Theory and simulations show harmonic Langevin PSDs approximate Paul trap x/y motion well only for small Mathieu q, with deviations exceeding factor of two at larger q, and permanent dipoles significantly alter those PSDs.
This will introduce an additional force on the nano-particle which has the form − ⃗∇ (−⃗ p·⃗E) with ⃗E(x,y,z ) = − ⃗∇ V (x,y,z ) the electric field at the nanoparticle
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Simulations and theory of power spectral density functions for time dependent and anharmonic Langevin oscillators
Theory and simulations show harmonic Langevin PSDs approximate Paul trap x/y motion well only for small Mathieu q, with deviations exceeding factor of two at larger q, and permanent dipoles significantly alter those PSDs.