Josephson Junction Phase Dynamics

The RCSJ model describes a superconducting junction via φ̈ + γφ̇ + sin(φ) = I/Ic. The phase particle rolls in a tilted washboard potential, giving DC and AC Josephson effects.

Visualization

Washboard Potential
I-V Curve
Phase vs Time

RCSJ Parameters

φ̈ + γφ̇ + sin(φ) = I/Ic
γ = 1/(ωc RC) (damping)
ωc = 2eIcR/ℏ

State

Phase φ (mod 2π)---
dφ/dt (voltage)---
Mode---
⟨V⟩ (avg)---
Shapiro steps:
RF drive locks φ̇ = nω_rf
→ V = nℏω_rf/2e steps
Josephson: 2e/ℏ ~ 484 MHz/μV