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Understanding Spin Relaxation using Conformal Transformations. Manuel Berrondo Dept. Physics & Astronomy Brigham Young University Provo UT 84602. In collaboration with: Wes Krueger. “The purpose of models is not to fit the data but to sharpen the questions”
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Understanding Spin RelaxationusingConformalTransformations Manuel Berrondo Dept. Physics & Astronomy Brigham Young University Provo UT 84602 BYU Physics
In collaboration with: Wes Krueger “The purpose of models is not to fit the data but to sharpen the questions” S. Karlin BYU Physics
Introduction • Dynamics of Heisenbergmodelwithdissipation • Look first at spin precession and relaxation w/ constantBfield • Dissipationterm (Gilbert) can besolvedexactly w/stereographicprojection BYU Physics
Spin precession and relaxation preserves S2,chosentobe 1. BYU Physics
ConformalTransformations in R3 Inverse of a vector a≠ 0 a-1 0 1 2 a BYU Physics
Mappingplaneontosphere w r BYU Physics
StereographicProjection • Tip of Sontheunitsphere, S2=1 • Projectionontoplane has twocomponents: W R2 BYU Physics
MixedRepresentation • Fromequation of motion: weget: BYU Physics
Equation of MotionforW (t) withsolution: BYU Physics
