Migration and separation of polymers in non-uniform active baths

Polymer-like structures are ubiquitous in nature and synthetic materials. Their configurational and migration properties are often affected by crowded environments leading to non-thermal fluctuations. Here, we study an ideal Rouse chain in contact with a non-homogeneous active bath, characterized by the presence of active self-propelled agents which exert time-correlated forces on the chain. By means of a coarse-graining procedure, we derive an effective evolution for the center of mass of the chain and show its tendency to migrate towards and preferentially localize in regions of high/low bath activity depending on the model parameters. In particular, we demonstrate that an active bath with non-uniform activity can be used to separate efficiently polymeric species with different lengths and/or connectivity.