AI 中文总结
受科贝诺盘磁输运实验启发，通过数值分析电子流，预测小磁场下奇偶效应使电阻灵敏度增强，此增强在特定转变处最显著，温度升高时消失，还扩展特征线方法处理奇谐波，为相关研究提供新视角。
AI 中文摘要
在二维中，由于泡利阻塞和守恒定律产生的几何约束导致电子 - 电子散射长度呈现奇偶效应：电子 - 电子碰撞在弛豫分布函数的偶角谐波方面比奇角谐波更有效。受近期科贝诺盘几何中磁输运实验启发，我们对该几何中所有流态的电子流进行数值分析。预测出奇偶效应的明显特征——在小磁场\(B\rightarrow 0\)时电阻灵敏度\(\partial R/\partial(B^2)\)增强。此增强在从弹道到层析流态的转变处最显著，温度进一步升高时逐渐消失。我们的估计表明在实验温度范围内该效应较小。这意味着将实验中观测到的运动粘度异常标度归因于奇偶效应可能需更谨慎考虑。另外，我们展示了如何扩展特征线方法来处理长寿命奇谐波，从而将线性化玻尔兹曼方程重铸为积分方程系统。
英文摘要
In two dimensions, the geometric constraints due to Pauli blocking and conservation laws lead to the even-odd effect exhibited by the electron-electron scattering lengths: electron-electron collisions are more efficient at relaxing the even angular harmonics of the distribution function than the odd ones. Inspired by a recent experiment on the magnetotransport in the Corbino disk geometry, we numerically analyze the electron flows in this geometry across all the regimes. We predict a clear signature of the even-odd effect - enhancement of the resistance sensitivity $\partial R/\partial(B^2)$ at small magnetic fields $B\rightarrow 0$. This enhancement is most prominent at the crossover from the ballistic to the tomographic regime, and gradually disappears when the temperature is further increased. Our estimates suggest that in the temperature range of the experiment, the effect should be small. This implies that the attribution of the anomalous scaling of the kinematic viscosity, that was observed in the experiment, to the even-odd effect might need more careful consideration. As a side note, we show how the method of characteristics can be extended to treat the long-lived odd harmonics, which allows one to recast the linearized Boltzmann equation as a system of integral ones.
