Energy transport between critical one-dimensional systems with different central charges

Energy transport can reveal information about interacting many-body systems beyond other transport probes. In particular, in one dimension it has been shown that the energy current is directly proportional to the central charge, thus revealing information about the degrees of freedom of critical systems. In this paper, we explicitly verify this result in two cases for translationally invariant systems based on explicit microscopic calculations. More importantly, we generalize the result to nontranslation invariant setups and use this to study a composite system of two subsystems possessing different central charges. We find a bottleneck effect, meaning the smaller central charge limits the energy transport.