相互作用常数为 $K = 1/2$ 的含杂质 Tomonaga-Lüttinger 液体：热电粒子输运相关的热电势研究、熵变和热容密度
Interacting Tomonaga-Lüttinger liquid with impurity for interaction constant $K = 1/2$: Thermopower investigation, entropy variation and heat capacity densities associated with thermoelectric particle transport
- University of Bouira（布依拉大学）
- Higher Normal School of Bouzareah, University of Bouira（布扎雷亚高等师范学院，布依拉大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对含杂质的 Tomonaga-Lüttinger 液体（$K=1/2$），利用玻色化和再费米化精确推导热电势，揭示低温下类 Mott 行为，并建立与熵和热容密度的联系，应用于分数量子霍尔点接触等系统。
AI中文摘要：
我们研究了在存在局域杂质的情况下，相互作用参数为 $K=1/2$ 的 Tomonaga-Lüttinger 液体的热电和热力学性质。利用玻色化和再费米化方法，我们推导出非线性区热电势的精确表达式，并在线性响应下得到相应的塞贝克系数。在低温下，塞贝克系数遵循由透射系数的能量依赖性决定的类 Mott 关系，并发现其与每个粒子的熵密切相关。这一联系使我们能够利用开尔文公式推导出热电势对熵密度变化的贡献以及载流子对热容密度的贡献。这两个量在低温区域均表现出类 Mott 行为。我们将结果应用于分数量子霍尔量子点接触以及耦合到欧姆环境的一通道量子导体。我们的结果证明了相互作用的一维量子系统中热电输运与热力学性质之间的密切联系。
英文摘要：
We investigate thermoelectric and thermodynamic properties of a Tomonaga-Luttinger liquid with interaction parameter $K=1/2$ in the presence of a localized impurity. Using bosonization and refermionization, we derive an exact expression for the thermopower in the nonlinear regime and obtain the corresponding Seebeck coefficient in linear response. At low temperature, the Seebeck coefficient follows a Mott-like relation governed by the energy dependence of the transmission coefficient and is found to be closely related to the entropy per particle. This connection allows us to derive using Kelvin formula the thermopower contribution to the entropy density variation and the charge-carriers contribution to the heat capacity density. Both quantities exhibit Mott-like behavior in the low-temperature regime. We apply our results to a fractional quantum Hall quantum point contact and to a one-channel quantum conductor coupled to an Ohmic environment. Our results demonstrate the close connection between thermoelectric transport and thermodynamic properties in interacting one-dimensional quantum systems.
