Abstract Scattering theory is a standard tool for the description of transport phenomena in mesoscopic systems. Here, we provide a detailed derivation of this method for nano-scale conductors that are driven by oscillating electric or magnetic fields. Our approach is based on an extension of the conventional Lippmann–Schwinger formalism to systems with a periodically time-dependent Hamiltonian. As a key result, we obtain a systematic perturbation scheme for the Floquet scattering amplitudes that describes the transition of a transport carrier through a periodically driven sample. Within a general multi-terminal setup, we derive microscopic expressions for the mean values and time-integrated correlation functions, or zero-frequency noise, of matter and energy currents, thus recovering the results of earlier studies in a unifying framework. We show that this framework is inherently consistent with the first and the second law of thermodynamics and prove that the mean rate of entropy production vanishes only if all currents in the system are zero. As an application, we derive a generalized Green–Kubo relation, which makes it possible to express the response of any mean currents to small variations of temperature and chemical potential gradients in terms of time integrated correlation functions between properly chosen currents. Finally, we discuss potential topics for future studies and further reaching applications of the Floquet scattering approach to quantum transport in stochastic and quantum thermodynamics.

中文翻译：

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周期性驱动介观导体中的相干输运：从散射振幅到量子热力学

摘要 散射理论是描述细观系统中输运现象的标准工具。在这里，我们提供了这种方法的详细推导，用于由振荡电场或磁场驱动的纳米级导体。我们的方法基于将传统的 Lippmann-Schwinger 形式主义扩展到具有周期性时间相关哈密顿量的系统。作为一个关键结果，我们获得了 Floquet 散射幅度的系统扰动方案，该方案描述了传输载体通过周期性驱动样本的转变。在一般的多终端设置中，我们推导出物质和能量流的平均值和时间积分相关函数或零频率噪声的微观表达式，从而在统一框架中恢复早期研究的结果。我们表明该框架本质上与热力学第一和第二定律一致，并证明只有当系统中的所有电流为零时，熵产生的平均速率才会消失。As an application, we derive a generalized Green–Kubo relation, which makes it possible to express the response of any mean currents to small variations of temperature and chemical potential gradients in terms of time integrated correlation functions between properly chosen currents. 最后，我们讨论了未来研究的潜在主题，并进一步应用 Floquet 散射方法在随机和量子热力学中的量子传输中的应用。