• Matter and Radiation at Extremes
  • Vol. 9, Issue 5, 057401 (2024)
Tobias Dornheim1,2,a), Sebastian Schwalbe1,2, Panagiotis Tolias3, Maximilian P. Böhme1,2,4..., Zhandos A. Moldabekov1,2 and Jan Vorberger2|Show fewer author(s)
Author Affiliations
  • 1Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
  • 2Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
  • 3Space and Plasma Physics, Royal Institute of Technology (KTH), Stockholm SE-100 44, Sweden
  • 4Technische Universität Dresden, D-01062 Dresden, Germany
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    DOI: 10.1063/5.0211407 Cite this Article
    Tobias Dornheim, Sebastian Schwalbe, Panagiotis Tolias, Maximilian P. Böhme, Zhandos A. Moldabekov, Jan Vorberger. Ab initio density response and local field factor of warm dense hydrogen[J]. Matter and Radiation at Extremes, 2024, 9(5): 057401 Copy Citation Text show less

    Abstract

    We present quasi-exact ab initio path integral Monte Carlo (PIMC) results for the partial static density responses and local field factors of hydrogen in the warm dense matter regime, from solid density conditions to the strongly compressed case. The full dynamic treatment of electrons and protons on the same footing allows us to rigorously quantify both electronic and ionic exchange–correlation effects in the system, and to compare the results with those of earlier incomplete models such as the archetypal uniform electron gas or electrons in a fixed ion snapshot potential that do not take into account the interplay between the two constituents. The full electronic density response is highly sensitive to electronic localization around the ions, and our results constitute unambiguous predictions for upcoming X-ray Thomson scattering experiments with hydrogen jets and fusion plasmas. All PIMC results are made freely available and can be used directly for a gamut of applications, including inertial confinement fusion calculations and the modeling of dense astrophysical objects. Moreover, they constitute invaluable benchmark data for approximate but computationally less demanding approaches such as density functional theory or PIMC within the fixed-node approximation.
    ĤH=12l=1Nl,e212mpl=1Nl,p2+k=1Nl=1Nl<kWE(r̂l,r̂k)+k=1Nl=1Nl<kWE(Îl,Îk)k=1Nl=1NWE(Îl,r̂k),

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    ZN,Ω,β=1N!N!σNSNσNSNξNpp×dRR|eβĤH|π̂σNπ̂σNR,

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    Fab(q,τ)=n̂a(q,0)n̂b(q,τ),

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    Ĥq,ω;Ae,Ap=ĤH+2Ael=1Ncos(qr̂lωt)+2Apl=1Ncos(qÎlωt).

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    δρ̂a(q,ω)=χaa(0)(q,ω)×Aa+bvab(q)[1Gab(q,ω)]δρ̂b(q,ω),

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    δρ̂a(q,ω)=Abχab(q,ω).

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    δρ̂a(q)=χab(1,1)(q)Ab+χab(1,3)(q)Ab3+O(Ab5),

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    δρ̂a(q)=c1Ab+c3Ab3+O(Ab5)

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    χab(q,0)=NaNbΩ0βdτFab(q,τ),

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    χee(q,ω)=χee(0)(q,ω)1vee(q)[1Gee(q,ω)]χee(0)(q,ω).

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    θab(q,ω)=vab(q)[1Gab(q,ω)],

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    δna(q,ω)=χaa(0)(q,ω)δUa(q,ω)+cχaa(0)(q,ω)θac(q,ω)δnc(q,ω),

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    χab(q,ω)=χaa(0)(q,ω)δab+cχaa(0)(q,ω)θac(q,ω)χcb(q,ω).

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    θee(q,ω)=1χee(0)(q,ω)χpp(q,ω)χee(q,ω)χpp(q,ω)χep2(q,ω),

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    θpp(q,ω)=1χpp(0)(q,ω)χee(q,ω)χee(q,ω)χpp(q,ω)χep2(q,ω),

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    θep(q,ω)=χep(q,ω)χee(q,ω)χpp(q,ω)χep2(q,ω).

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    I(q,ω)=See(q,ω)R(ω),

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    See(q,ω)=Im{χee(q,ω)}πne(1eβω).

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    χee(q)=2nedωSee(q,ω)ω.

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    Fee(q,τ)=L[See(q,ω)]=dωSee(q,ω)eτω,

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    L[See(q,ω)]=L[See(q,ω)R(ω)]L[R(ω)],

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    See(q,ω)=Sel(q,ω)+Sbf(q,ω)+Sff(q,ω)Sinel(q,ω).

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    Sel(q,ω)=WR(q)δ(ω),

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    τFab(q,τ)τ=0=δabq22ma.

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    ne(r)=n0+2Aecos(qr)χee(q),

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    Tobias Dornheim, Sebastian Schwalbe, Panagiotis Tolias, Maximilian P. Böhme, Zhandos A. Moldabekov, Jan Vorberger. Ab initio density response and local field factor of warm dense hydrogen[J]. Matter and Radiation at Extremes, 2024, 9(5): 057401
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