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Quantum Ising heat engines: a mean field study

  • Topical Review - Statistical and Nonlinear Physics
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Abstract

We have studied the efficiencies of both classical and quantum heat engines using an Ising model as working fluid and the mean field equation for its non-equilibrium dynamics, formulated earlier (Acharyya et al. J Phys A Math Gen 27:1533, 1994; Acharyya and Chakrabarti Phys Rev B 52:6550, 1995) to study the dynamical hysteresis and the dynamical phase transitions in the quantum Ising ferromagnets. We studied numerically the Ising magnet’s nonintegrable coupled nonlinear first order differential equations of motion for a four stroke heat engine and compared the efficiencies in both classical and quantum limits using the quasi-static approximation. In both the pure classical and pure quantum cases, the numerically calculated efficiencies are much less than the corresponding Carnot values. Our analytical formulations of the efficiencies (both in pure classical as well as in pure quantum Ising heat engines) are found to agree well with the numerical estimates. Such formulations also indicate increased efficiency for the mixed case of a transverse field driven Ising engine in presence of nonzero longitudinal field. We also numerically checked and found that the efficiency of such a (mixed) quantum Ising heat engine can indeed have much higher efficiency for appropriate values of the transverse and longitudinal fields.

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Data availability statement

The data may be available on request to the corresponding author.

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Acknowledgements

Amit Dutta wanted us to explore the application of quantum mean field equation we had studied earlier in the context of dynamic hysteresis in quantum Ising systems to quantum Ising heat engines. He promised to teach us about the development and literature on quantum heat engines. We missed that opportunity because of his very sudden and untimely demise. We are thankful to Heiko Rieger and Eduardo Hernandez, former and present Editor-in-Chief of European Physical Journal B (EPJB), for taking the initiative of this Topical Issue on “Quantum phase transitions and open quantum systems: A tribute to Prof. Amit Dutta”, in memory of their one long time Editor. We would like to thank the Guest Editors of this Special Issue of EPJB, Uma Divakaran, Ferenc Iglói, Victor Mukherjee and Krishnendu Sengupta for kind invitation to contribute in it. We are extremely thankful to Victor Mukherjee for a careful reading of the paper and giving important suggestions. We are indebted to an anonymous referee for suggesting an extended study of the quantum Ising engine under external field. MA is grateful to the Presidency University for the FRPDF grant and BKC is grateful to the Indian National Science Academy for their Senior Scientist Research Grant.

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Authors and Affiliations

  1. Department of Physics, Presidency University, Kolkata, 700073, India

    Muktish Acharyya

  2. Saha Institute of Nuclear Physics, Kolkata, 700064, India

    Bikas K. Chakrabarti

Authors
  1. Muktish Acharyya
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  2. Bikas K. Chakrabarti
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Contributions

Bikas K. Chakrabarti conceptualized the problem, analysed the results, developed the approximate analytic formulations, wrote the manuscript. Muktish Acharyya developed the code for numerical simulation, collected the data, prepared the figures, analysed the results, wrote the manuscript.

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Correspondence to Muktish Acharyya.

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We declare that this manuscript is free from any conflict of interest. The authors have no financial or proprietary interests in any material discussed in this article.

Additional information

Dedicated to the loving memory of Prof. Amit Dutta, Indian Institute of Technology, Kanpur.

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Acharyya, M., Chakrabarti, B.K. Quantum Ising heat engines: a mean field study. Eur. Phys. J. B 97, 45 (2024). https://doi.org/10.1140/epjb/s10051-024-00681-9

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