An Optimized Quantum Heat Engine With Singular Interactions

Abstract

A quantum Otto engine is investigated for adiabatic operation at both high and low temperature limits, using a single interaction harmonic oscillator as its working material. Analytical calcula tions are used to determine the heat engine’s power and efficiency as functions of the oscillator frequencies. The heat engine is efficiently adjusted and found to produce superior operating con ditions in various ranges of frequency and temperature ratios by using the optimization techniques proposed, by A.C. Hernandex et al. The figure of merit, which is the product of scaled power and scaled efficiency, ψ, was found to be greater than one in the range 0.05 < βτ βc ≤ 0.22 at the high temperature limit. In the range 0.22 < βτ βc ≤ 0.35,ψ was shown to be less than one with the identi cal temperature limit. In a similar way at the low temperature limit, the range 0.75 < ωc ωτ ≤ 8 was shown to have a figure of merit, ψ, greater than one. In the range 0 ≤ ωc ωτ ≤ 0.75, ψ was shown to be less than one with the identical temperature limit. It suggests that it performs better at maximum conditions in certain regions and at optimal conditions in others, depending on the ratio range. A figure of merit greater than one indicates that the engine is using the available heat input to do work at a higher efficiency level. Whenever an engine has a figure of merit less than one, this indicates that it can produce more work output with the same amount of heat input. In order to convert heat energy into useful work, engines are considered to be more efficient and effective if their figure of merit is greater than one.