Abstract
Brownian motors are out of equilibrium nano-scale devices that can convert chemical energy to mechanical work. Due to their scale, they are subject to random collisions with water molecules producing behaviour that substantially differs from macroscopic motors. Many Brownian motors have discrete chemical and mechanical degrees of freedom, which enables them to be described by a discrete master equation.
There is growing interest in studying many interacting Brownian motors as motors often work in crowded environments. Very recently, a general many-body master equation for interacting Brownian motors has been formulated using creation and annihilation operators for identical classical particles.
The many-body master equation is formally similar to the quantum Bose- Hubbard model. By exploiting this similarity, we adapt well-known quantum methods, such as the Bogoliubov and Gutzwiller approximations, to this interacting Brownian system.
Using an adapted Bogoliubov approximation, we diagonalise the master equation for weakly interacting Brownian motors and find simple analytical expressions for the steady-state drift and on-site number fluctuations (two key measurable quantities). Using an adapted Gutzwiller approximation, we explore the entire interaction range from non-interacting to strongly repulsive motors. This transition is not captured in existing models for interacting Brownian motors and has not been explored previously.