Understanding Spin Relaxation Through Conformal Transformations
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This presentation explores the dynamics of the Heisenberg model featuring dissipation, focusing on spin precession and relaxation in the presence of a constant magnetic field. By employing conformal transformations and stereographic projection, we obtain exact solutions for the dissipation term, providing insights into the behavior of spins in two-dimensional space. The study underscores the importance of theoretical models in refining research inquiries, demonstrating the intricate relationship between spin dynamics and conformal mapping techniques.
Understanding Spin Relaxation Through Conformal Transformations
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Presentation Transcript
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
