全息探针膜金属中慢电流的非线性极点拓扑
Nonlinear pole topology of slow currents in holographic probe-brane metals
- General Education College, Shanxi Institute of Science and Technology（山西科学技术学院通识教育学院）
- College of Physics and Optoelectronic Engineering, Taiyuan University of Technology（太原理工大学物理与光电工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过极点拓扑分类全息探针膜金属中慢电流的非线性响应，揭示拓扑由动力学选择而非DBI结构强加，并给出稠密极限标度函数与交叉场。
AI中文摘要：
低频德鲁德响应本身并不能确定哪个近守恒扇区承载电流。我们通过极点拓扑对孤立、反演对称的慢矢量的领先三次延迟响应进行分类。本构非线性仅产生入射频率极点，而非线性弛豫在发射频率处增加传播子；与第二个标量慢模式耦合会产生成对频率极点。然后，我们计算了Lifshitz黑膜背景中有限密度Dirac–Born–Infeld探针膜的全复三次谐波响应。在边缘$z=2$理论中，稠密红外响应接近弛豫拓扑，具有带符号的红外权重$p_{\rm IR}=0.994\pm0.002$和归一化无关的零点$\omega_\times/\Gamma_J=0.2918$。非边缘$z=1$和$z=3/2$背景反而实现混合本征–弛豫权重，表明拓扑是动态选择的，而非由DBI平方根强加。精确的非线性直流解进一步提供了无参数的稠密极限标度函数和$z=2$处的交叉场$E_{\rm nl}\propto T^{3/2}$。这些结果将涌现的高阶慢电流、非线性响应理论和全息输运联系起来，而双模式扩展识别了当能量或形变模式保持缓慢时预期的额外极点结构。
英文摘要：
Low-frequency Drude response does not by itself determine which nearly conserved sector carries an electric current. We classify the leading cubic retarded response of an isolated, inversion-symmetric slow vector by its pole topology. Constitutive nonlinearity produces only incoming-frequency poles, whereas nonlinear relaxation adds a propagator at the emitted frequency; coupling to a second scalar slow mode generates pair-frequency poles. We then compute the full complex third-harmonic response of finite-density Dirac--Born--Infeld probe branes in Lifshitz black-brane backgrounds. In the marginal $z=2$ theory, the dense infrared response approaches the relaxation topology, with a signed infrared weight $p_{\rm IR}=0.994\pm0.002$ and a normalization-independent zero at $ω_\times/Γ_J=0.2918$. Nonmarginal $z=1$ and $z=3/2$ backgrounds instead realize mixed constitutive--relaxation weights, demonstrating that the topology is selected dynamically rather than imposed by the DBI square root. The exact nonlinear dc solution further yields a parameter-free dense-limit scaling function and a crossover field $E_{\rm nl}\propto T^{3/2}$ at $z=2$. These results connect emergent higher-form slow currents, nonlinear response theory, and holographic transport, while the two-mode extension identifies the additional pole structures expected when energy or deformation modes remain slow.
