Theory and two-electron systems

This review article is about the role of electron-electron interactions in low dimensional systems and its transport properties in nano-structures. It begins with a review of the pair-distribution function theory of electron liquid systems taking into account the electron-electron interactions. We extend the theory for highly correlated system such two- and one-dimensional electron liquids. We then review the microscopic theory of the local-field factors and calculate the quasiparticle properties in two-dimension electron liquid and compare our results with those measured by recent experiments. The physics of two-dimension bilayer structures are revised and are immediately applied to the study of charged Coulomb drag effects in a bilayer electron-electron system and results are compared with experimental data. As a final application, the Luttinger theory is discussed and we compare our recent calculations with those obtained from quantum Monte Carlo simulation for one dimensional electron liquid.This review article is about the role of electron-electron interactions in low dimensional systems and its transport properties in nano-structures. It begins with a review of the pair-distribution function theory of electron liquid systems taking into account the electron-electron interactions. We extend the theory for highly correlated system such two- and one-dimensional electron liquids. We then review the microscopic theory of the local-field factors and calculate the quasiparticle properties in two-dimension electron liquid and compare our results with those measured by recent experiments. The physics of two-dimension bilayer structures are revised and are immediately applied to the study of charged Coulomb drag effects in a bilayer electron-electron system and results are compared with experimental data. As a final application, the Luttinger theory is discussed and we compare our recent calculations with those obtained from quantum Monte Carlo simulation for one dimensional electron liquid.

Iranian Journal of Physics ResearchJun 15, 20080 citations

Thermodynamic extension of density-functional theory. II. Finite-temperature ensemble spin-density functional theory

Robert Balawender, A. Holas

The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable (the internal electron energy) and two local (position-dependent) observables (the total electron density and the spin density). The two-component potential of the many-electron system of interest is constructed of a scalar external potential and a collinear magnetic field (coupled only with the spin operator). Various equilibrium characteristics of two systems are defined and investigated. Conditions for the equivalence between two systems (the same equilibrium density matrix demanded) are derived and thoroughly discussed. The applicability of the Hohenberg-Kohn theorem is extended to the thermodynamic spin-density functional theory. Obtained results provide a rigorous mathematical foundation for future derivation of the zero-temperature limit of this theory and determination of its chemical reactivity indices.The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable (the internal electron energy) and two local (position-dependent) observables (the total electron density and the spin density). The two-component potential of the many-electron system of interest is constructed of a scalar external potential and a collinear magnetic field (coupled only with the spin operator). Various equilibrium characteristics of two systems are defined and investigated. Conditions for the equivalence between two systems (the same equilibrium density matrix demanded) are derived and thoroughly discussed. The applicability of the Hohenberg-Kohn theorem is extended to the thermodynamic spin-density functional theory. Obtained results provide a rigorous mathematical foundation for future derivation of the zero-temperature limit of this theory and determination of its chemical reactivity indices.

