Physics Notes
Bloch equations (infinite-temperature bath, Bz_eq=0):
dBx/dt = −Bx/T₂ | dBy/dt = −By/T₂ | dBz/dt = −Bz/T₁
Constraint: 1/T₂ = 1/(2T₁) + 1/T_φ — so T₂ ≤ 2T₁ always.
T₂ equals 2T₁ only when T_φ → ∞ (no pure dephasing).
Initial state: |θ=60°, φ=45°⟩ →
Bx₀=By₀=√6/4≈0.612, Bz₀=0.5
Shows spiral inward: faster transverse (T₂) vs longitudinal (T₁) decay.
Purity: Tr(ρ²) = (1+|B|²)/2. Pure state=1.0; fully mixed=0.5.
Physics checks:
P1 (T_φ→∞ ⟹ T₂→2T₁): — |
P2 (T₁→∞ ⟹ Bz const): — |
P3 (t=5T₂ nearly mixed): —