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Josephson Junction Dynamics
Quantum
Superconductivity
Parameters
Bias current I/I_c
0.80
Damping β
0.20
Noise T/T_c
0.02
Live State
Phase φ
0.00 rad
Voltage ⟨V⟩
0.00 μV
Regime
DC Josephson
Frequency f_J
0.00 GHz
Physics
dφ/dt = (2e/ℏ) V
I = I_c sin(φ)
ℏ/(2e) dφ/dt + β⁻¹ sin(φ) = I/I_c
RCSJ model (Stewart–McCumber):
φ̈ + (1/βQ) φ̇ + sin φ = i_bias
DC effect: φ static, I = I_c sin φ₀
AC effect: ⟨V⟩ ≠ 0 → f_J = 2eV/h