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Based on the Landauer-B\"{u}ttiker theory, we explore the thermal regimes oftwo-terminal nanoscale systems with an energy-peaked transmission function. Thedevice is in contact with two reservoirs held at different temperatures andchemical potentials. We identify the operation regions where the system acts asenergy pump (thermal machine) or heat pump (refrigerator machine), or where itis working in dissipative modes. The corresponding thermoelectric parametersare obtained without numerical calculations. The recent literature, by focusingon systems with box-like or step-like shapes of the transmission functions,demonstrated that bounds of quantum origin exist for output power and heatcurrents of thermal machines and refrigerators. The simple model we adopt inthis paper allows us to grasp easily and without numerical calculations thepresence of quantum bounds for the above thermoelectric quantities, as functionof the position of the transmission peak with respect to the chemicalpotentials of the left and right reservoirs. In spite of the simple model andtreatment, our results are in qualitative agreement with analytic findings inprevious researches obtained with more realistic description of the electronictransmission function.

Regimes and quantum bounds of nanoscale thermoelectrics with peaked transmission function