Nearsightedness of electronic matter.

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Computational chemistry

Background:

• Introduced by W. Kohn, electron "nearsightedness" is a key concept in many-atom systems.
• It underlies important ideas like Pauling's "chemical bond" and Yang's "divide and conquer" computational principle.
• Local electronic properties depend significantly only on nearby effective external potentials.

Purpose of the Study:

• To quantitatively define and sharpen the concept of electron "nearsightedness" for uncharged fermions.
• To investigate the influence of electron-electron interactions on this property.
• To analyze the effects of perturbing external charges on local electronic properties.

Main Methods:

• Developing theoretical models for uncharged fermions in external potentials.
• Analyzing the mathematical formulation of electron "nearsightedness" in these models.
• Investigating electron-electron interactions and external charge perturbations within the theoretical framework.

Main Results:

• The concept of electron "nearsightedness" is rigorously defined for specific fermionic models.
• The study quantifies the limited effect of distant potential changes on local electronic properties.
• The influence of electron-electron interactions and external charges on "nearsightedness" is elucidated.

Conclusions:

• Electron "nearsightedness" provides a fundamental understanding of electronic behavior in complex systems.
• The findings offer insights into the transferability of electronic properties and computational strategies.
• This work establishes a more precise theoretical foundation for analyzing local electronic behavior.