JOSEPHSON JUNCTION PLASMA

RSJ model: phase dynamics and plasma oscillations

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The Josephson junction obeys the RSJ (Resistively Shunted Junction) model: the phase difference φ across the junction evolves as a particle in a tilted washboard potential V(φ) = −EJ·cos φ − (ℏI/2e)·φ. Plasma oscillations occur at ωp = √(2eIc/ℏC). Below Ic: phase oscillates near a minimum (zero voltage). Above Ic: phase runs continuously — AC Josephson effect, voltage V = (ℏ/2e)·dφ/dt. McCumber parameter β = 2eIcR²C/ℏ controls damping (β≫1: underdamped, hysteresis).