= Josephson coupling energy
{c}
{title2=$U_J=-E_J\cos\phi,\quad E_J=\hbar I_c/(2e)$}
The ideal <Josephson junction> has a phase-dependent <energy>
$$
U_J(\phi)=-E_J\cos\phi,\qquad E_J=\frac{\hbar I_c}{2e}.
$$
Differentiating and using the voltage–phase relation yields
$$
\frac{dU_J}{dt}=E_J\sin\phi\,\dot\phi=VI_s.
$$
Thus the ideal pair element stores and returns <energy>. At $V=0$ it carries a static <electric current> without electrical power loss. Under a nonzero periodic drive its instantaneous power need not vanish, but its <energy> returns after a full phase cycle. Real junctions also have a <capacitance>, <quasiparticle> transport and an external circuit; their total losses cannot be inferred from this conservative pair term alone.
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