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Sum-over-modes approach to the Casimir effect in dissipative systems

It is, however, possible to generalize Casimir’s sum-over-modes expression to a dissipative system using these complex frequencies [1], where those are the poles of the complex (dissipative) Green function. Those are complex (even pure imaginary) frequencies. The expression shows analogies with the energy of quantum dissipative oscillator. The previous expression is equivalent to the scattering formula for the Casimir Effect, which allows one to calculate the free energy between two bodies if we know the scattering operator of each isolated object. Sum-over-modes approach to the Casimir effect in dissipative systems