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arXiv 1801.01348cond-mat.mes-hallphysics.atom-phquant-ph
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球上非相对论Dirac振子的自旋力和力矩

Spin Force and Torque in Non-relativistic Dirac Oscillator on a Sphere

M. S. Shikakhwa

摘要:

非相对论性狄拉克振子(在非相对论性极限下,狄拉克振子是具有强自旋-轨道相互作用的自旋二分之一3D谐振子)上的自旋力算符是使用海森堡运动方程导出的,并且被认为在形式上类似于运动带电粒子上的电磁场的力。当被限制在半径为R的球中时,证明了这种非相对论振子的哈密顿量可以表示为一个带有反常部分的纯动能算符。结果,在这种情况下,自旋力和转矩算子的功率被视为消失。的自旋力运营商的球体上的明确计算和其扭矩被证明是等于动力学轨道角动量运营商的变化率,再次与异常的一部分。这与总角动量守恒一起表明,自旋力对动力学轨道角动量算符施加了自旋相关的力矩,以保持总角动量守恒。动力学轨道角动量算符中反常自旋部分的存在引起了类似于\textit{Zitterbewegung}的振荡行为。这表明,在NRDO和表现出自旋霍尔效应的系统中,产生自旋力和\textit{Zitterbewegung}的基本物理是相同的。

英文摘要:

The spin force operator on a non-relativistic Dirac oscillator ( in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin-orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle . When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggest that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the \textit{Zitterbewegung}. It is suggested that the underlying physics that gives rise to the spin force and the \textit{Zitterbewegung} is one and the same in NRDO and in systems that manifest spin Hall effect.

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