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We analyse the stationary current of Bose particles across the Bose-Hubbardchain connected to a battery, focusing on the effect of inter-particleinteractions. It is shown that the current magnitude drastically decreases asthe strength of inter-particle interactions exceeds the critical value whichmarks the transition to quantum chaos in the Bose-Hubbard Hamiltonian. We foundthat this transition is well reflected in the non-equilibrium many-body densitymatrix of the system. Namely, the level-spacing distribution for eigenvalues ofthe density matrix changes from Poisson to Wigner-Dyson distributions. With thefurther increase of the interaction strength, the Wigner-Dyson spectrumstatistics changes back to the Poisson statistics which now marksfermionization of the bosonic particles. With respect to the stationarycurrent, this leads to the counter-intuitive dependence of the currentmagnitude on the particle number.

Signatures of Quantum Chaos and fermionization in the incoherent transport of bosonic carriers in the Bose-Hubbard chain