Path Parameters
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Berry Phase Information
Solid Angle Ω: 0.000 rad
Berry Phase γ: 0.000 rad
Dynamic Phase θ_dyn: 0.000 rad
Total Phase: 0.000 rad
Progress: 0%
Berry Phase γ: 0.000 rad
Dynamic Phase θ_dyn: 0.000 rad
Total Phase: 0.000 rad
Progress: 0%
About Berry Phase
The Berry phase is a geometric phase acquired when a quantum system undergoes adiabatic evolution along a closed path in parameter space.
For a spin-½ particle in a slowly rotating magnetic field B⃗(t):
- State follows: |ψ(t)⟩ ∝ exp(iθ_total) |n̂(t)⟩
- Total phase = Dynamic + Geometric
- Dynamic: θ_dyn = -(1/ℏ) ∫ E(t) dt
- Geometric (Berry): γ = ∮ ⟨ψ|i∇_R|ψ⟩ · dR
- For spin-½: γ = -Ω/2 (half the solid angle)
Circular cone at angle θ:
Ω = 2π(1 - cos θ)
γ = -π(1 - cos θ)
Berry phase is geometric—it depends only on the path shape, not the speed of evolution.