Josephson Junction — Washboard Potential

The RCSJ model maps the Josephson junction phase φ to a particle in a "washboard" potential U(φ) = −E_J cos(φ) − (ħI/2e)φ. Below the critical current I_c, the phase is trapped (zero voltage). Above I_c, it runs (finite voltage = AC Josephson effect).

I/I_c (bias) 0.80

β_c (capacitance) 1.0

Init φ 0.00

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Top: washboard U(φ) with particle trajectory | Bottom: V(t) = ħφ̇/2e (zero=trapped, oscillating=running)