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Semiclassical dynamics of a spin-1/2 in an arbitrary magnetic field

Adrian Alscher·Hermann Grabert
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Abstract

The spin coherent state path integral describing the dynamics of a spin-1/2-system in a magnetic field of arbitrary time-dependence is considered. Defining the path integral as the limit of a Wiener regularized expression, the semiclassical approximation leads to a continuous minimal action path with jumps at the endpoints. The resulting semiclassical propagator is shown to coincide with the exact quantum mechanical propagator. A non-linear transformation of the angle variables allows for a determination of the semiclassical path and the jumps without solving a boundary-value problem. The semiclassical spin dynamics is thus readily amenable to numerical methods.

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Adrian Alscher, Hermann Grabert. 1999-04-29. Semiclassical dynamics of a spin-1/2 in an arbitrary magnetic field. https://doi.org/10.1088/0305-4470%2F32%2F26%2F309

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