Optimized Efficiency of a stochastically driven quantum dot Heat Engine*

We take a stochastically driven single level quantum dot embedded between two metallic leads at
different temperatures which works as a heat engine. We analytically study the optimized efficiency
that lies between the maximum efficiency and minimum efficiencies. The minimum efficiency
either takes the efficiency value at maximum power or the lowest possible value which is zero.
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, is 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 takes into account 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 1 st optimization criteria
is 3 times better than the 2nd optimization criteria as a function of ηC