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格子 QCD による有限密度系 シミュレーション S. Muroya Tokuyama Women’s College in collabolation with A. Nakamura, C. Nonaka and T. Takaishi
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最近のレヴューです Muroya, Nakamura, Nonaka and Takaishi : PTP 110 ( 03 ) 615, hep-lat/0306031
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物理学最前線 “ クォークマター ” 宮村修 1986
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物理学最前線 “ クォークマター ” 宮村修
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高密度 QCD 複雑な相構 造 Thomas Schafer, hep-ph/0304281 RHIC JPARC Ferro-Mgn.? Q-Hall st ?
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流体モデルのインプットに使っている 状態方程式の例( Nonaka, Honda, Muroya )
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化学ポテンシャル 統計力学 場の理論 constant gauge field P.A.M. Dirac (‘56) Y. Nambu (‘68) 保存量 (保存電荷) Lagrange 未定定数
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Introducing the chemical potential on a lattice (Wilson fermion) : hopping parameter quark mass Chemical Potential on a Lattice
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Phase (sign) problem
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quench 計算では、化学ポテンシャ ルの影響がいつから見え出すか? chiral limit では μc = 0 か ? プロットはシミュレーション 実線は π による μ c評価 点線はバリオンによる μ c評価 破線は平均場近似 Dynamical Quark is indispensable I. Barbour et al, NP275 (’86) M.A. Stephanov, PRL(‘96)
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μ=0.0 μ=0.2 μ=0.4μ=0.3 Wilson Fermion の固有値分布 β= 5.7, κ=0.16, 4x4x4x4 Lattice
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K-S Fermion の固有値分布 ( m =0.1, beta = 5.7) μ=0.2 μ=0 μ=0.3μ=0.4
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Approach to high density state of the Lattice QCD Reweighting method –Fodor & Katz –Grasgow Taylor expansion Imaginary Chemical Potential Density of the state Positive Measure model Susceptibility against chemical potential Nishimura’s talk Irina’s talk
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Susceptibility against chemical potential クォーク数密度 MILC Collabolation
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second derivative for chemical potential 擬スカラー meson mass の応 答 QCD-TARO Collaboration
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高次の微係数を計算する⇔物理量を で展開 /T Gavai and Gupta, quenched QCD, 4 th order of
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Fodor-Katz, JHEP03(2002)014 Standard gauge + Staggered fermion
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Reweighting Fodor and Katz Multi-reweighting method
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Glasgow approach
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Allton et al. (Bielefeld-Swansea) hep-lat/0204010 Improved action + Improved staggered fermion MeV a=0.29 Taylor expansion at high T and low
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微分の4次まで
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Imaginary Chemical Potential deForcrand and Philipsen NPB642(02)290; hep-lat/0307020 D’Elia and Lombardo Phys.Rev. D67 (2003) 014505 At small Standard gauge + Staggered fermion Z(3) symmetry
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Fodor-Katz Allton et al. deForcrand-PhilipsenD’Elia and Lombardo Consistent !? YES
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Effective theory Finite Isospin Two-color QCD Pseudo-Real Monte Carlo Calculation Works Well ! Models free from Sing Problem
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Color SU(2) at Finite Density 4 X8 3 Clear evidence of meson mass decrease at finite chemical potential !
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Color SU(2) at Finite Chemical Potential Peculiar behavior of a vector meson at finite density Mass of becomes small ! Remind us of the CERES Experiment a a =0.160 =0.175
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N f = 2, 4 Thermodynamical Quantities 4 aa aa aa Gluon energy density Polyakov line Baryon number density
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Polyakov Line Susceptibility Anti periodic (spatial direction) periodic (spatial direction) 0 0.0002 4 X8 3 0.0001 00.4 0.8 aa
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Polyakov Line Susceptibility 4 periodic 4 aa
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粒子対凝縮 ? Kogut-Toublan-SInclare 外場の入ったシミュレーション
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Sinclare and Kogut, condensation with I diquark condensation in colorSU(2) ( see Nishida’s talk )
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phase quenching 重みだと思う 2 flavor finite iso-spin model phase quench model Configulation の update は可能なはず
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の大きいところは揺らぎが小さ い? Bilic, Demeterfi and Petersson, NPB337(‘92)
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R-algorithm Nakamura, Sasai, Takaishi, 基研研究会(2003)
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位相の揺らぎ Nakamura, Sasai, Takaishi, 基研研究会(2003) Bielfelt-Swansea,PRD68(03)
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Thomas Schafer, hep-ph/0304281 高密度 Lattice QCD Lattice simulation for small seems to work enough SU(3) の複雑な相構造まで届いてはいない カラーを持った凝縮を出せるか? 高密度状態は計算可能か? RHIC JPARC Ferro-Mgn.? Q-Hall st ? Muroya, Nakamura, Nonaka and Takaishi : PTP 110 ( 03 ) 615, hep-lat/0306031
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