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arXiv:quant-ph/9807016 · Comptes Rendus de l Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy

Spin in a variable magnetic field: the adiabatic approximation

M. S. Marinov, Eugene Strahov

Published Feb 1, 1999• 0 citations
arXivHTMLPDF
DOI
10.1016/s1287-4620(99)80063-5

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By making use of the improved Born-Oppenheimer approximate method, we deal with the separation of spin variable and space variable of neutral particle with arbitrary spin in inhomogeneous magnetic field and non-adiabatic corrections for the problems are thereby computed as perturbations. We also analysis the geometrical properties of loop phase of the induced gauge potential and point out its observable effects relating to Bitter and Dubbers' experiment. Finally, we discuss the transitions between the instantaneous spin states as non-;-adiabatic effects resulting from inhomogeneity of the magnetic field.
By invoking the Rabi rotation technique, the Schrödinger wavefunction of a neutral particle with a magnetic moment and a high-spin is exactly solved in a harmonically-changing magnetic field. This result is then applied to illustrate what the accuracy of the quantum adiabatic approximation is exactly and how the non-adiabatic transition vanishes in accompaniment with the appearence of Berry's geometrical phase. The discussion of this paper verifies C. N. Yang's point of view about the generalization of the quantum adiabatic approximation in connection with Berry's phase.
With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.