Spin Precession and Rate Equations

D. Dubbers, H.‐J. Stöckmann

Herbert E. Spohn

Abstract. We study the Dirac equation with slowly varying external potentials. Using matrix-valued Wigner functions we prove that the electron follows with high precision the classical orbit and that the spin precesses The high precision experiments of the anomalous magnetic moment of the electron or the muon use in their interpretation the BMT equation for spin precession [1]. The derivation of Bargmann, Michel, and Telegdi [2] does not even mention quantum mechanics, however. Rather their arguments are

Liang Jiu-Qing, Ding Xiu-xiang

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.

Philippe Martin, Massimiliano Sassoli de Bianchi

Yue Chang, Shuangai Wan, Jie Qin

Nuclear-magnetic-resonance gyroscopes that detect rotation as a shift in the precession frequency of nuclear spins have attracted a lot of attention. Under a feedback-generated drive, the precession frequency in the steady state is supposed to be dependent only on the angular momentum and an applied magnetic field. However, nuclei with spins larger than 1/2 experience electric quadrupole interaction with electric-field gradients at the cell walls. This quadrupole interaction shifts the precession frequencies of the nuclear spins, which brings inaccuracy to the rotation measurement as the quadrupole interaction constant ${C}_{q}$ is difficult to precisely measure. In this paper, the effects of quadrupole interaction on nuclear-magnetic-resonance gyroscopes are theoretically studied. We find that, when the constant ${C}_{q}$ is small compared to the characteristic decay rate of the system, which is the case in most gyroscopes for practical use, as the strength of the feedback-driving field increases, the quadrupole shift monotonically decreases, regardless of the system parameters in including ${C}_{q}$. Furthermore, the larger driving amplitude can reduce the quadrupole shift's fluctuation caused by fluctuations of the system parameters, and, thus, it can reduce systematic errors resulted from the quadrupole interaction. In the large-${C}_{q}$ regime, more than one precession frequency exists, and the nuclear spins may precess with a single frequency or multifrequencies depending on initial conditions. In this regime with large driving amplitudes, the nuclear spin can restore the single-frequency precession. These results are obtained by solving an effective master equation of the nuclear spins in a rotating frame from which both the steady-state solutions and the dynamics of the system are shown.

D. Dubbers, H.‐J. Stöckmann