TY - JOUR

T1 - Statistical Mechanics in Collective Coordinates

AU - Edwards, S. F.

AU - Schwartz, Moshe

PY - 2003/3

Y1 - 2003/3

N2 - We study the transformation of the statistical mechanics of N particles to the statistical mechanics of fields, that are the collective coordinates, describing the system. We give an explicit expression for the functional Fourier transform of the Jacobian of the transformation from particle to collective coordinate and derive the Fokker-Planck equation in terms of the collective coordinates. Simple approximations, leading to Debye-Huckel theory and to the hard sphere Percus-Yevick equation are discussed.

AB - We study the transformation of the statistical mechanics of N particles to the statistical mechanics of fields, that are the collective coordinates, describing the system. We give an explicit expression for the functional Fourier transform of the Jacobian of the transformation from particle to collective coordinate and derive the Fokker-Planck equation in terms of the collective coordinates. Simple approximations, leading to Debye-Huckel theory and to the hard sphere Percus-Yevick equation are discussed.

KW - Collective coordinates

KW - Fokker-Planck equation

KW - Jacobian

KW - Statistical mechanics

UR - http://www.scopus.com/inward/record.url?scp=0037277226&partnerID=8YFLogxK

U2 - 10.1023/A:1022191214859

DO - 10.1023/A:1022191214859

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AN - SCOPUS:0037277226

SN - 0022-4715

VL - 110

SP - 497

EP - 502

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3-6

ER -