Multilevel quantum Otto heat engines with identical particles

A quantum Otto heat engine is studied with multilevel identical particles trapped in one-dimensional box potential as working substance. The symmetrical wave function for Bosons and the anti-symmetrical wave function for Fermions are considered. In two-particle case, we focus on the ratios of $$W^i$$Wi ($$i=B,F$$i=B,F) to $$W_s$$Ws, where $$W^\mathrm{B}$$WB and $$W^\mathrm{F}$$WF are the work done by two Bosons and Fermions, respectively, and $$W_s$$Ws is the work output of a single particle under the same conditions. Due to the symmetrical of the wave functions, the ratios are not equal to 2. Three different regimes, low-temperature regime, high-temperature regime, and intermediate-temperature regime, are analyzed, and the effects of energy level number and the differences between the two baths are calculated. In the multiparticle case, we calculate the ratios of $$W^i_M/M$$WMi/M to $$W_s$$Ws, where $$W^i_M/M$$WMi/M can be seen as the average work done by a single particle in multiparticle heat engine. For other working substances whose energy spectrum has the form of $$E_n\sim n^2$$En∼n2, the results are similar. For the case $$E_n\sim n$$En∼n, two different conclusions are obtained.