Josephson Junction — RCSJ Model

Resistively-Capacitively Shunted Junction · washboard potential · IV curve

IV Characteristic

Washboard Potential + Phase

Phase vs Time



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⟨V⟩/V_c
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State
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Stewart-McCumber β_c
RCSJ model: β_c·φ̈ + φ̇ + sin(φ) = I/I_c (normalized).
β_c = ω_p²RC (McCumber parameter). Underdamped (β_c ≫ 1): hysteresis — junction stays resistive until I drops below I_r ≪ I_c. Overdamped (β_c ≪ 1): no hysteresis, V = R√(I²-I_c²) for I>I_c. Washboard tilts under bias current.