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¬ K 44;53þHI<=P 7(BD7(@Nò474;=As9£ N ϕ 4>(743695357(7r(>4<=P <1(<£=<mHN8£=1(7(514<8£=<.4<K ü©< 3658;=1(14f;¦EF14N ?(;=147(M£N8HI7û58<147N814N ¬ K ¨ ¡!36<<858;6583659ÿ ýv74;^@47(>N1(<365û(H λ = ±1 74HI;6ÿ 5 7P q ¬ Kñ (~ p) = p /2m − λ α |p| − 2αp H + H , 73;P <!N58;814<4¡#3=<35<û41(7(í;6@(5>4<814<3k<=P 7414N8@<fH 7(HI(9û3=<8Hf¡Æ14<(>4741N P4;6ùkNýv74H >NE=14fH λ = ±1 ¢v;6>4HI7<8@4>(9ùM1(<365û(Hf¡Æí=14;6>4£=;574?4;63=@47>NEP;;614 ;74?47(14<A 2αp ¡ 3è>N P 7(983=<H p = p2mµ + m α ± mα ¡£ P ; µ mα ø(7(HI74?4;=36@474Az4<858;=14ò(7N#¡Á36HfK QI743K ¬ K ì¦<85814<36587R3=<35<û4147R1NDP 89!ø¢è;6>4HI7 <@4>(9ù14<365ûøR4<?57R<=P 741N8@<82¡ ν = 1 ± ¡ 7RP 74<8HI;DHIs4>4;614;=>(;=£N8;6H.>NE74?474;6H ν − ν K 2<£ PNè4>(74@ N Pf!N8;6583þ3 N8<8;D814;6úD 14;6;GHN£=147(5814<;G4<; H αp P <C<83=7 x ¡Áí6587zP ;G¢v;6>4HI7<8@4>(9ùM1(<365873=HI;ýèN8ÿ 53þ 4>4<574<84<<ûù14©ø y 1N84>4N8;6147(ø1Nè;74?47419 Q = ±H/v ¡@N@G(<@NEûN81(<1N-QI7438K ¨K L89!ø(?4N8365874?414fA£N8HI7 58<147N1_8EûN74HI<=P ;=A4357C &¬ K H¬ M74HI(9û83=14<H4>4;P365N8;=14747 74HI;6;657P U X ¬ Kô a a , a − a
αpy − H ϕp (H) = arcsin p , 2 (αp) − 2αpy H + H 2 p
2
λ
2
2
2
y
F
F
2
2
2
±
+
−
F
F
2
+ + 0 0 αp+q/2 β−p+q/2 β−p +q/2 αp +q/2
pp0 q
ô
m 2π
α vF
λ=+1
−>
e
p
−>
s
−>
λ=−1
s
IQ 7438K ¬ !^7(>N1(<3658 λ = ±1 3=<8<85;535898;65:(<<>4<5893=47414Nví;6@(5>4<81Nè4;=>4(;=1P 7(@(9û4>41(< 4>4N844;61P 74@9 44>414<;6<<514N84>N8;=1477(HI(9û3FNkí;=@(58>4<1N(K
H
IQ 7438K ¨*ì2>47.4>47<ûùè;=147(73 N8<8£=<814;6ú14;=£6<mHN£=147(5814<£6<4< H αp P <n<3=7 x ¡ P ;¢v;=>(HI7<@(>(9ùM14<83657 ¡36<<858;6583659ÿ ýv74;kP 89H @47(>N1(fH;65884H λ = ±1 ¡Æ3=HI;ýèN8ÿ 5 3þmn(>4<857(<4<< ù14©ø y14N84>N8;=147ø14N;74?47(1(9 Q = ±H/v KI¥ HI;=>(9zN>N8HI;658>N <@4>(9ù14<36584¡(36<<858;6583659ÿ ýèNG<=P 14<8A:@474>N 14<357¡(<8ú;8¡?4;=Hz36<<858;653589ÿ ýèN α/v P >(9£6<AK F
F
F
