We consider the effective theory of perturbative quantum gravity coupled to a point particle, quantizing fluctuations of both the gravitational field and the particle’s position around flat space. Using a recent relational approach to construct gauge-invariant observables, we compute one-loop graviton corrections to the invariant metric perturbation, whose time-time component gives the Newtonian gravitational potential. The resulting quantum correction consists of two parts: the first stems from graviton loops and agrees with the correction derived by other methods, while the second one is sourced by the quantum fluctuations of the particle’s position and energy-momentum, and may be viewed as an analog of a “Zitterbewegung”. As a check on the computation, we also recover classical corrections which agree with the perturbative expansion of the Schwarzschild metric.

Autonomous active Brownian ratchets rectify active Brownian particle motion solely by means of a spatially modulated but stationary activity, without external forces. We argue that such ratcheting requires at least a two-dimensional geometry. The underlying principle is similar to the ratcheting induced by steric obstacles in microswimmer baths: suitably polarized swimmers get channeled, while the others get trapped in low-activity regions until they loose direction. The maximum current is generally reached in the limit of large propulsion speeds, in which the rectification efficiency vanishes. Maximum efficiency is attained at intermediate activities and numerically found to be on the order of a few percent, for ratchets with simple wedge-shaped low-activity regions.