Behavior of the Electron

Matthias Ernzerhof, Kieron Burke, John P. Perdew

The asymptotic behavior of an N-electron ground-state wave function is analyzed, as one electron wanders far from the system. Implications for the one-matrix and pair density are described. The asymptotic behavior currently discussed in the literature, in which the remaining (N−1) electrons relax to their ground state, is generalized to the case where the (N−1)-electron ground state is degenerate. Infinitely long-ranged correlations are reported, in which the selected (N−1)-electron ground state depends upon the direction along which one electron wandered off. We correct a standard limit for the one matrix. Numerical and analytic studies of accurate correlated wave functions illustrate and support the standard asymptotic behavior for the nondegenerate case and its generalization derived here. We extract the (N−1)-electron density from the correlated N-electron wave function. We also discuss the question how large the separation of one electron must be to realize the limiting behavior.

Yu-Liang Liu

In framework of eigen-functional bosonization method, we introduce an imaginary phase field to uniquely represent electron correlation, and demonstrate that the Landau Fermi liquid theory and the Tomonaga-Luttinger liquid theory can be unified. It is very clear in this framework that the Tomonaga-Luttinger liquid behavior of one-dimensional interacting electron gases originates from their Fermi structure, and the non-Landau-Fermi liquid behavior of 2D interacting electron gases is induced by the long-range electron interaction, while 3D interacting electron gases generally show the Landau Fermi liquid behavior.

Konstantin V. Kazakov

Victor Francis Hess

Yu-Liang Liu

In framework of eigen-functional bosonization method, we introduce an imaginary phase field to uniquely represent electron correlation, and demonstrate that the Landau Fermi liquid theory and the Tomonaga-Luttinger liquid theory can be unified. It is very clear in this framework that the Tomonaga-Luttinger liquid behavior of one-dimensional interacting electron gases originates from their Fermi structure, and the non-Landau-Fermi liquid behavior of 2D interacting electron gases is induced by the long-range electron interaction, while 3D interacting electron gases generally show the Landau Fermi liquid behavior. Typeset using REVTEX 1 Since the discovery of high Tc cuprate superconductors [1], the strongly correlated electron systems has been extensively studied theoretically [2–10]. Now a common consensus is reached that the low energy physics properties of cuprate superconductors, such as anomalous normal state behavior and high superconducting transition temperature, are determined