Optimized Efficiency at Two Optimum Operations of a Stochastically Driven Quantum Dot Heat Engine

Abstract

We take a stochastically driven single-level quantum dot embedded between two metallic leads at different temperatures works as a heat engine. We numerically study the optimized efficiency at two optimum operations, which lies between the maximum and minimum efficiency. The minimum efficiency either takes the efficiency value at maximum power or the lowest possible value, zero. Using a unified criterion for energy converters, we find the optimum working condition for the heat engine. We study the optimized efficiency of a quantum dot heat engine according to the optimization criteria to find their corresponding optimized quantities in an external magnetic field (stochastic driving force). Accordingly, we found (1) efficiency-wise, optimized efficiency is better than efficiency at maximum power; (2) power-wise, the optimized power is smaller than its value at maximum power by $35\%$ ; and (3) period-wise, it performs the task in a cycle twice that of the period at maximum power. We study the overall performance of the heat engine by introducing a figure of merit that considers the contribution of each of the above quantities as a function of Carnot efficiency. Based on the proposed figure of merit, the model shows that the second optimization criteria are 3 times better than the first optimization criteria as a function of Carnot efficiency.