Josephson Junction — RCSJ Model

Parameters

Bias current I / I_c: 0.8 Damping β_c (McCumber): 1.0 AC drive amplitude I_AC/I_c: 0.0 AC frequency ω_AC: 1.0

RCSJ model: The Josephson junction equation is a damped pendulum: (ℏC/2e)φ̈ + (ℏ/2eR)φ̇ + I_csin(φ) = I_bias. Below I_c: supercurrent state. Above I_c: resistive state with oscillating voltage V = (ℏ/2e)φ̇. AC drive creates Shapiro steps at V = nℏω/2e. High β_c (underdamped) shows hysteresis.