Classical-map hypernetted-chain method: Difference between revisions

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{{for|the Canadian radio station|CHNC-FM }}

The '''classical-map hypernetted-chain method''' ('''CHNC method''') is a method used in [[many-body problem|many-body]] [[theoretical physics]] for interacting uniform electron liquids in two and three dimensions, and for non-ideal [[plasma_(physics)|plasma]]s. The method extends the famous [[Hypernetted-chain equation|hypernetted-chain method]] (HNC) introduced by [[J. M. J. van Leeuwen]] et al.<ref>

{{cite journal

|author1=J.M.J. van Leeuwen |author2=J. Groenveld |author3=J. de Boer |year=1959

|title=New method for the calculation of the pair correlation function I

|journal=[[Physica (journal)|Physica]]

|volume=25 |issue=7–12 |page=792

|doi=10.1016/0031-8914(59)90004-7

|bibcode = 1959Phy....25..792V }}</ref> to [[quantum fluid]]s as well. The classical HNC, together with the [[Percus–Yevick approximation]], are the two pillars which bear the brunt of most calculations in the theory of interacting [[classical fluid]]s. Also, HNC and PY have become important in providing basic reference schemes in the theory of fluids,<ref>

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|title=Simple Classical Mapping of the Spin-Polarized Quantum Electron Gas: Distribution Functions and Local-Field Corrections

|journal=[[Physical Review Letters]]

|volume=84 |issue=5 |pages=959–962

|doi=10.1103/PhysRevLett.84.959

|pmid=11017415

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|arxiv = cond-mat/9909056 }}</ref> The value of the method lies in its ability to calculate the ''interacting'' pair distribution functions ''g''(''r'') at zero and finite temperatures. Comparison of the calculated ''g''(''r'') with results from Quantum Monte Carlo show remarkable agreement, even for very strongly correlated systems.

The interacting pair-distribution functions obtained from CHNC have been used to calculate the exchange-correlation energies, [[Landau parameter]]s of [[Fermi liquid]]s and other quantities of interest in many-body physics and [[density functional theory]], as well as in the theory of hot plasmas.<ref>M. W. C. Dharma-wardana, M. W. C.; and François Perrot,

Phys. Rev. B '''66''', 014110 (2002) </ref><ref>R. Bredow, Th. Bornath, W.-D. Kraeft, M.W.C. Dharma-wardana and R. Redmer,

Contributions to Plasma Physics,

''55'', 222-229 (2015)

DOI 10.1002/ctpp.201400080

</ref>

==See also==

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|title=Spin-dependent analysis of two-dimensional electron liquids

|journal=[[Physical Review B]]

|volume=65 |issue=19 |pages=195116

|doi=10.1103/PhysRevB.65.195116

|bibcode = 2002PhRvB..65s5116B |url=http://repository.bilkent.edu.tr/bitstream/11693/24708/1/Spin-dependent%20analysis%20of%20two-dimensional%20electron%20liquids.pdf|hdl=11693/24708 |hdl-access=free}}

*{{cite journal

|author1=M.W.C. Dharma-wardana |author2=F. Perrot |year=2002

|title=Equation of state and the Hugoniot of laser shock-compressed deuterium: Demonstration of a basis-function-free method for quantum calculations

|journal=[[Physical Review B]]

|volume=66 |issue=1 |pages=014110

|doi=10.1103/PhysRevB.66.014110

|bibcode = 2002PhRvB..66a4110D |arxiv=cond-mat/0112324}}

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|title=Electron correlation in two-dimensional systems: CHNC approach to finite-temperature and spin-polarization effects

|journal=[[Solid State Communications]]

|volume=129 |issue=1 |pages=3737–42

|doi=10.1016/j.ssc.2003.09.010

|bibcode = 2004SSCom.129...37K }}

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|title=Spin and temperature dependent study of exchange and correlation in thick two-dimensional electron layers

|journal=[[Physical Review B]]

|volume=72 |issue=12
|pages=125339

|doi=10.1103/PhysRevB.72.125339

|arxiv = cond-mat/0506804 |bibcode = 2005PhRvB..72l5339D }}