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In Numerical methods for computing Casimir interactions, we have this expression for the Casimir force between two plates:
where
I am trying to interpret this physically on a per-frequency and per-mode basis, before actually looking at the complete integral.
If we focus on a single frequency ##\omega##, it seems that the force contribution as a function of the mode parameter ##p## can vary wildly and become arbitrarily large.
If we consider a narrow-band or even a single-frequency "excitation", the expression is telling us that certain modes will produce an infinite force. This infinite force would change sign abruptly from attractive to repulsive if we make small changes to ##p## or ##\omega## around those critical values.
How are we to interpret this physically? The authors focus more on how to tame this numerical headache, but not on why the force should behave this way.
where
p is relatedto the plate-parallel momentum of the contributing modes/fluctuations.
I am trying to interpret this physically on a per-frequency and per-mode basis, before actually looking at the complete integral.
If we focus on a single frequency ##\omega##, it seems that the force contribution as a function of the mode parameter ##p## can vary wildly and become arbitrarily large.
If we consider a narrow-band or even a single-frequency "excitation", the expression is telling us that certain modes will produce an infinite force. This infinite force would change sign abruptly from attractive to repulsive if we make small changes to ##p## or ##\omega## around those critical values.
How are we to interpret this physically? The authors focus more on how to tame this numerical headache, but not on why the force should behave this way.
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