Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field

Abstract

Article:Littlejohn, Robert and Weigert, S. orcid.org/0000-0002-6647-3252 (1993) Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field. Physical Review A. pp. 924-940. ISSN 1094924-940. ISSN -1622 https://doi.org/10.1103/PhysRevA.48.924 eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. The motion of a neutral particle with a magnetic moment in an inhomogeneous magnetic field is considered. This situation, occurring, for example, in a Stern-Gerlach experiment, is investigated from classical and semiclassical points of view. It is assumed that the magnetic field is strong or slowly varying in space, i.e., that adiabatic conditions hold. To the classical model, a systematic Lie-transform perturbation technique is applied up to second order in the adiabatic-expansion parameter. The averaged classical Hamiltonian contains not only terms representing fictitious electric and magnetic fields but also an additional velocity-dependent potential. The Hamiltonian of the quantum-mechanical system is diagonalized by means of a systematic WKB analysis for coupled wave equations up to second order in the adiabaticity parameter, which is coupled to Planck's constant. An exact term-by-term correspondence with the averaged classical Hamiltonian is established, thus confirming the relevance of the additional velocity-dependent second-order contribution.

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

“…Similar equations have been derived in [55] in the course of the Lagrange description of the wave packet dynamics. Particular cases of these are discussed in many papers on the topological spin transport [21][22][23][24][25][26][54][55][56][57][58][59]63,65,68,76,84,[86][87][88][89][90][91]. The first terms in the right-hand sides of Eqs.…”

“…Indeed, just after the discovery of the Berry phase the manifestations of the socalled geometric force were revealed [17][18][19][20][21][22][23][24][25][26]. And almost simultaneously with the discovering of the Berry phase, Thouless proposed a mechanism of adiabatic transport of particles [26].…”

Newtonian adiabatics unified

“…Robert Littlejohn made illuminating remarks about the approach in [12]. Evan Fink made interesting comments and suggestions during a visit in summer 2002 as a Research Experiences for Undergraduates scholar.…”

Pumping angular momentum by driven chaotic scattering

“…For a correct handling of these subtleties, we follow the development in [28] and obtain the equations of motion…”

“…The subject bears on various of the research lines mentioned above: We shall invoke much of what is known about chaotic scattering, in particular in periodically driven systems [26,27]. The coupling of a magnetic dipole to an inhomogeneous magnetic field [28] is crucial for our modelling. Also concerning chaotic dynamics in such a configuration we refer to earlier work [29]; in fact, it is the essential ingredient of one of the first models proposed for irregular scattering [30].…”