Space-fractional quantum heat engine based on level degeneracy

Ekrem Aydiner

doi:10.1038/s41598-021-97304-5

Abstract

In order to examine the work and efficiency of the space-fractional quantum heat engine, we consider a model of the space-fractional quantum heat engine which has a Stirling-like cycle with a single particle under infinite potential well as an example. We numerically compute the work and efficiency for various fractional exponents. We show the work and the efficiency of the engine depending on the length of the potential well and fractional exponent of the engine. Furthermore, we show that fractional exponent plays a substantial role in the operating range of the quantum heat engine. Thus, we conclude that the fractional parameter can be used as a tuning parameter to obtain positive work and efficiency for the large size of the quantum heat engine. Additionally, the numerical results and model imply that the size of the engine can be enlarged in the nano-scale by using fractional deformations. As a result, in this study, we have not only shown that fractional deformations in space play an important role on the work and efficiency of the quantum heat engines but also introduced the concept of fractional quantum heat engines to the literature.

Highlights

In order to examine the work and efficiency of the space-fractional quantum heat engine, we consider a model of the space-fractional quantum heat engine which has a Stirling-like cycle with a single particle under infinite potential well as an example
In the present study, we discuss the fractional quantum Szilard engine as an example and we show that fractional exponent plays an important role in the work and efficiency
The remain of the paper is organized as follows: Firstly, we summarize the solution of the space-fractional Schrödinger equation for a single particle under the infinite potential well

Summary

Ekrem Aydiner

In order to examine the work and efficiency of the space-fractional quantum heat engine, we consider a model of the space-fractional quantum heat engine which has a Stirling-like cycle with a single particle under infinite potential well as an example. A similar version of the quantum Szilard engine has been studied by Thomas et al.[23] for the infinite well potential based on level degeneracy They proposed a quantum heat engine that has a Stirling cycle and it produces work that only depends on quantum features. In the present study, we discuss the fractional quantum Szilard engine as an example and we show that fractional exponent plays an important role in the work and efficiency. In this study, we consider a quantum engine which has Stirling-like cycles and we discuss the work and efficiency based on the space-fractional Schrödinger equation for a single particle under the infinite well potential. To proceed discussion, we consider a one-dimensional space-fractional Schrödinger equation for a single particle in a box of length 2a under the infinite well potential. The energy eigenvalue for the particle in box A and D is given by Scientific Reports | (2021) 11:17901 |

AB B

The work for the Striling like cycle can be obtained from

Conclusion

Additional information