Quantum tunneling and anti-tunneling across entropic barriers.

We study the dynamics of a quantum particle in a constricted two-dimensional channel and analyze how the onset of quantum corrections impacts the (semi-)classical high-temperature behavior as temperature is lowered. We characterize both equilibrium and non-equilibrium (transport) properties of the system, considering the case of a narrow and disorder-free channel. Counterintuitively, we find that quantum corrections do not monotonically enhance the particle current as the temperature is lowered, as naively expected from the activation of coherent tunneling, but they rather inhibit transport at intermediate temperatures, increasing the effective free-energy barrier. We illustrate this "anti-tunneling" effect numerically by computing the non-equilibrium steady-state of a quantum master equation describing the system and confirm it analytically by adopting the quantum Smoluchowski limit.