We analyse the time-dependence of currents in a 1D Bose gas in an optical
lattice. For a 1D system, the stability of currents induced by accelerating the
lattice exhibits a broad crossover as a function of the magnitude of the
acceleration, and the strength of the inter-particle interactions. This differs
markedly from mean-field results in higher dimensions. Using the infinite Time
Evolving Block Decimation algorithm, we characterise this crossover by making
quantitative predictions for the time-dependent behaviour of the currents and
their decay rate. We also compute the time-dependence of quasi-condensate
fractions which can be measured directly in experiments. We compare our results
to calculations based on phase-slip methods, finding agreement with the scaling
as the particle density increases, but with significant deviations near unit
filling.Comment: 19 pages, 10 figure