7 HI<ûùè;5_ 5894>4<8ý;=1z@47(>N1(<H!NE=743=; ¬ K ï _4>4;P 4<<ûùè;614747 H αp µ K¥ P7(1414<<14<<8H4>(;P ;; q p <1RHI<ûùè;65- 58BDN8@(58<>47(E=<!N81G3;P9ÿ ý74H<>4NEF<Hf X &¬ K ˆ q ), ˆ = −U Aˆ (~q)A(~ H 4 £ P ; X ¬ K ˆ q) = A(~ λe a a ;=35<4;=>4N5<>R91474?(58<ûùè;=147_N8>(2K LDè5<£6<4¡!?(58<8f?47437(5D5;=>(HI47(>4<!N81(7(_<-HI1474HI<8H.>4;6HI;=1474<MóÆ>N3=3=HN14<fH í;=@(58>4<1414fH 4<(H a , a¯ 7z8N83 ýv;6(ÿ ýv;6;?;=1 H ¡ ¬ LK G©B^B^;=@5741(fA N8£6>N81(ù7N81R74HI;6;657P X ¬ K¬ ª L [a, a ¯, ∆, ∆ ] = a¯ (−∂ − (~ p)) a + F
F
+
int
q
iϕp
λ−p+q/2 λp+q/2
pλ
λ,p
λ,p
int
∗
+
Xh
λp
τ
λ
λp
p,λ
i |∆q |2 1 X −iϕp ∗ iϕp ∆q λe a ¯λ,p+q/2 a ¯λ,−p+q/2 + ∆q λe aλ,−p+q/2 aλ,p+q/2 . − + U 2 pλ
;6>4HI<=P 741NHI74?4;=36@474A(<85;614ò47N Ω = −T ln Z <84743=fN8;653=7435;=HÁ9nG>N814<8;=36747¡#£ P ; Z 365N5743574?4;63=@N369HIHN(K#¤rf>NùkN8;=H Ω @N8@C4>4;P ;n4>(<7(EF8
η→0
Z
Ω[η, η¯, ∆, ∆∗ ] exp = D∆D∆ exp − T Z Z 1/T = DaD¯ aD∆D∆∗ exp L[a, a ¯, ∆, ∆∗ ] + 0 X + (¯ η (τ p)a(τ p) + a ¯(τ p)η(τ p)) dτ . Ω[η, η¯] − T
∗
=
¬ K ¬¬H
2T 7(ùè;¦HI9ûP;=Hz>N8<5N5v4>4747(ùè;=1(7473=>4;P 14;6£=<è4<4¡@<5<>4<8;¦94>N844;6583þRHN< 3658ÿN8>4N8HI;658>NóÆ741EF89>4£N Gi K!LD?47435<£6<èP89HI;=>414<8£=ø((>4<<=P 147(@N Gi ∼ T /E 7 HI<ûùè;65^>4N83=36HN5>47(!N583þM@N8@kHN;614@<;¡8ø!<85û-7k14;f4>4;614;=8>4;6ù74HI<; HIm<39ùkPN;=HB249@ 589N8ò474<81414f;í6B^BD;6@(5 @4>N58@<k@<814ò4;UP 74<8HN K ü©>4;P14; 4<;6<;*4>4747(ùè;=1(74;bí6@474N;=1514< 4>4747(ùè;=1(74ÿ36;P<<A^5<?(@472P4DB^914@ ò474<81N1(<£=4N N4< ∆ 7 ∆ 4;6>4<;°9>N814;61474; &¬ K ¬8H¬ M ¡85N8@474H<8>NE=<HHI.9ûP;=H p
c
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Ω[∆, ∆∗ ]
¡ 4<û4(ÿ ý;=£=<83þ4<83;è£NF9363=<N741(58;=£6>474>4<N
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∗
0 0
∗
δ η¯(τ r)δη(τ 0 r0 )
η→0
η→0
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Qi
i
i
~i Q
∗
Ωsn = +
Z
X
X ijkl
+
X i
i
0
0
∗
αQi Qi |∆Qi (~r)|2 +
βQi Qj Qk Ql ∆Qi (~r)∆∗Qj (~r)∆Qk (~r)∆∗Ql (~r)δQi +Qk −Qj −Ql +
¨K ¨
2 2 ∂ ∂ 2e 2e y cxQi Qi −i + Ax (~r) ∆Q~ i (~r) + cQi Qi −i + Ay (~r) ∆Q~ i (~r) d2~r ∂x c ∂y c
»
G(ω,p+Q/2)
∆*Q
∆Q
G(- ω,-p+Q/2)
