Теория сверхтока в цепочке ромбиков из джозефсоновских контактов

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Author: Протопопов И.В.

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2πΦc 2πΦc πΦc πΦc I = 2I4e cos sin 2φ + + 2I2e cos sin φ + . Φ0 Φ0 Φ0 Φ0

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ef f (x, y)

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8

2(n1 + n7 ) − 2(n2 + n8 ) + n3 − n4 + n5 − n6 = 1 , n3 − n 4 − n 5 + n 6 = 1 .

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L = n 2 + n8

M = n 4 + n5 = n3 + n6 − 1 .

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X

b

hy2 , x2 | e−T H |y1 , x1 i =

K,L,n3 ,n4 ≥0 M ≥max(n4 ,n3 −1) K−L+n3 −n4 =1

(T α4e )K+L (T α2e )2M +1 (M + 1)!M ! . K!L!n3 !n4 !(2M + 1)!(M − n4 )!(M − n3 + 1)!

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b

hy2 , x2 | e−T H |y1 , x1 i =

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4

Z = n3 − 1 − n 4 n3 n4 Z +∞ Z π T α2e X dϕI|Z| (2T α4e )I|Z| (T α2e sin ϕ)I|Z+1| (T α2e sin ϕ) . Q= 2 Z=−∞ 0

1 In (z) = 2π

Z

+∞ X z 1 exp t+ = tk Ik (z) , 2 t k=−∞

2π

dθ exp (inθ + z cos θ) ,

HI HI< ;6H (;=>4;64743FN5 ) ©$b7P ; 0

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u = (θ1 + θ2 )/2 v = (θ1 − θ2 )/2 Z

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Z

π

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) !$

sinh2 z π 2 I1/2 (z) = , 2 z Q(α2e , α4e )

) $

du {cosh (2T α2e cos u) − 1} exp (2T α4e cos 2u) . 2π

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b(e γ ) = −4α4e cos 2e γ − 4α2e cos γ e.

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