V. DISCUSSION We propose a continuous-space model of interacting Brownian particles in a pe- riodic potential as a possible realization of the TASEP. The particles are subject to a constant drive in a periodic external potential. Using numerical integration of the Langevin equation and Monte Carlo simulation, we study systems of L = 100, 200, and 500 wells. Our results show that the continuous-space model exhibits continuous and discontinuous phase transitions analogous to those observed in the lattice TASEP. The phase diagram of the continuous-space model is similar to that of the lattice model, but exhibits some differences due to the absence of particle- hole symmetry. This difference appears to be associated with fluctuations of particle positions around potential minima. Such fluctuations, together with the repulsive interactions between neighboring particles, cause the current to attain its maximum value at a density somewhat greater than 1/2, the density marking the maximum current in the lattice model. We expect these changes (relative to the lattice model) to be generic for continuous-space systems exhibiting TASEP-like phase transitions. We believe that the present study demonstrates the possibility of observing TASEP-like behavior in laboratory experiments on systems of interacting colloidal particles in a one-dimensional optical tweezer array. The essential features of the TASEP - localization of particles in potential wells, with multiple occupancy prohib- ited, and bias hopping along the line - are readily accomplished with a appropriate choice of particle, fluid, and tweezer array parameters. It is however less obvious how to implement random insertion and removal of particles at the first and last wells of the array. Particle manipulation can be accomplished using optical tweezers to transfer particles between wells and reservoirs. To transfer particles in a random fashion, these tweezers would have to be intrinsically noisy or chaotic, controlled by a random number generator, or driven by a noise signal. A simpler alternative may 23