## Hermitian one-particle density matrix through a semiclassical gradient expansion

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**Hermitian one-particle density matrix through a semiclassical gradient expansion.** / Bencheikh, K.; Räsänen, E.

Research output: Contribution to journal › Article › Scientific › peer-review

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*Journal of Physics A: Mathematical and Theoretical*, vol. 49, no. 1, 015205. https://doi.org/10.1088/1751-8113/49/1/015205

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*Journal of Physics A: Mathematical and Theoretical*,

*49*(1), [015205]. https://doi.org/10.1088/1751-8113/49/1/015205

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TY - JOUR

T1 - Hermitian one-particle density matrix through a semiclassical gradient expansion

AU - Bencheikh, K.

AU - Räsänen, E.

PY - 2015/12/9

Y1 - 2015/12/9

N2 - We carry out the semiclassical expansion of the one-particle density matrix up to the second order in h. We use the method of Grammaticos and Voros based on the Wigner transform of operators. We show that the resulting density matrix is Hermitian and idempotent in contrast with the well-known result of the semiclassical Kirzhnits expansion. Our density matrix leads to the same particle density and kinetic energy density as in the literature, and it satisfies the consistency criterion of the Euler equation. The derived Hermitian density matrix clarifies the ambiguity in the usefulness of gradient expansion approximations and might reignite the development of density functionals with semiclassical methods.

AB - We carry out the semiclassical expansion of the one-particle density matrix up to the second order in h. We use the method of Grammaticos and Voros based on the Wigner transform of operators. We show that the resulting density matrix is Hermitian and idempotent in contrast with the well-known result of the semiclassical Kirzhnits expansion. Our density matrix leads to the same particle density and kinetic energy density as in the literature, and it satisfies the consistency criterion of the Euler equation. The derived Hermitian density matrix clarifies the ambiguity in the usefulness of gradient expansion approximations and might reignite the development of density functionals with semiclassical methods.

KW - density matrix

KW - density-functional theory

KW - Wigner transform

U2 - 10.1088/1751-8113/49/1/015205

DO - 10.1088/1751-8113/49/1/015205

M3 - Article

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 1

M1 - 015205

ER -