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Josephson energy : ウィキペディア英語版
Josephson energy

In superconductivity, the Josephson energy is the potential energy accumulated in the Josephson junction when a supercurrent flows through it. One can think of a Josephson junction as a non-linear inductance which accumulates (magnetic field) energy when a current passes through it. In contrast to real inductance, no magnetic field is created by a supercurrent in Josephson junction—the accumulated energy is a Josephson energy.
== Derivation ==
For the simplest case the current-phase relation (CPR) is given by (aka the first Josephson relation):
:I_s = I_c \sin(\phi),
where I_s\, is the supercurrent flowing through the junction, I_c\, is the critical current, and \phi\, is the Josephson phase, see Josephson junction for details.
Imagine that initially at time t=0 the junction was in the ground state \phi=0 and finally at time t the junction has the phase \phi. The work done on the junction (so the junction energy is increased by)
:
U = \int_0^t I_s V\,dt
= \frac \int_0^t I_s \frac\,dt
= \frac \int_0^\phi I_c\sin(\phi) \,d\phi
= \frac (1-\cos\phi).

Here E_J = / sets the characteristic scale of the Josephson energy, and (1-\cos\phi) sets its dependence on the phase \phi. The energy U(\phi) accumulated inside the junction depends only on the current state of the junction, but not on history or velocities, i.e. it is a potential energy. Note, that U(\phi) has a minimum equal to zero for the ground state \phi=2\pi n, n is any integer.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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