IQ 7438K«(LU94;=>4<83=@N4;65F_34>44<=P 1(<£=< 3=8;=>ø4>4<<=Pýv;6£=<:36<3658< (147( K ¥n@<í6BDB^74ò(74;=1(5 α ø!<=P 7(5¦741(58;=£=>4N-<85 @(94;=>4<83=@<Av(;65F7v3*4;6>4;PN1414fHC74HI(9û83=<H ¡@<5<>N(<@NEûN814NO1NDQI7438K I« ND@<í6B^BD7(ò474;=15 β 7 β P N8ÿ 583þM7415;=£6>N NHI7¡ Q 3=<8<85;53589ÿ ý74HI7C?4;5f>4;ø(8;=>(ú741414fHs4;65F;6fHmP 74N8£=>NHIHN8H 4<@NEûN1414fH.1NkQI743K ï T X 1 ¨K « ~ ~ α = − G ω, p~ + Q/2 G −ω, −~ p + Q/2 ; QQ
QQQQ
QQ
βQQQQ = T
U
X ω~ pλ
βQQ−Q−Q = T
2
λ
QQ−Q−Q
λ
ω,λ,~ p
~ ~ p + Q/2 ; G2λ −ω, −~ G2λ ω, p~ + Q/2
X ω~ pλ
¨K ï
~ ~ ~ G2λ ω, p~ + Q/2 Gλ −ω, −~ p + Q/2 Gλ −ω, −~ p − 3Q/2 , cµQQ =
¨K
1 ∂2 α(Q~ey + qµ~eµ ), 2! ∂qµ2
£ P ; B2914@4ò(7(èóÆ>47414N¦14<>4HN 14<£64<1NU8<¦14;úv14;6HHN8£=147514<H4<; k<3=@<357_;6365 αp
H
¨ K ñ EP;=3=3=?47(5N;=Hf¡4?(58(3=7(@(!NEF7(?N8365874ò4 ξ = p /2m − λαp − µ HNNO4N8814;=147(ÿ3 K 021(5;6£=>N 4< 74HI(9û3=N8H ¨K « 7 ¨K ï ;6>(953þO @(!NEF7(@ N8363=74?4;63=@<HC4>(747(ùv;=14747 αp Z Z Z dp dϕ ¨K ô = ν( ) dξ , F
Gλ (ω, ~p) =
1 , iω − ξ − λH sin ϕp 2
F
F
∞
2
(2π)2
2π
F
−∞
¬¬
0
2π
∆Q -p+Q/2
∆Q p+Q/2
∆*Q
∆*Q p+Q/2
p+Q/2
-p+Q/2
∆*Q
-p+Q/2
∆*-Q -p-3Q/2
p+Q/2
∆Q
∆ -Q
IQ 7438K#ï4L7N£=>N8HIHI2¡#36<<858;653589ÿ ýv74;?;=1N8H ?4;658;=>(58<£=<4<>!P @NG4< ∆ >NE6<ûùè;614747 K óÆ741(E=89>4£N JON81PNF9 β |∆ | 7 β |∆ | |∆ | <858@(9FPN(¡4<8E=943=4<;EF14<8AB^<>4HÁ9û<8A SK ¬¬H 7(EOì2>47<ûùè;6147( ¡4<9?N8;6H X 1 1 ¨K p , α = − πν( )T max QQQQ
Q
4
QQ
QQ−Q−Q
F
U
βQQQQ = βQQ−Q−Q =
Q
Q
2
−Q
ω>0,λ
2
ω 2 + Hλ2
X 2ω 2 − H 2 ν(F ) λ πT ; 2 + H 2 )5/2 4 (ω λ ω>0,λ
X (2ω 2 + H 2 ) Hλ ν(F ) λ πT , 2 (ω 2 + H 2 )3/2 v Q 2 ω F λ ω>0,λ
X 1 1 vF 2 , = =− πν(F )T 2 3/2 2 2 2 ω,λ (ω + Hλ ) X 2H 2 − ω 2 1 v F 2 λ cyQQ = cy−Q−Q = − , πν(F )T 2 5/2 2 2 2 (ω + H ) ω,λ λ
cxQQ
cx−Q−Q
¨K
¨K ¬ ª
£ P ; H = λH + v Q/2. NHI;657(Hf¡ ?(58< β = β 2@<í=B^B^74ò47(;=1(582¡*35<û(ý74; 3=<8<85;535;61414<4;6>4;P.?;61N8HI7 |∆ | 7 |∆ | B2914@4ò(74<1N;óÆ741EF89>4£N JON81PNF9 ¨K ¨ @<í=B^B^74ò47(;=1(5 ¡3658< ýv74An4;=>(;Pz?;=14<8H |∆ | |∆ | ¨K ¨ í5<39HIHNG?4;5f>4;øn>N814©ø 4 ;
