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Functional differentiation, line integration, and departures from homogeneity of the single-particle kinetic energy functional for one-dimensional systems of N fermions
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| Abstract |
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| The differential virial theorem of March and Young for N fermions moving in a common one-dimensional potential energy V(x) is here combined with the Euler equation of density functional theory expressing the constancy of the chemical potential throughout the entire inhomogeneous particle density. The functional derivative of the single-particle kinetic energy is thereby expressed directly in terms of the kinetic energy density; a line integral being involved in establishing the connection. This result is then used to establish a formula measuring departures from simple homogeneity of the kinetic energy functional: a matter of current interest in density functional theory. Finally, the general theory of the functional derivative of the single-particle kinetic energy with respect to the particle density is exemplified for the case of harmonic confinement of fermions in one dimension. (C) 2001 American Institute of Physics. | | |
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English
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Journal of mathematical physics. - New York, N.Y. | |
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New York, N.Y. : 2001
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0022-2488
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42:8(2001), p. 3361-3371
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000169929700010
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