Search for: All records

Abstract Diffusion in heterogeneous energy and diffusivity landscapes is widespread in biological systems. However, solving the Langevin equation in such environments introduces ambiguity due to the interpretation parameter $$\alpha$$, which depends on the underlying physics and can take values in the range $$0<\alpha<1$$. The typical interpretations are It\^o ($$\alpha=0$$), Stratonovich ($$\alpha=1/2$$), and Hanggi-Klimontovich ($$\alpha=1$$). Here, we analyse the motion of a particle in an harmonic potential---modelled as an Ornstein-Uhlenbeck process---with diffusivity that varies in space. Our focus is on two-phase systems with a discontinuity in environmental properties at $x=0$. We derive the probability density of the particle position for the process, and consider two paradigmatic situations. In the first one, the damping coefficient remains constant, and fluctuation-dissipation relations are not satisfied. In the second one, these relations are enforced, leading to a position-dependent damping coefficient. In both cases, we provide solutions as a function of the interpretation parameter $$\alpha$$, with particular attention to the It\^o, Stratonovich, and Hanggi-Klimontovich interpretations, revealing fundamentally different behaviours, in particular with respect to an interface located at the potential minimum.