Mean first-passage time of an anisotropic diffusive searcher

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 $x\left(t\right)$ of the positions of the particle non Markovian. Using scaling arguments, a Gaussian approximation and numerical methods, we determine the mean first passage time $⟨T⟩$ of the particle to a target of radius a and show in particular that $⟨T⟩\sim a^{-1/2}$ for $a\to 0$, in contrast with the classical logarithmic divergence obtained in the case of an isotropic 2D Brownian particle. (paper)