Resistively and Capacitively Shunted Junction: plasma oscillations, IV curve, and chaos
Parameters
ℏ/(2e) · φ̈ + (ℏ/2eR)φ̇ + I_c sin φ = I_b
RCSJ: C φ̈ + φ̇/R + sin φ = I/I_c
⟨V⟩/V₀ = 0.000
ω_p/ω_J = 0.000
State: subgap
The RCSJ model treats the Josephson junction as a nonlinear inductor in parallel with resistance R and capacitance C.
The phase φ obeys a driven pendulum equation — a tilted washboard potential.
For I > I_c, the phase runs and voltage appears (AC Josephson effect).
High Q (low damping) produces plasma oscillations and chaos near I_c.