P ; 4 ; 5 4 7 4 1 4 7 \ ÿ 4 6 ; 4 > ; ø F <
P N 8 8 5 < 4 > < 6 £ < ( > F <
P N ;=37 HI;ùkP9 α =0 β >0 14<>(HN14fHHI;65N(<H.7G3=;6>ø((>4<<=P 147(@<8Hf X π 1 ¨K ¬H ¬ p = ν( )T max . λ
F
−Q−Q−Q−Q
QQQQ
Q
4
−Q 2
Q
QQ−Q−Q
4
−Q
2
Q−Q−QQ
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U
F
Q
ω>0,λ
¬
ω 2 + (λH + vF Q/2)2
1
T / Tc0 = H
critical temperature
∆
0,8
L 0,6
τ
BCS
0,4
h. τ’
0,2
0
S
s t r i p e
O 0
1
2
3
in-plane magnetic field
H / Tc0
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0
¬«
10
pairing wave vector
vFQ/Tc0
5
S
0
L 0
1
2
3
4
in-plane magnetic field
H/Tc0
5
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c
c
c0
D
c
2
c
2
c0
c
c0
c0
γ
c0
F
F
3
c2
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2 c0
F
2
F
c
L
L
∂ 2 αQQ = 0, ∂Q2 Q=0
•
c0
QQ
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L
L
L
L
c
2 L
2
F
4
F
4 c0 2γ
c0
3
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c
c
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λ
n
L
c
c
+
iQy
−
−iQy
c
2
sn
2
+
2
−
4
s
a
+
2
−
2 2
2
+
s
2
Q
∗ Q
−
QQQQ
2
−Q
∗ −Q
s,a
QQ−Q−Q
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c
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a
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ratio
β QQ-Q-Q β QQQQ
L
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H/Tc0
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x
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x y
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+
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−
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1
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1
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z=
