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.

Graphic abstract

中文翻译：

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量子伊辛热机：平均现场研究

摘要

我们研究了经典热机和量子热机的效率，使用伊辛模型作为工作流体以及早期制定的非平衡动力学平均场方程（Acharyya 等人，J Phys A Math Gen 27:1533, 1994；Acharyya和 Chakrabarti Phys Rev B 52:6550, 1995）研究量子伊辛铁​​磁体中的动态磁滞和动态相变。我们对四冲程热机的伊辛磁体不可积耦合非线性一阶运动微分方程进行了数值研究，并使用准静态近似比较了经典极限和量子极限的效率。在纯经典和纯量子情况下，数值计算的效率远低于相应的卡诺值。我们发现效率的分析公式（无论是纯经典热机还是纯量子伊辛热机）与数值估计非常吻合。这种公式还表明，在存在非零纵向场的情况下，横向场驱动伊辛发动机的混合情况的效率有所提高。我们还进行了数值检查，发现这种（混合）量子伊辛热机的效率在横向和纵向场的适当值下确实可以具有更高的效率。

图文摘要