Dynamical Casimir effect with $δ-δ^{\prime}$ mirrors

We calculate the spectrum and the total rate of created particles for a real massless scalar field in $1+1$ dimensions, in the presence of a partially transparent moving mirror simulated by a Dirac $δ-δ^{\prime}$ point interaction. We show that, for this model, a partially reflecting mirror can produce a larger number of particles in comparison with a perfect one. In the limit of a perfect mirror, our formulas recover those found in the literature for the particle creation by a moving mirror with a Robin boundary condition.

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