Manipulation and amplification of the Casimir force through surface fields using helicity.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Surface Science

Background:

• The Casimir force arises from quantum fluctuations and is sensitive to boundary conditions and system geometry.
• Understanding Casimir forces in finite systems is crucial for applications in nanotechnology and materials science.
• Surface fields can induce complex behaviors, such as helicity, in the system's order parameter.

Purpose of the Study:

• To investigate the behavior of the Casimir force in O(n) systems with finite size (L) under specific surface field conditions.
• To analyze the temperature dependence of the Casimir force, particularly around the critical temperature (T_{c}).
• To determine whether the Casimir force can be attractive or repulsive in these systems.

Main Methods:

• Exact analytical calculations for 1D XY and Heisenberg models with twisted boundary conditions.
• Numerical simulations for 3D Gaussian and O(2) models with phase-shifted plane wave surface fields.
• Application of finite-size scaling analysis to interpret the results.

Main Results:

• The Casimir force scales as L^{-2} in certain temperature ranges, both above and below T_{c}.
• The force can be either attractive or repulsive, contingent upon system-specific parameters.
• Observed behaviors are consistent with predictions from finite-size scaling theory.

Conclusions:

• Finite surface fields significantly influence Casimir forces in finite O(n) systems.
• The L^{-2} scaling provides a universal characteristic of the Casimir force in these configurations.
• The study offers insights into controlling Casimir forces through surface engineering.