We consider one dimensional potential trap that connects two reservoirs containing cold Bose atoms. The thermal current and single-particle bosonic Green functions are calculated under non-equilibrium conditions. The bosonic statistics leads to Lutti
nger liquid state with non-linear spectrum of collective modes. This results in suppression of thermal current at low temperatures and affects the single-particle Green functions.
An interplay between the increase in the number of carriers and the decrease in the scattering time is expected to result in a saturation of the in-plane resistivity, $rho_{ab}$, in graphite above room temperature. Contrary to this expectation, we ob
serve a pronounced increase in $rho_{ab}$ in the interval between 300 and 900 K. We provide a theory of this effect based on intervalley scattering of charge carriers by high-frequency, graphene-like optical phonons.
