Nonperturbative theory of atom-surface interaction: corrections at short separations

Area of Science:

• Condensed Matter Physics
• Surface Science
• Atomic Physics

Background:

• The interaction between atoms and surfaces is fundamental to many physical phenomena.
• Existing theories, like Lifshitz theory, often rely on perturbative approximations.
• Understanding these interactions is key for applications in nanotechnology and materials science.

Purpose of the Study:

• To derive nonperturbative expressions for atom-surface interaction free energy and force at any temperature.
• To compare nonperturbative results with traditional perturbative Lifshitz theory.
• To investigate the validity and limitations of perturbative approaches.

Main Methods:

• Transition to the Matsubara representation for nonperturbative calculations.
• Comparison with standard Lifshitz theory based on perturbative results.
• Numerical computations for He and Na atoms interacting with an Au surface.
• Derivation of analytic expressions in the classical limit and for ideal metals.

Main Results:

• Nonperturbative expressions for free energy and force were derived.
• Lifshitz formulas were shown to be the lowest-order approximation of the nonperturbative ones.
• Maximum deviations between theories occur at short atom-surface separations (~1 nm).
• Analytic expressions in the classical limit agree with perturbative results.

Conclusions:

• The study provides a more general, nonperturbative framework for atom-surface interactions.
• Perturbative Lifshitz theory is an approximation valid for larger separations.
• Results have implications for van der Waals adsorption theories and nanoscale phenomena.