arXiv:0904.3990Apr 25, 20095 citations

Many-electron theory

S. Raimes

Jan 1, 197295 citations

Towards a practical pair density-functional theory for many-electron systems

Filipp Furche

In pair density-functional theory, the only unknown piece of the energy is the kinetic energy $T$ as a functional of the pair density $P({x}_{1},{x}_{2})$ . Although $T\phantom{\rule{0.1em}{0ex}}[P]$ has a simpler structure than the Hohenberg-Kohn functional of conventional density-functional theory, computational requirements are still moderate. In the present work, a particularly convenient model system to represent many-electron pair densities is introduced. This ``boson pair model'' (BPM) approximately treats electron pairs as noninteracting bosons. The resulting explicit model for the kinetic energy ${T}_{2}[P]$ is shown to be exact for two-electron systems and a lower bound to $T\phantom{\rule{0.1em}{0ex}}[P]$ for more than two electrons. The one- and two-particle density matrices obtained from the BPM yield upper bounds for the corresponding many-electron quantities. This suggests a partitioning $T\phantom{\rule{0.1em}{0ex}}[P]={T}_{2}[P]+{T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]$ , where only the remainder ${T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]\ensuremath{\geqslant}0$ needs to be approximated. If the BPM is constrained to yield the exact ground-state pair density, a two-electron Schr\"odinger equation with an effective local two-particle potential results; the latter is identified as a sum of the bare Coulomb interaction and the functional derivative of ${T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]$ . This self-consistent scheme to minimize the energy with respect to $P$ is more efficient than previous procedures. Further information on the functional derivative of ${T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]$ is derived from a contracted Schr\"odinger equation. Since ${T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]$ is explicitly known in the two-electron and noninteracting (Hartree-Fock) limits, the present method provides an alternative to density-matrix functional theories, which can be exact in the same limits and are similar in computational cost.In pair density-functional theory, the only unknown piece of the energy is the kinetic energy $T$ as a functional of the pair density $P({x}_{1},{x}_{2})$. Although $T\phantom{\rule{0.1em}{0ex}}[P]$ has a simpler structure than the Hohenberg-Kohn functional of conventional density-functional theory, computational requirements are still moderate. In the present work, a particularly convenient model system to represent many-electron pair densities is introduced. This ``boson pair model'' (BPM) approximately treats electron pairs as noninteracting bosons. The resulting explicit model for the kinetic energy ${T}_{2}[P]$ is shown to be exact for two-electron systems and a lower bound to $T\phantom{\rule{0.1em}{0ex}}[P]$ for more than two electrons. The one- and two-particle density matrices obtained from the BPM yield upper bounds for the corresponding many-electron quantities. This suggests a partitioning $T\phantom{\rule{0.1em}{0ex}}[P]={T}_{2}[P]+{T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]$, where only the remainder ${T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]\ensuremath{\geqslant}0$ needs to be approximated. If the BPM is constrained to yield the exact ground-state pair density, a two-electron Schr\"odinger equation with an effective local two-particle potential results; the latter is identified as a sum of the bare Coulomb interaction and the functional derivative of ${T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]$. This self-consistent scheme to minimize the energy with respect to $P$ is more efficient than previous procedures. Further information on the functional derivative of ${T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]$ is derived from a contracted Schr\"odinger equation. Since ${T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]$ is explicitly known in the two-electron and noninteracting (Hartree-Fock) limits, the present method provides an alternative to density-matrix functional theories, which can be exact in the same limits and are similar in computational cost.

Physical Review AAug 30, 200464 citations

Many-electron systems

Springer eBooksApr 6, 20080 citations

In pair density-functional theory, the only unknown piece of the energy is the kinetic energy

T

as a functional of the pair density

P({x}_{1},{x}_{2})

. Although

T\phantom{\rule{0.1em}{0ex}}[P]

has a simpler structure than the Hohenberg-Kohn functional of conventional density-functional theory, computational requirements are still moderate. In the present work, a particularly convenient model system to represent many-electron pair densities is introduced. This ``boson pair model'' (BPM) approximately treats electron pairs as noninteracting bosons. The resulting explicit model for the kinetic energy

{T}_{2}[P]

is shown to be exact for two-electron systems and a lower bound to

T\phantom{\rule{0.1em}{0ex}}[P]

for more than two electrons. The one- and two-particle density matrices obtained from the BPM yield upper bounds for the corresponding many-electron quantities. This suggests a partitioning

T\phantom{\rule{0.1em}{0ex}}[P]={T}_{2}[P]+{T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]

, where only the remainder ${T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]\ensuremath{\geqslant}0$ needs to be approximated. If the BPM is constrained to yield the exact ground-state pair density, a two-electron Schr\"odinger equation with an effective local two-particle potential results; the latter is identified as a sum of the bare Coulomb interaction and the functional derivative of

{T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]

. This self-consistent scheme to minimize the energy with respect to

P

is more efficient than previous procedures. Further information on the functional derivative of

{T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]

is derived from a contracted Schr\"odinger equation. Since

{T}_{\mathrm{eff}}\phantom{\rule{0.1em}{0ex}}[P]

is explicitly known in the two-electron and noninteracting (Hartree-Fock) limits, the present method provides an alternative to density-matrix functional theories, which can be exact in the same limits and are similar in computational cost.