Mean first-passage time of an anisotropic diffusive searcher

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We consider an anisotropic needle-like Brownian particle with nematic symmetry confined in a 2D domain. For this system, the coupling of translational and rotational diffusion makes the process of the positions of the particle non Markovian. Using scaling arguments, a Gaussian approximation and numerical methods, we determine the mean first passage time of the particle to a target of radius a and show in particular that for , in contrast with the classical logarithmic divergence obtained in the case of an isotropic 2D Brownian particle.