  We investigate the transport properties of an anharmonic oscillator, modeled
by a single-site Bose-Hubbard model, coupled to two different thermal baths
using the numerically exact thermofield based chain-mapping matrix product
states (TCMPS) approach. We compare the effectiveness of TCMPS to probe the
nonequilibrium dynamics of strongly interacting system irrespective of the
system-bath coupling against the global master equation approach in
Gorini-Kossakowski-Sudarshan-Lindblad form. We discuss the effect of on-site
interactions, temperature bias as well as the system-bath couplings on the
steady state transport properties. Last we also show evidence of non-Markovian
dynamics by studying the non-monotonicity of the time evolution of the trace
distance between two different initial states.
