We analyse the stationary current of Bose particles across the Bose-Hubbard
chain connected to a battery, focusing on the effect of inter-particle
interactions. It is shown that the current magnitude drastically decreases as
the strength of inter-particle interactions exceeds the critical value which
marks the transition to quantum chaos in the Bose-Hubbard Hamiltonian. We found
that this transition is well reflected in the non-equilibrium many-body density
matrix of the system. Namely, the level-spacing distribution for eigenvalues of
the density matrix changes from Poisson to Wigner-Dyson distributions. With the
further increase of the interaction strength, the Wigner-Dyson spectrum
statistics changes back to the Poisson statistics which now marks
fermionization of the bosonic particles. With respect to the stationary
current, this leads to the counter-intuitive dependence of the current
magnitude on the particle number.Comment: 5 pages, 5 figure