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Comment on “Spin evolution of a neutral particle in an oscillating magnetic field”

Apoorva G. Wagh, Veer Chand Rakhecha

Physics Letters ADec 1, 19940 citations

Semiclassical dynamics of a spin-½ in an arbitrary magnetic field

Adrian Alscher, Hermann Grabert

The spin coherent state path integral describing the dynamics of a spin-½ 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 nonlinear 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.The spin coherent state path integral describing the dynamics of a spin-½ 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 nonlinear 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.

arXiv:quant-ph/9904102Journal of Physics A Mathematical and GeneralJan 1, 199917 citations

Reply to a Comment by J. Bolte, R. Glaser and S. Keppeler on: Semiclassical theory of spin-orbit interactions using spin coherent states

Mikhail Pletyukhov, Ch. Amann, Mehta, M. +1 more

We reply to a Comment on our recently proposed semiclassical theory for systems with spin-orbit interactions.

arXiv:nlin/0209028Sep 13, 20020 citations

On the Hamiltonian and Lagrangian formulation of classical dynamics for particles with spin

Th.W. Ruijgrok, H. van der Vlist

Physica A Statistical Mechanics and its ApplicationsMay 1, 198010 citations

A comment on relativistic Hamiltonian equations for any spin

David Leo Weaver

Annals of PhysicsDec 1, 19750 citations

Comment on `Semiclassical dynamics of a spin-½ in an arbitrary magnetic field'

E. A. Kochetov

In a recent paper Alscher and Grabert claim to prove that a dominant (tree-level) stationary phase approximation to the Wiener regularized continuum su(2) coherent-state path integral for the quantum propagator : = ⟨zF | T exp (-i∫0τH ds ) | zI⟩ becomes exact, provided H is a linear combination of the su(2) generators with arbitrary time-dependent coefficients. I find the derivation of this in fact obvious result unduly complicated and somewhat obscure. The authors start from a classical spin action inconsistent with necessary boundary conditions and therefore are forced to invoke a nontrivial regularization of the action to render the latter meaningful. Alternatively, when a su(2) symplectic potential consistent with the boundary conditions is employed, no regularization is required to obtain the leading quasiclassical asymptotics.In a recent paper Alscher and Grabert claim to prove that a dominant (tree-level) stationary phase approximation to the Wiener regularized continuum su(2) coherent-state path integral for the quantum propagator : = ⟨zF | T exp (-i∫0τH ds ) | zI⟩ becomes exact, provided H is a linear combination of the su(2) generators with arbitrary time-dependent coefficients. I find the derivation of this in fact obvious result unduly complicated and somewhat obscure. The authors start from a classical spin action inconsistent with necessary boundary conditions and therefore are forced to invoke a nontrivial regularization of the action to render the latter meaningful. Alternatively, when a su(2) symplectic potential consistent with the boundary conditions is employed, no regularization is required to obtain the leading quasiclassical asymptotics.

Journal of Physics A Mathematical and GeneralMay 3, 20001 citation

Classical and quantum dynamics of a spin-½

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