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Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases
Physical Review A ( IF 2.9 ) Pub Date : 
Y. Y. Atas, A. Safavi-Naini, K. V. Kheruntsyan

We develop a general approach for calculating the characteristic function of the work distribution of we use the determinant representation of the many-body wave function to characterise the nonequilibrium thermodynamics of the TG gas and obtain exact and computationally tractable expressions—in terms of Fredholm determinants—for the mean work, the work probability distribution function, the nonadiabaticity parameter, and the Loschmidt amplitude. When applied to a harmonically trapped TG gas, our results for the mean work and the nonadiabaticity parameter reduce to those derived previously using an alternative approach. We next propose to use periodic modulation of the trap frequency in order to drive the system to highly non-equilibrium states by taking advantage of the phenomenon of parametric resonance. Under such driving protocol, the nonadiabaticity parameter may reach large values, which indicates a large amount of irreversible work being done on the system as compared to sudden quench protocols considered previously. This scenario is realizable in ultracold atom experiments, aiding fundamental understanding of all thermodynamic properties of the system.

中文翻译:

行列式多体系统的非平衡量子热力学:在唐克斯-吉拉多和理想费米气体中的应用

我们开发了一种通用的方法来计算功分布的特征函数,我们使用多体波函数的行列式表示来表征TG气体的非平衡热力学,并根据Fredholm行列式获得精确且易于计算的表达式。对于平均功,工作概率分布函数,非绝热参数和Loschmidt振幅。当应用于谐波捕集的TG气体时,我们的平均功和非绝热参数的结果将减少到以前使用替代方法得出的结果。接下来,我们建议使用陷波频率的周期性调制,以便通过利用参数谐振现象将系统驱动到高度非平衡状态。在这样的驾驶协议下 非绝热参数可能达到较大的值,这表明与先前考虑的突然猝灭协议相比,系统上进行了大量不可逆的工作。在超冷原子实验中可以实现这种情况,有助于对系统的所有热力学性质有基本的了解。
更新日期:2020-09-16
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