$1;ID: jh200013-NAH

GPUL\TAEDB7,GZMYPVF'>?<QCD%2C)*/ (0)1,2= # (0)2,3=
-2=434=Seung-il Nam5
1.
. &52. 9 %&)*Q[R\3. )*8("!
4. 9  WSHGQ[R\
5. : 6
+12 JHPCN$N[UOJV202079, K[XI[B@M. Wakayama

1/14 (QCD)  " ;:='B6AECIE?FGIDH=!&8/A( $ (QCD)=),=#>&8>*8/A.
 "8>QCD+&<%459283A=8/A QCDB07QCD'= 'B@1<6A.
M. Wakayama

2/14 

%8 QCD79+(,6:=<&. 1<*μ ()GLBM@JK
8$

μ=0μ>0μ2 < 0 (")←+(,. ←+(,9 32 QCD#.!O

@DC@J
"FBLAHJ' 5 QCD#-;;=4 >
ENI? 1<065)' 58 >/1*
M. Wakayama

3/14
Z (T, V )n

AEDAH6

=>C=A. Hasenfrantz & D. Toussaint,! 2π Nucl. Phys. B371 (1992)

d(µqI /T ) −inµqI /T
Z(n, T,6KV) =e
ZGC (µq = iµqI , T, V )(&)FJG?
2π0AEDAH#%

I 'LI 6"2,

R.Fukuda, A.Nakamura, S.Oka,! PRD93 (2016)!

ZGC (iµqI , T, V ) !37(0*=DU det D(iµqI )
e−SG

831+1.9</4,3-5*)(2k + 1)πi
ξB = −1 ⇔ $!37(:;µq /T =
3* 831.9</4,3-<)nq (µq = iµqI , T, V )M. Wakayama

B@JB

4/14

qI

(Nmax , V ) → ∞qI
n=−Nmax(10)(2k + 1)πi
ξB =nq−1 ⇔1 µ∂q /T =∗∗[detD(µ)]=detD(−µq3q)=ln ZGC
32T
V T ∂µq(Nmax , V )" → ∞µ!
#! iµqIq = ZGC (µB , T, V )

) =

# 2π
0

N$max

11
∂D−S−S−1
Gn3QCD
DU )
det
D(µq ) e)
V=)V V)ξ=TB
D(iµe TrG DN ∂(µq /T )= ZGC (iµZ(3n,qI , T, T,qI (11)ZGCDU detsin!
%nqI
n=−Nmaxnq (µq = iµqI , T,# V)(θ)∼f−(Ĥ−µq N̂k sin(kθ)
3 V)
ZGC (µq ,TT,=TreNmax$1 det∂ D(µq ) e−SG k=1
ZGC (µq , T, V ) =nq DU' Z(3n, T, V
= (µln ZVGC) =B ,qT,T 3 ZGC
V(2kT 2 ∂µ+ 1)πi=⟨n| e−(Ĥ−µd(µqI /T ) −inµξqI /T= −1 ⇔ µ /T =n=−Nmax
B ZGC (µq = iµqqI , T, V ) %(!#"'e(12)f3 sin(3θ) n31∞ ∂2π nq'(µ=iµ)=lnZ(µ=iµ)$−Ĥ/TqqqIGCqIn1∂B2 ∂µ5000=⟨n|enµ/Tq#T 3 Z$)&
V
T=lnZq GC T, V2π=T 2 ∂µ Z(n,)ξd(µ= e)
GC (µqT,3T, V ) 3V3ξ /T!
qqI−inµn qI /T Z # (µ"! #"'
1n=−∞
Z(n,T,V)=efsin(3kθ)
3k' ∂D GC
11−S−12πG
DUe
Tr= D
nq =
(µq 3V=Tiµ) det0 D(µq ) k=1
qI , T, V
T, V )3Z∂(µZ(n,q /T )GCnq1 ∂nN$
%(!#"'max=lnZGC
72 ∂µ!
T3VZTGC(µqq, T, V ) =Z(n, T, V )ξ n ξ = eµ1q /T
f3k sin(3kθ) #"iµqI , T )!nq (µq =n=−NmaxnB = inBI k=1
11∂D−SG−1=
DU det D(µq ) e $
Tr D * ξ = eµq /T
3
V T ZGC∂(µq /T )!
max nqInq (µq , T ) N$
(θ)∼aθ2k−1n3ξ
ZGC (µB , T, V ) =Z
T3n)
nq = inqI BnB1∂=ln ZGC
M. Wakayama
32Tnq 3V T ∂µqn=−Nmax1∂5!

