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External torques affect the trajectories of swimming microorganisms. We calculate analytically the effective three-dimensional diffusivity of a spherical active particle subject to both a constant external torque and thermal noise. We find that the presence of a torque renders the effective diffusive behavior anisotropic. The analytical results are compared with Brownian dynamics simulations and we obtain excellent agreement. For steady swimmers an external torque always decreases the effective swimmer diffusivity whereas it may be enhanced for time-reversible swimmers.
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