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Calculation Methods for the Casimir Force
Different models have been proposed throughout the past fifty years to calculate the Casimir force for different configurations and geometries whilst also considering different practical aspects such as thermal and finite conductivity corrections. Unfortunately there is no general method to calculate the Casimir force, instead for each specific configuration there a specific method exists. The calculation of the Casimir effect in situations with real practical use is limited by the lack of an efficient and numerically fast method of determining the eigenmode structure of the field for several configurations, geometries and boundary conditions. Thus a practical solution for these problems is to use approximated methods which are easily modelled numerically and can be applied in a wide range of configurations. Presently there exist two main numerical methods for the calculation of the Casimir force in complex geometries: the lattice QED techniques and the phenomenological methods, such as Proximity force method. The lattice QED can mimic and reproduce, in a detailed way, both global and local features of continuum Casimir systems with simple geometries, while failing to produce results with sufficient correctness (accuracy, precision, fidelity) for most highly complex systems. In terms of computational power, adequate choices of lattice geometry can increase the efficiency of the method, reducing the number of grid points and enhancing the precision of the calculations. Nevertheless such choices are still limited by the complexity of the physical objects considered. The Proximity force method considers the sum of the contributions of small surface elements which compose two close objects, assuming that they behave as infinitesimal parallel plates. This phenomenological approach is limited to objects with surfaces that have a small degree of non-parallelism and requires a high degree of parameterization of the system. Finally, there is the method based on the Additive Principle. This is the most versatile and easy to use method to calculate the Casimir force in complex geometries, and it can take into account some of the physical properties (the atomic polarizability) of the materials of the object.
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