2k−1k5/14

    W  "BQCD+$AC2MJNC A243x24
A4H=E2RVOKTUI5@1.2x107.!B+$I&+/>:)6*94H3W QCD+$AC2GPU-CUDAPULSQI<H=E21 BGPUI-;=OCTOPUS9A4H3W PULSQC;@8GOCTOPUSAB 'F4H3W GPUA4#@BAB 2?DG2243x24(=331776)9 (3W 5000I,7H 0%AB+$I)6*94H3M. Wakayama

6/14
: QCDµ =0(46)qµq ̸= 0(47)V = (Ns a)3(48)Nmax(49)

Ns3(50)Nmax"&%!$   µB /T ∼ 5-6 ' #Nmax'
M. Wakayama

4M.Wakayama,V.Bornyakov,
D.Boyda, V.Goy, H.Iida,A.Molochkov, A.Nakamura,(51)
V.Zakharov, Phys. Lett.
B793 227-233, May, 2019.
7/14

qI

(Nmax , V ) → ∞qI
n=−Nmax(10)(2k + 1)πi
ξB =nq−1 ⇔1 µ∂q /T =∗∗[detD(µ)]=det
D(−µq3q)=ln ZGC32(15)TV T ∂µq(Nmax , V )" → ∞µ!
#! iµqIq = nq (µq = iµqI , T, V )N$max
11∂D−S−S−1Gn3QCD
DU 74C7det
D(µq ) e) e TrG DV=)
=TB
D(iµZGC (µB, T, V ) = ZGC (iµZ(3n,V V)ξ
qI , T, T,qI (11) N ∂(µq /T )ZGCDU detsin!
%nqInq (µq = iµqI , n=−NT ) max nq (µq = iµqI , T,
(16)
# V)
(θ)
∼f−(Ĥ−µq N̂k sin(kθ)
3 V)
ZGC (µq ,TT,=TreNmax$1 det∂ D(µq ) e−SG k=1
ZGC (µq , T, V ) =nq DU' Z(3n, T, V
= (µln ZVGC) =B ,qT,# 2πT 3 ZGC
V(2kT 2 ∂µ+ 1)πi=⟨n| e−(Ĥ−µd(µqI /T ) −inµξqI /T= −1 ⇔ µ /T =n=−Nmax
B ZGC (µq = iµqqI , T, V ) 8?B;5=<5A"$) =e(12)f3 sin(3θ) n31∂n1∂2πq'∞= iµqI ) 0=lnZ(µ=iµ)(17)(µ=iµ)=lnZ(µ=iµ)$qGCqI−Ĥ/TqqqIGCqIn1∂B
2 ∂µ
/#,5000=⟨n|enµ/T
V T 2 ∂µTq3 Z>C@3q#VT=lnZ
q GC T, V2π=T 2 ∂µ Z(n,)ξd(µ= e)
GC (µqT,3T, V ) 3V3ξ /T!
qqI−inµn qI /T Z # (µ" ).0(! 5=<5A"$
1n=−∞
Z(n,T,V)=efsin(3kθ)
3k' ∂D GC
11−S−12πGDUe
Tr= Dnq =(µq 3V=Tiµ) det0 D(µq ) k=1
qI , T, VT, V )QCD/1'+&3Z∂(µZ(n,q /T )GC
∂ 5=<5A/nq1 ∂nN$8?B;5=<5Amax
lnZ(18)=lnZGCGC
72 ∂µ32!
TVT∂µ
Z(n, T, V )ξ n "$
ξ = eµ1q /Tq !%. ZGC (µqq, T, V ) =" !nq (µq = iµqI#, T )f3k sin(3kθ) #!
"n=−NmaxnB = inBI k=1
1 *'+D−S∂D
1G 1∂D−1−SG (19) −1
DU
det
D(µ)
e
Tr
D=q
DU det D(µq ) e >69:2E
Tr D ξ = eµq /T3Z3∂(µ/T)
V T ZGC∂(µq /T )qGC!
N$max nqInq (µq , T )%,/(θ)∼aθ2k−1nZGC (µB , T, V ) =ZT3n3 ξB74C7nq = inqI∂nB1∂lnZ=ln ZGC
GC 32 ∂µM. Wakayama
2Tq
nq 3V T ∂µq

n=−Nmax

(20)

1

∂5!

