Scattering Theory Approach to Electrodynamic Casimir Forces (0908.2649v1)

Abstract: We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

• The paper introduces a unified scattering theory framework to compute electrodynamic Casimir forces in complex geometries.
• It combines classical electromagnetic scattering amplitudes with translation matrices to handle arbitrary shapes and media.
• This approach extends traditional methods and offers precise, adaptable computations for nanoscale device analysis.

Scattering Theory Approach to Electrodynamic Casimir Forces

The paper "Scattering Theory Approach to Electrodynamic Casimir Forces" by Rahi et al. presents a comprehensive framework for calculating the Casimir force in various configurations, emphasizing the applicability of this method across a wide array of shapes, susceptibilities, separations, and environmental conditions. The authors employ a scattering approach that combines the classical electromagnetic scattering amplitudes of objects with translation matrices, enabling calculations for objects immersed in media other than the vacuum, at nonzero temperatures, and within complex spatial arrangements.

The paper's primary contribution lies in unifying and extending various methods to provide a robust, efficient means for calculating Casimir forces. Traditional approaches, like the Lifshitz theory, cater to specific scenarios—typically flat, parallel surfaces within a vacuum. In contrast, the scattering theory approach allows for the exploration of geometries like spheres opposite plates or cylinders either nested or adjacent, regardless of their electromagnetic properties.

Key highlights include:

• Comprehensive Framework: The authors provide methodologies to compute the Casimir interaction energy with arbitrary precision, leveraging the ability to switch between geometrical and material configurations.
• Translation Matrices: Utilizing universal translation matrices ensures translational and rotational adaptability in computing forces across different coordinate systems.
• General Geometry: This formalism applies to general geometries, including configurations with multiple (n-body) interactions, addressing arbitrary shapes with rough or smooth surfaces, edges, and cusps.
• Material Response and Temperature: The inclusion of frequency-dependent, lossy electric permittivity, and magnetic permeability tensors, as well as both zero and nonzero temperature scenarios, ensures the model's relevance to practical applications.

Several applications illustrate the method's capability. The paper revisits the Lifshitz formula for infinite half-spaces, establishes the Casimir-Polder to van der Waals crossover, and analyzes Casimir interactions between various configurations, such as two parallel perfect metal cylinders and a sphere opposite a plane.

From a computational standpoint, these calculations demonstrate significant flexibility. For instance, one can capture asymptotic results analytically at large separations, and numerical results across a range of separations can be derived utilizing standard computing resources.

In practical terms, this framework can significantly impact the design and analysis of nanoscale devices, where Casimir forces influence operational dynamics. Theoretically, the authors speculate on further developments in AI to automate the computation of scattering matrices across more complex configurations, potentially leveraging machine learning to predict force interactions in less idealized conditions.

Overall, the scattering theory approach constitutes a versatile and powerful tool for studying Casimir forces, transcending previous limitations by embracing the complexity and diversity of real-world configurations.