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We investigate the particle and heat transport in quantum junctions with the geometry of star graphs. The system is in a nonequilibrium steady state, characterized by the different temperatures and chemical potentials of the heat reservoirs connected to the edges of the graph. We explore the Landauer-Buettiker state and its orbit under parity and time reversal transformations. Both particle number and total energy are conserved in these states. However the heat and chemical potential energy are in general not separately conserved, which gives origin to a basic process of energy transmutation among them. We study both directions of this process in detail, introducing appropriate efficiency coefficients. For scale invariant interactions in the junction our results are exact and explicit. They cover the whole parameter space and take into account all nonlinear effects. The energy transmutation depends on the particle statistics.
When noninteracting fermions are confined in a $D$-dimensional region of volume $mathrm{O}(L^D)$ and subjected to a continuous (or piecewise continuous) potential $V$ which decays sufficiently fast with distance, in the thermodynamic limit, the groun
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We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion paper (J.