2k−1

k8/14

PNJL   nB

Two-flavor
G=11GeV-2
mq=5.5MeV
Λ=631MeV

Real: (T,μB) ~ (114,965) [MeV]
M. Wakayama

9/14

( &)85): PNJL

PNJL 2" /;>=;A8,.67-?@:B0'2?@:B22Nsin *<9C<Nsin!
nqI(θ) ∼fk sin(kθ)
T3k=1

M. Wakayama,
f3 sin(3θ)S-i. Nam,
A. Hosaka, Phys. Rev. D
1#(2020).
3!
f3k sin(3kθ)
k=1

Nsin=3+73)$%2( 4/);>=;A/
1 !*7!

f3k sin(3kθ) 10/14

M. Wakayama

k=1

( #(@9)

: PNJL

PNJL16BFEBH6"%6Nsin )
CJGH1.?/?,<?0;= +(BFEB
H1<?0 2&6 26DI+10%
24>(BFEBH6"' 1*>)
M. Wakayama, S-i. Nam,
A. Hosaka, Phys. Rev. D
5 (2020).

Nsin=4*?7($-!:682A36' 1BFEBH+"1*>)
M. Wakayama

11/14

33Nt N×N=16×163×sN = 4 × 163
ts

Nt × Ns = 24 × 24

QCD333 3
33N×
N
=6×24
N × N = 24 × 24mπ /mρ = 0.80 m /m = 0.48π
ρt Nt ×sNs = 4 × 24(1)ts(V( A QCDARTSWQmπ /mρ = 0.48 m /m = 0.44(2)V KJWK &X π ρ333333N×N=16×16t N s = 6 × 24 + Nt × N = 8 × 24
V  MIO: Nt ×ssmπ /mρ = 0.44N>?F
(3)
33RTSWQ(β,κ)BEG<.?.A=+t × Ns =3 4 × 163=24×24C9BPU( Nt × N3s3 )=+:GEARTSWQH
33
Nt × Ns = 12 × 24
N×N
=12×24ts
82-F,3
Nt × Ns3 = 4 × 16(4)33N×N=4×24sPUAt33
Nt × Ns = 6 × 24

((4)
(2)

(5)((3)(6)((4)

(7)

((5)

(8)

5GC=@(β,κ)AH32/<+1236%=H.+! ∗"33! ∗"∗!#ARTSWQAH.3;1, (5)∗Nt × Ns = 4 (det×N24D33(µ))=
det
D−µ(1q =316 × 16 (detq (µq ))
N(6)
D
=
det
D−µ3t×sq (9)Nt × Ns = 12 × 24
(3@ 6<+( @04FH ,*'7"DX 3140LWN%(&B)Nt × Ns3 = 16 ×N16×(6)33N=24×24(7)t 180LWN%(&B)
!#:s! ∗"∗∗∗(det(detD (iµ))=detD)'7"DX
10LWN%($))qIq ))D (µ= det(detD (iµ−µ(10)q(iµqI ))D qI= det D (iµqI)(133N×N=24×24(7)t12/14(8)M. Wakayamas
N × N 3 = 6 × 243ts


L jlQCDd;c?PPNJL# _d62n4PMryxr|%dcG[m.0(K)n9cf`gmN(( M9/)LtouU243x8dMsqsU$=+<P;EI _dQCDd@62`5n4QN

L d62]X_bWMp~w}zi-1badd')Ed!7hBgmN
L &J_d QCD62Tk# edo~{vwnRmY`U_Vm\gM# n*P\dD"Ad5c X\:9nBgmN
L PNJL# n*P^MJ&dHFZ>g,cSP^hryxr|%
UC* 3_OmTaQTd8n4QN
M. Wakayama

13/14(!))(1)* M. Wakayama, S-i. Nam, A. Hosaka, Phys. Rev. D &(2020).

( 1+3 )* ( ) S-i. Nam, Nuclear Physics School 2020, Online, June, 2020.
* S-i. Nam, KPS Spring meeting, Online, 2020. (4"(7&)* ( ) M. Wakayama, the Korean-Japan Pioneer Symposium of the 2020
KPS Autumn meeting, Changwon, South Korea, Oct., 2020.+ ,* M. Wakayama, The 8th Asian Triangle Heavy-Ion Conference (ATHIC2020),
Inha University, 2020. (6"(11& ) $'(  %#)M. Wakayama

14/14