Moving mirrors and the fluctuation-dissipation theorem

Understand

We investigate the random motion of a mirror in (1 + 1)-dimensions that is immersed in a thermal bath of massless scalar particles which are interacting with the mirror through a boundary condition.

• Imposing the Dirichlet or the Neumann boundary conditions on the moving mirror, we evaluate the mean radiation reaction force on the mirror and the correlation function describing the fluctuations in the force about the mean value.
• From the correlation function thus obtained, we explicitly establish the fluctuation-dissipation theorem governing the moving mirror.
• Using the fluctuation-dissipation theorem, we compute the mean-squared displacement of the mirror at finite and zero temperature.