Analytic propagators for spin-orbit interactions

doi:10.1088/1751-8113/42/47/475304

Analytic propagators for spin–orbit interactions

Bailey C Hsu et al 2009 J. Phys. A: Math. Theor. 42 475304 (17pp) doi: 10.1088/1751-8113/42/47/475304

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Bailey C Hsu and Jean-François S Van Huele
Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA
E-mail: bailey.c.hsu@gmail.com and vanhuele@byu.edu

Abstract. We derive analytic expressions for propagators in spin–orbit coupled systems. In addition to their kinetic energy, these systems exhibit a potential energy that mixes position, momentum and spin operators. We consider Hamiltonians with limited noncommutativities: the confined spin–orbit coupled Hamiltonian $H_{\rm SO}^{c}=\frac{{\bf p}^2}{2m}+\gamma {\bm \sigma} {\,\bm \cdot\,} {\bf L}+\frac{1}{2}m\eta ^2 (x^2+y^2)$ , the confined Equal–Strength–Rashba–Dresselhaus Hamiltonian $H_{\rm ESRD}^{c}=\frac{{\bf p}^2}{2m}+\frac{\alpha}{\hbar}(p_x+ p_y)(\sigma _x-\sigma _y)+\frac{1}{2}m\eta ^2(x^2+y^2)$ and the confined Opposite–Strength–Rashba–Dresselhaus Hamiltonian $H_{\rm OSRD}^{c}=\frac{{\bf p}^2}{2m}+\frac{\alpha}{\hbar}(p_x- p_y)(\sigma _x+\sigma _y)+\frac{1}{2}m\eta ^2(x^2+y^2)$ . We use both a classical action method and an algebraic method in our derivations. We mention specific applications for these propagators and illustrate their significance with examples of wavepacket evolution.

PACS numbers: 03.65.Fd, 31.15.aj, 72.25.Dc

Print publication: Issue 47 (27 November 2009)
Received 22 June 2009, in final form 28 September 2009
Published 6 November 2009

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Analytic propagators for spin–orbit interactions

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