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K 54<4<8>4ò474<14N14fAN8>4N8HI;658>(9 a 7(Ek9>N8814;=147 ï4K K N8@474Hî<>4NEF<Hf¡Æ14N:7414747 JD74B2úv74ò4N LT 14;65D1474@N8@<£6ø4>4<84N8;614747k4;=>(4;=1P7 @(9û(>414<H@GHN£=147(5814<HÁ9R4<ÿK2<HI(<14;=15N n 147(£ P ;^14;^743=?4;EûN8;5:k@474>4N14<8AG<8 N8357 7G4<>!P @N n $&'(G3=<8365<û(147( ∂ Ω 4m v 1 ∂Ω ∂ K − n = . ∆ 2 ∂∆ ∆ ∂∆ ∂Q h ¯ Gb5<85R39?N8A3=714<<85F74?N8;53þ<85@N83=3674?4;=36@<A EûN PNû?47 ¡ £ P ;v(<@NEûN81(<4¡ ?(58< @474>4N14<8H 3=<8365<û(14747 n ;6EP ;<8>NývN8;6583þR14< ñ K#QNE674?474;k¦8;=>4<û(5814<83;P 365874; 5<8£=<4¡?(5<:M1Núv;6AEûNûPNû?4;v1N8(>N8;61474; Q BD7(@3674>(98;653þ4>(74@ N Pf!N8;=HIfH4<;=H h ¡-5< >4;6HÁ@N8@nP39?NBD;6>4>4<HN£=147(5814<£6<36;=>ø4>4<8<=P 1474@N<144<87(EF<14<4K ì2<9?4;=1 14<; 4<8;P ;61474;°5;=1EF<>N n 9@NEFf!N8;5è1N^369ýv;63658;=141(<N147(EF<5>4<(14fA:í;=@(58>4<HN8£6147(51(fA <858@74@4<;6>!ø14<83651(<£=<3=;6>!ø4>(<<=P 1474@NM87(E=7R7(14747RJO7(B^ú74òN LT K nyy s
m ∂2Ω , =4 h ¯ ∂Q2
xx s
s
xx s
2 F
2
hel
2
hel 2
s
αβ s
¯
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®
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F
F
λ
F
F
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F
F
λ
λω
hel
∂Q Q=0
F
ω
α = − ν(F )T H
X
"
# p (ω 2 + H 2 + ∆2 ) p K(k) − ω 2 + (H + ∆)2 E(k) = 6 0, 2 2 ω + (H + ∆)
_7 >NE6<ûùè;61474;58;=>4HI<=P 7414N8HI74?4;63=@<£=
η=
∂Ωhel ∂Q
7 Q=0
ω
Q
89FP ;6536<=P ;=>!ùkN58M7414;6A ñ(K «
Ωhel (Q) = Ωhel (0) + ηQ + a ˜Q2 + ... , 2Ω hel a˜ = 2!1 ∂ ∂Q 2
¡Nè85<8>NG4>4<7EF<=P 1NP N8;6583þf>4Nùè;=1(74;=H
Q=0
ñK ï
X ∂f (H, ω) vF2 ∂ 2 Ωhel = ν( )T = F 2 ∂Q Q=0 2 ∂H ω " # X (ω 2 + ∆2 ) vF2 (ω 2 + ∆2 )2 + H 2 (ω 2 − ∆2 ) ν(F )T −p E(k) , = K(k) + p 2 + (H + ∆)2 2H 2 ω ω 2 + (H + ∆)2 (ω 2 + (H − ∆)2 ) ω
*HI<=P9û^@<87 ï4K ñ K ¥©7P9_HN<83657C@<í6B^BD7(ò474;=15N η HI<ûùè;=Hî;EP ;:< N3657_;6;=;D7414747CJD74B2úv7(òN LT Pk36;=>ø4>4<8<=P(ý;=AMí614;=>(£=7474<8E=<!N583þk>NE<ûùè;=1(74;=H ñ(K « ¡87(E°@<85<>(<£=N8814<;63=14fA;=@(58<>G3 N88<AHI<=P9û(ò4747GN8>NHI;65>4N4<>!P @N-kí658<A<8 N8357
k
Qhel
H
P
p ω 2 + (H + ∆)2 E(k) K(k) − 2
(ω 2 +H 2 +∆2 )
√ 2 ω ω +(H+∆) 2αH η =− = 2 × P 2 2 2 2 2 2 (ω 2 −∆2 ) 2˜ a vF √ (ω2 +∆ ) 2 K(k) + √ (ω2 +∆ ) +H ω − 2 2
