氢状态方程的路径积分蒙特卡罗研究
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摘要
采用直接路径积分蒙特卡罗(DPIMC)方法计算氢在温稠密区的状态方程参数.在大部分区域压强与RPIMC的偏差在10%以内,温度较低时,有部分偏差超过20%.指出了RPIMC两个压强数据点的错误.在离解和电离区,DPIMC压强位于TF和TFC模型之间,在离解区与RPIMC的偏差达到15%,在电离区两者一致.在低密度区,DPIMC的内能与RPIMC的内能接近,小于QMD和IG模型,在高密度区,DPIMC的压强位于TFC和IG模型之间,内能则略小于IG模型.
We computed equations of state of hydrogen in warm dense matter regime by using DPIMC method. In large part of the regime, pressure difference between DPIMC and RPIMC is less than 10%. In low temperature regime, some difference beyond 20%. We pointed out two clerical errors in pressure of RPIMC. In dissociation and ionization regime, pressures of DPIMC lie between results of TF and TFC model. In dissociation regime, the largest pressure difference between DPIMC and RPIMC is 15%. In ionization regime, pressures of DPIMC are agree with RPIMC. In low density regime, internal energies of DPIMC are close to those of RPIMC, less than those of QMD and those of IG model. In high density regime, pressures of DPIMC lie between results of TFC and IG model, internal energies of DPIMC less than those of IG model.
We computed equations of state of hydrogen in warm dense matter regime by using DPIMC method. In large part of the regime, pressure difference between DPIMC and RPIMC is less than 10%. In low temperature regime, some difference beyond 20%. We pointed out two clerical errors in pressure of RPIMC. In dissociation and ionization regime, pressures of DPIMC lie between results of TF and TFC model. In dissociation regime, the largest pressure difference between DPIMC and RPIMC is 15%. In ionization regime, pressures of DPIMC are agree with RPIMC. In low density regime, internal energies of DPIMC are close to those of RPIMC, less than those of QMD and those of IG model. In high density regime, pressures of DPIMC lie between results of TFC and IG model, internal energies of DPIMC less than those of IG model.
引文
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[7] FOULKES W M C,MITAS L,NEEDS R J,et al.Quantum Monte Carlo simulations of solids [J].Rev Mod Phys,2001,73:33.
[8] CEPERLEY D M.Path integrals in the theory of condensed helium [J].Rev Mod Phys,1995,65:279.
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[10] KITAMURA H,TSUNEYUKI SH,TADASHI O,et al.Quantum distribution of protons in solid molecular hydrogen at megabar pressure [J].Nature,2000,404:259-262.
[11] JOHNSON K A,ASHCROFT N W.Structure and bandgap closure in dense hydrogen [J].Nature,2000,403:632-635.
[12] WANG Y,PERDEW J P.Correlation hole of the spin-polarized electron gas,with exact small-wave-vector and high-density scaling [J].Phys Rev B,1991,44:13298.
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[15] 张其黎,张弓木,赵艳红,等.氘、氦及其混合物状态方程第一原理研究[J].物理学报,2015,64:094702.
[16] KNUDSON M D,DESJARLAIS M P,BECKER A,et al.Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium [J].Science,2015,348(6242):1455.
[17] MILITZER B,CEPERLEY D M.Path integral Monte Carlo calculation of the deuterium hugoniot [J].Phys Rev Lett,2000,85:1890-1893.
[18] TUBMAN N M,LIBERATORE E,PIERLEONI C,et al.Molecular-atomic transition along the deutrium Hugoniot curve with coupled electron-ion Monte Carlo simulations [J].Phys Rev Lett,2015,115:45301.
[19] FILINOV V S,FORTOV V E,BONITZ M.Fermionic path integral Monte Carlo results for the uniform electron gas at finite temperature [J].arXiv:1407.3600v1 [cond-mat.str-el],2014.
[20] LI Q,LIU H F,ZHANG G M,et al.The thermodynamical instability induced by pressure ionization in fluid helium [J].Phys Plasmas,2016,23:112709.
[21] WANG C,ZHANG P.Wide range equation of state for fluid hydrogen from density function theory [J].Phys Plasmas,2013,20:092703.
[22] HU S X,MILITZER B,GONCHAROV V N.First-principles equation-of-state table of deuterium for inertial confinement fusion applications [J].Phys Rev B,2011,84:224109.
[23] PIERLEONI C,CEPERLEY D M,HOLZMANN M.Coupled electron-ion Monte Carlo calculations of dense metallic hydrogen [J].Phys Rev Lett,2004,93(14):146402.
[24] MORALES M A,PIERLEONI C,CEPERLEY D M.Equation of state of metallic hydrogen from coupled electron-ion Monte Carlo simulations [J].Phys Rev E,2010,81:021202.
[25] KNUDSON M D,DESJARLAIS M P.High-precision shock wave measurements of deuterium:Evaluation of exchange-correlation functionals at the molecular-to-atomic transition [J].Phys Rev Lett,2017,118:035501.
[26] KERLEY G I.A theoretical equation of state for deuterium[R].Technical Report No.LA-4776,Los Alamos Scientific Laboratory,1972.
[27] KERLEY G I.Equation of state for hydrogen and deuterium[R].Technical Report No.SAND2003-3613,Sandia National Laboratories,2003.
[28] BECKER A,LORENZEN W,FORTNEY J J,et al.Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of brown dwarfs [J].The AstroPhy J Supp Ser,2014,215:21.
[29] LIU H F,SONG H F,ZHANG Q L,et al.Validation for equation of state in wide regime:Copper as prototype [J].Matter and Radiation at Extremes,2016,1:123-131.
[30] FILINOV V S,FORTOV V E,BONITZ M.Pair distribution functions of dense partially ionized hydrogen [J].Phys Lett A,2000,274:228-235.
[31] FILINOV V S,BONITZ M,EBELING W.Thermodynamics of hot dense H-plasmas:Path integral Monte Carlo simulations and analytical approximations [J].Plasmas Phys Control Fusion,2001,43:743-759.