Classical-map hypernetted-chain method: Difference between revisions

Revision as of 03:32, 18 January 2006

Latest revision as of 06:59, 4 December 2024

(47 intermediate revisions by 26 users not shown)

Line 1:

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

'''CHNC''' is used as the acronym for a method in many-body theoretical physics known as the '''C'''lassical-map '''H'''yper-'''N'''etted-'''C'''hain technique. It has been applied to interacting uniform [[electron liquid]]s in two and three dimensions, and to interacting [[hydrogen plasmas]].

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>

{{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 function]]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 analogy.

In this 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. 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.

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

|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

In|arxiv this= method, the paircond-distributionsmat/9909056 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> 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==

== Selected References. ==

*[[Fermi liquid]]

*[[Many-body theory]]

*[[Quantum fluid]]

*[[Radial distribution function]]

== Selected References. ==

M.W. C. Dharma-wardana and Francois Perrot,<br>

{{reflist}}

Physcial Review Letters, vol. 84, page 959-962 (2000)

==Further reading==

C. Bulutay and B. Tanatar,<br>

*{{cite journal

Physical Review B, volume 65, page 195116 (2002)

|author1=C. Bulutay and |author2=B. Tanatar,<br> |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 and |author2=H. Totsuji,<br> |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,<br>

|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]]

M. W. C. Dharma-wardana and Francois Perrot,<br>

Physical Review B, volume 66, page 014110 (2002)

N. Q. Khanh and H. Totsuji,<br>

Solid State Com., vol.129, page 37 (2004)

M. W. C. Dharma-wardana,<br>

Physical Review B, volume72, page 125339 (2005)

{{catneeded}}