N8HI;65874Hf¡ ?5<:4>4;P;;
E(k)
ñK
f>Nùè;6147( (ñ K ¨ 7 (ñ K ï HI<ûùM14<->NE<ûùM75M>!P4<
ω +(H+∆)
H →0
ω +(H+∆) (ω +(H−∆)2 )
X α ∂Ωhel αH π∆2 H ≈ − ν( )T =− ν(F )(1 − Y (T, ∆)), F 2 2 3/2 ∂Q Q=0 2 (ω + ∆ ) 2 ω X π∆2 ∂ 2 Ωhel vF2 vF2 ≈ ν( )T = ν(F )(1 − Y (T, ∆)) F ∂Q2 Q=0 4 (ω 2 + ∆2 )3/2 4 ω
«!¨
ñ(K ñ
3
vFQ / Tc0 pairing wave-vector
2,5
critical point
T/Tc0= 0.542
2
1,5
1
0,5
0.1 0
0
0.01 1
0,5
1,5
in-plane magnetic field
H / Tc0
2
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F
F
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2 F
c0
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H −>
j
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s
hel
s
yy s
(1) y
(2) y
£ P ;
λ
2 F
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(chir) y
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ω,p,λ
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«8ï
j/jmax quintized current
1
0
-1
0
1
2
H/Ho
in-plane magnetic field
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e¯ h 2m
2 F
o
s
o
c0
c0
s
(1) s
(2) s
(1) s
hel
(2) s
jquant
2πn e¯ h ns −Qhel + = , 2m 2πR
£ P ; R >N P 793ò(7741P>N(¡ Q = 2αH/v K1¿2;<;?47(3< n 89FP ;65>N83658739;74?4;61474;=H 4<45N8@¡?(5<85<@_8©HI741474HN ;=1 n = ò4;N_?N365 [H/H ], £ P ; H = . <@89FP ;5 « hel
2 F
o
o
2 vF 2αR
< >4NýèN583þG1(<è5<@<M4>47 H = nH ¡ n = 0, ±1, ±2, ... ¤N8@3=7(HN14<8;DE=1Nû?4;=147(;D58<@N 89FP ;5M>N14< j = n /R. N8743674HI<3658-58<@N-<5MHN8£6147(5814<£=<-4<49ûP;6547<<8>NE=14<A @N8@G4<@NEûN14<14N-QI743K ¬8¬ K o
max
e¯ h 2m
s
´"U ® ö ´"Q ¯¶´"7*²´ 55 ´ ö ;R²R¶+9 3 ?9? ö ¶R¶ µR± 5 ´47*µR¶C?¦µ V A³;R²R¶Y< 5 ±9©±'S ¥í658<H>NEP;;èHI\7(E69?4N8;=H7((1474;è14;6HN8£=1(7(514©ø(>474HI;=36;=A¡ øN8>N@(5;6>47(E=9ÿ ýv7ø3þ>4; HI;=1(;=H τ HI;ùkP9z94>(9£674HI73658<@414<8;=1474HI7¡ 14NnBDNEF<889ÿ P 7N£=>N8HIHÁ98K ¥bEFN874HI<=P ;6A4365874ÿ HI;6ùèP9í;=@5>4<14N8HI77N5<8HN8HI7(>474HI;=36736<<858;6535898;65£NHI7û5<1(7N81 À
XZ
ˆ int = H
ψα+ (r)ψα (r)u(r − Ri )d2 r.
