Fluctuation-induced interactions between dielectrics in general geometries.

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Nanoscale Interactions

Background:

• The Casimir effect describes quantum vacuum fluctuations leading to forces between objects.
• Lifshitz theory extends this to include thermal effects and realistic dielectric properties.
• Calculating these forces in arbitrary geometries is computationally challenging.

Purpose of the Study:

• To develop a robust numerical method for calculating thermal Casimir and quantum nonretarded Lifshitz interactions.
• To investigate these interactions in general dielectric geometries.
• To compare established approximations with a novel numerical approach.

Main Methods:

• Mapping the classical partition function to a determinant, discretized and evaluated using Cholesky factorization.
• Quantizing the quantum partition function via path integrals of interacting dipoles, resulting in a product of determinants.
• Comparing numerical results with pairwise additivity and proximity force approximations.

Main Results:

• The developed numerical methods accurately compute Casimir and Lifshitz forces.
• The proposed
• factorization approximation
• yields good numerical results across studied geometries.
• Discrepancies with pairwise additivity and proximity force approximations highlight the need for precise calculations.

Conclusions:

• The numerical determinant-based approach provides an accurate way to calculate thermal Casimir and quantum Lifshitz forces.
• The factorization approximation offers a computationally efficient and reliable alternative for specific geometries.
• This work advances the understanding and calculation of nanoscale forces in dielectric systems.