Classical-map hypernetted-chain method: Difference between revisions

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

The '''Classicalclassical-map Hyperhypernetted-Netted-Chainchain method''' ('''CHNC method''') technique is a method used in [[many-body problem|many-body]] [[theoretical physics]] for interacting uniform [[electron liquid]]sliquids in two and three dimensions, and tofor interactingnon-ideal [[hydrogen plasma_(physics)|plasma]]s. The method extends the famous hyper[[Hypernetted-nettedchain equation|hypernetted-chain method]] (HNC) introduced by [[J.M.J. van Leeuwen]] et al.<ref>

{{cite journal

method (HNC) introduced by van Leeuwen et al.<ref>J. M. J. van Leeuwen, J. Groenveld, J. de Boer: Physica '''25''', 792 (1959)</ref> to [[quantum fluid]]s as well. The classical HNC, together with the Percus-Yevik (PY) equation, are the two pillars which bear the brunt of most calculations in the theory of interacting [[classical fluids]]. Also, HNC and PY have become important in providing basic reference schemes in the theory of fluids<ref> R. Balescu, ''Equilibrium and Non-equilibrium Statistical Mechanics'' (Wiley 1975) p257-277 </ref>, and hence they are of great importance to the physics of many-particle systems.

|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

method|bibcode (HNC)= introduced by van Leeuwen et al1959Phy.<ref>J. M. J. van Leeuwen, J25. Groenveld, J.792V de Boer: Physica '''25''', 792 (1959)}}</ref> to [[quantum fluid]]s as well. The classical HNC, together with the Percus-Yevik[[Percus–Yevick (PY) equationapproximation]], are the two pillars which bear the brunt of most calculations in the theory of interacting [[classical fluidsfluid]]s. Also, HNC and PY have become important in providing basic reference schemes in the theory of fluids<ref> R. Balescu, ''Equilibrium and Non-equilibrium Statistical Mechanics'' (Wiley 1975) p257-277 </ref>, and hence they are of great importance to the physics of many-particle systems.

{{cite book

|author=R. Balescu

|year=1975

|title=Equilibrium and Non-equilibrium Statistical Mechanics

|pages=257–277

|publisher=[[John Wiley & Sons|Wiley]]

|isbn=

}}</ref> and hence they are of great importance to the physics of many-particle systems.

The HNC and PY integral equations provide the [[pair- distribution functionsfunction]]s of the particles in a classical fluid, even for very high coupling strengths. The coupling strength is measured by the ratio of the potential energy to the kinetic energy. In a classical fluid, the kinetic energy is proportional to the temperature. In a quantum fluid, the situation is very complicated as one needs to deal with quantum operators, and matrix elements of such operators, which appear in various perturbation methods based on [[Feynman diagram]]s. The CHNC method provides an approximate "escape" from these difficulties, and applies to regimes beyond perturbation theory. In [[Robert B. Laughlin]]'s famous Nobel Laureate work on the [[fractional quantum Hall effect]], an HNC equation was used within a classical plasma diagramsanalogy.

The CHNC method provides an approximate "escape" from these difficulties, and applies to regimes beyond perturbation theory.

In [[Laughlin]]'s famous Nobel Laureate work on the fractional

[[quantum hall effect]], an HNC equation was used within a classical plasma analogy.

In the CHNC method, the pair-distributions of the interacting particles are calculated using a mapping which ensures that the quantum mechanically correct non-interacting pair distribution function is recovered when the Coulomb interactions are switched off.<ref>

{{cite journal

<ref>M.W. C. Dharma-wardana and François Perrot, Physical Review Letters, '''84''', page 959-962 (2000)</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.

|author1=M.W.C. Dharma-wardana |author2=F. Perrot |year=2000

|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

|bibcode=2000PhRvL..84..959D

<ref>M.W.|arxiv C.= Dharmacond-wardanamat/9909056 and François Perrot, Physical Review Letters, '''84''', page 959-962 (2000)}}</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 parametersparameter]]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==

*[[Fermi liquid]]

*[[Many-body theory]]

*[[Quantum fluid]]

*[[Radial distribution function]]

== References ==

{{reflist}}

==See also==

[[Fermi liquid]]

[[Many-body theory]]

[[Quantum fluid]]

*C. Bulutay and B. Tanatar, Physical Review B, '''65''', page 195116 (2002)

*M. W. C. Dharma-wardana and François Perrot, Physical Review B, '''66''', page 014110 (2002)

*N. Q. Khanh and H. Totsuji, Solid State Com., '''129''', page 37 (2004)

==Further reading==

*M. W. C. Dharma-wardana, Physical Review B, '''72''', page 125339 (2005)

*{{cite journal

|author1=C. Bulutay |author2=B. Tanatar |year=2002

|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}}

*{{cite journal

|author1=N.Q. Khanh |author2=H. Totsuji |year=2004

|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=37–42

|doi=10.1016/j.ssc.2003.09.010

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

*{{cite journal

|author=M.W.C. Dharma-wardana

|year=2005

|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 }}

[[Category:Theoretical physics]]

[[Category:Classical fluids]]

[[Category:Quantum fluids]]