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At low temperature, only charge carriers tunneled through the junction are regarded as superconducting Cooper pairs.
The system is described by Hamiltonian ,
H = 4 Wc ( n − nG )^2 + Wj cos φ
( 4 )
Here, φ indicates the phase of the superconducting order-parameter of the island.
The variable φ is the quantum mechanical conjugate of the number of excess Cooper pair charges n on the island ,
n = − i h ∂ / ∂ ( h φ )
( 5 )