ôK ¬H
¥C4<3;P 1(;=H8<14<9ÿB2914@4ò(74ÿzí;6@(5>4<81N >4N83=@N P f!N8;6H4(74HI;=367R58<?4;6?414fHI7 Kì2<9?N8;6Hm(>474HI;=3 e a (p) u(r − R ) = uδ(r − R ) 14fAG£N8HI7û58<147N817(HI(9û3=1(<H4>(;P 35N8;614747_-3=47(14<<Hm!NE=743=; XX ôK ¨ ˆ = 1 H ue ψ (p)ψ (p ). i
α
p
ipr
α
i
int
V
−i(p−p0 )Ri
+ α
i
0
α
ì2;=>4;ø!<=PnM@(74>N814fA_!NE=743 a (p) = η (p)ˆa EûNûPN8;6583þCHN58>474ò4;6A_7(Ev35<ò4<3=4741(<>N ¬ K ï 47G4>474HI;63=14fA£N8HI7û5<8147N81_k@47(>N1(<H!NEF7436;D7(HI;=;657P# XX ôK « ˆ = 1 ue a M (p, p )a , H V £ P ; 1 ôK ï M (p, p ) = 1 + λµe . ì2<3;v365N81PN8>(5814<A4>4<ò4;P9>4 3=HfK ¬ ñ ¡2365> K «!¨ P_4>474HI;63=14<£6N14<Hn4>4;P365N8;=14747 ôK « ¡!HI.1N ø!<=P 74HB2914@4ò47(ÿóÆ>4741NDO(>474369583658747R14;=HN8£6147(5814©ø 4>47(HI;=3=;6ARP41(<>4HN814<£=
p,p0
α
λα
λp
−i(p−p0 )Ri + pλ
int
i
λµ
0
λµ
p,p0
0
i(ϕp −ϕp0 )
λ
p
imp
2
F
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∗ ∗ 3Q v−3Q uQ v−Q
11
l13
l14
Q Q 3Q 3Q Ts X 2 2 G p+ = G −p + G p− G −p − ; 2 ω,p,λ 2 2 2 2 X
5Q = Ts G p+ 2 ω,p,λ
Q Q 3Q 3Q 2 G p+ G −p + G p− G −p − . 2 2 2 2
+
¥ K¬ ª ¥ K ¬¬K
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2π dϕ 0 2π
2
2
S
S
c0
S
c0
«
c0
u*Q
uQ
-p-Q/2
p+3Q/2
coeff.=1
p+3Q/2
u3Q
u*Q -p-Q/2
-p+3Q/2
coeff.=1 u*Q -p-Q/2 p+3Q/2
u*Q
v-Q
p-Q/2
v-Q*
-p+3Q/2 p-5Q/2
-p-Q/2
v-Q
p-Q/2
u3Q
u*Q
-p+3Q/2
coeff.=1/2
u*Q
p+3Q/2
p-Q/2
u3Q
v-Q
v-Q* -p-Q/2
-p+3Q/2 p-Q/2
v-Q
u*Q
v-Q
QI7438K ¨«(L7N8£=>4N8HIHI <83=HI<£6!P @Nk4< u ¡436<<858;6583659ÿ ýv74;?;=14N8H l u u v |u | 7 (l + l )u u v |v | -K }Áý;M;=35_(;65F7@<HI;=@3=1(<_3=<(>ùè;=1(14f;M4<8@NEûN8141(fH1N >4743914@;8¡NR5N8@ùè;k3kEFN8HI;=1(<A36;ø u 1N v K 1Nû?4;=147n7ø5;èùè;k3FN8HIf;¡#4<í658<HÁ9HI 7ø14; >47439;6HfK 13
14
∗2 3Q Q −Q
−Q
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2
ï
Q
2
@ <í=B^B^74ò474;61(54;=>4;P |u| 7 |v| k<83=HI<H[(>4<3658<H#^4<8>P @; ; @<í6B^BD7(ò474;=15:4;6>4;P (|u| |v| + |u| |v| ) k<83=HI<H[(>4<3658<H# ; 0.00152674 − @<í6B^BD7(ò474;=15:4;6>4;P |u| |v| k<3=8HI<H 4>4<35<H# ; −0.00120067 − 8
D1 = 0.00106053 − D2 = D3 =
8
2
6
4
6
2
4
l7 = 0.674254; l8 = 0.103447; l9 = 0.191039; l13 = 0.00491175;
l10 = 0.170477;
l11 = 0.206894;
l12 = 0.0325726;
l14 = 0.021198.
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