistic spinning particle with an anomalous magnetic moment, Lienard-Wiechert potentials are constructed within the pseudoclassical approach. Some specific cases of the motion of a spinning particle are considered on the basis of general expressions obtained in this study for the Lienard-Wiechert potentials. In particular, the intensity of the synchrotron radiation from a transversely polarized particle moving along a circle at a constant speed is investigated as a function of the particle spin. In the specific case of particles having no anomalous magnetic moment and moving in an external uniform magnetic field, the resulting expressions coincide with familiar formulas from the quantum theory of radiation. The spin dependence of the polarization of synchrotron radiation is investigated.     

LARMOR PRECESSION AND THE BARRIER INTERACTION TIME

The Larmor precession of a spinning particle in a magnetic field confined in the region of one dimensional-rectangular barrier is investigated with the spin coherent state of incoming particle, which has advantage to recognize the equation of the spin precession. Our new observation is that the precession time of spin is uniquely determined and is seen to be equal to the dwell time.     

Spin and torsion in the very early universe

In the very early universe with temperature T between 10²⁴ K and 10³² K the gravitational effect of torsion is dominant if particles with spin are sufficiently polarized. The source of the torsion is the spin density and the latter is usually described by a classical theory of Weyssenhoff and Raabe. In this article the spinning particles are described quantum mechanically, i.e. with a Dirac field and the spin density is defined as the source of the torsion. The macroscopic average of the spin density is obtained by the relativistic Wigner function formalism. The expression of the spin density, as derived in this article, is different from the classical one, except when both are zero.     

Semiclassical dynamics of Dirac particles interacting with a static gravitational field

The semiclassical limit for Dirac particles interacting with a static gravitational field is investigated. A Foldy–Wouthuysen transformation which diagonalizes at the semiclassical order the Dirac equation for an arbitrary static spacetime metric is realized. In this representation the Hamiltonian provides for a coupling between spin and gravity through the torsion of the gravitational field. In the specific case of a symmetric gravitational field we retrieve the Hamiltonian previously found by other authors. But our formalism provides for another effect, namely, the spin hall effect, which was not predicted before in this context.     

On the effect of spin on the gravitational field

Using a solution of Trautman's recently formulated Einstein-Cartan equations, it is shown that if an isolated body is embedded in an expanding universe consisting of a dust of spinning particles, then the local gravitational field of the body is influenced by spin, even when the cosmological constant is neglected.     

Hall effect of light

We derive the semiclassical equation of motion for the wave packet of light taking into account the Berry curvature in momentum-space. This equation naturally describes the interplay between orbital and spin angular momenta, i.e., the conservation of the total angular momentum of light. This leads to the shift of wave-packet motion perpendicular to the gradient of the dielectric constant, i.e., the polarization-dependent Hall effect of light. An enhancement of this effect in photonic crystals is also proposed.