1. Understanding Spin Relaxation using Conformal Transformations
Manuel Berrondo
Dept. Physics & Astronomy
Brigham Young University
Provo UT 84602
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2. In collaboration with: Wes Krueger
“The purpose of models is not to fit the data
but to sharpen the questions”
S. Karlin
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3. Introduction Dynamics of Heisenberg model with dissipation
Look first at spin precession and relaxation w/ constant B field
Dissipation term (Gilbert) can be solved exactly w/stereographic projection
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4. Spin precession and relaxation
preserves S2, chosen to be 1.
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5. Conformal Transformations in R3
Inverse of a vector a ≠ 0
a-1 1 a 2
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6. Mapping plane onto spherew r
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7. Stereographic Projection
Tip of S on the unit sphere, S2=1
Projection onto plane has two components: W  R2
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8. Mixed Representation
From equation of motion:
we get:
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9. Equation of Motion for W (t)
with solution:
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