Classical-map hypernetted-chain method: Difference between revisions

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The '''classical-map hypernetted-chain method''' ('''CHNC method''') is a method used in [[many-body problem|many-body]] [[theoretical physics]] for interacting uniform [[electron liquid]]s in two and three dimensions, and for interacting [[hydrogen 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

|authorauthor1=J.M.J. van Leeuwen, |author2=J. Groenveld, |author3=J. de Boer |year=1959

|year=1959

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

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

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|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.

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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

|authorauthor1=M.W.C. Dharma-wardana, |author2=F. Perrot |year=2000

|year=2000

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

|journal=[[Physical Review Letters]]

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==Further reading==

*{{cite journal

|authorauthor1=C. Bulutay, |author2=B. Tanatar |year=2002

|year=2002

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

|journal=[[Physical Review B]]

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|bibcode = 2002PhRvB..65s5116B }}

*{{cite journal

|authorauthor1=M.W.C. Dharma-wardana, |author2=F. Perrot |year=2002

|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]]

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|bibcode = 2002PhRvB..66a4110D }}

*{{cite journal

|authorauthor1=N.Q. Khanh, |author2=H. Totsuji |year=2004

|year=2004

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

|journal=[[Solid State Communications]]