Singapore-MIT Alliance for Research and Technology (SMART) Center, 1 CREATE Way, Singapore 138602, Singapore.
State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China.
J Chem Phys. 2018 Jun 21;148(23):234104. doi: 10.1063/1.5025367.
To investigate frequency-dependent current noise (FDCN) in open quantum systems at steady states, we present a theory which combines Markovian quantum master equations with a finite time full counting statistics. Our formulation of the FDCN generalizes previous zero-frequency expressions and can be viewed as an application of MacDonald's formula for electron transport to heat transfer. As a demonstration, we consider the paradigmatic example of quantum heat transfer in the context of a non-equilibrium spin-boson model. We adopt a recently developed polaron-transformed Redfield equation which allows us to accurately investigate heat transfer with arbitrary system-reservoir coupling strength, arbitrary values of spin bias, and temperature differences. We observe a turn-over of FDCN in the intermediate coupling regimes, similar to the zero-frequency case. We find that the FDCN with varying coupling strengths or bias displays a universal Lorentzian-shape scaling form in the weak coupling regime, and a white noise spectrum emerges with zero bias in the strong coupling regime due to distinctive spin dynamics. We also find that the bias can suppress the FDCN in the strong coupling regime, in contrast to its zero-frequency counterpart which is insensitive to bias changes. Furthermore, we utilize the Saito-Utsumi relation as a benchmark to validate our theory and study the impact of temperature differences at finite frequencies. Together, our results provide detailed dissections of the finite time fluctuation of heat current in open quantum systems.
为了研究稳态开放量子系统中依赖于频率的电流噪声（FDCN），我们提出了一种将马尔可夫量子主方程与有限时间全计数统计相结合的理论。我们的 FDCN 公式推广了以前的零频表达式，可以看作是 MacDonald 公式在热传递中对电子输运的应用。作为一个演示，我们考虑了非平衡自旋-玻色子模型中量子热传递的范例。我们采用了最近发展的极化子变换 Redfield 方程，该方程允许我们以任意的系统-储库耦合强度、任意的自旋偏置和温度差来准确地研究热传递。我们观察到在中间耦合区域 FDCN 的翻转，类似于零频情况。我们发现，在弱耦合区域，随着耦合强度或偏置的变化，FDCN 呈现出普遍的洛伦兹形状标度形式，而在强耦合区域由于独特的自旋动力学，出现了白噪声谱。我们还发现，偏置可以抑制强耦合区域的 FDCN，与对零频情况的无偏置状态相反，零频情况对偏置变化不敏感。此外，我们利用 Saito-Utsumi 关系作为基准来验证我们的理论，并研究有限频率下温度差的影响。总之，我们的结果提供了对开放量子系统中热流有限时间涨落的详细分析。
