AI 中文总结
该研究从黑洞矩阵量子力学发展微观量子膜范式，由模糊球拓扑诱导贝里单极子，部分子形成LLL态产生相关电流，通过特定矩阵配置耦合电流与外场，给出量子修正，为探测视界微观量子结构提供可能。
AI 中文摘要
我们从黑洞的矩阵量子力学出发发展了一种微观量子膜范式。有人提出量子黑洞由模糊球以及视界部分子的半充满费米海描述。我们表明模糊球的拓扑诱导出贝里单极子，为量子黑洞衰变隧穿描述中出现的单极子提供微观起源。部分子作为基本自由度与模糊球耦合，形成最低朗道能级（LLL）态而非普通传播的二维费米子，其导向中心动力学在视界上产生欧姆、霍尔和极化电流。为将这些电流与外部电磁场耦合，引入包含黑洞、环境和双基本链接扇区的两块矩阵配置。非对角链接模式在模糊球附近变为快子并凝聚，将视界规范场动态锁定到外部麦克斯韦场的边界值。部分子电流因此成为外部场的物理边界源。我们的构建用由微观LLL自由度构成的动态量子膜取代了经典范式中的虚拟膜。所得边界条件推广了经典的内向膜条件，产生明确的量子、频率依赖和螺旋度依赖的修正，为探测视界的微观量子结构提供了可能。
英文摘要
We develop a microscopic quantum membrane paradigm from the matrix quantum mechanics of black holes [1]. It was proposed that a quantum black hole is described by a fuzzy sphere together with a half-filled Fermi sea of horizon partons. We show that the topology of the fuzzy sphere induces a Berry monopole, providing a microscopic origin for the monopole appearing in the tunneling description of the decay of quantum black hole. Because the partons couple to the fuzzy sphere as fundamental degrees of freedom, they are sensitive to this monopole and form Lowest-Landau-Level (LLL) states rather than ordinary propagating two-dimensional fermions. Their guiding-center dynamics generates Ohmic, Hall, and polarization currents on the horizon. To couple these currents to an external electromagnetic field, we introduce a two-block matrix configuration comprising black-hole, environmental, and bifundamental link sectors. Off-diagonal link modes become tachyonic near the fuzzy sphere and condense, dynamically locking the horizon gauge field to the boundary value of the external Maxwell field. The parton current thereby becomes a physical boundary source for the exterior field. Our construction replaces the fictitious membrane of the classical paradigm with a dynamical quantum membrane populated by microscopic LLL degrees of freedom. The resulting boundary condition generalizes the classical ingoing membrane condition and yields explicit quantum, frequency-dependent, and helicity-dependent corrections, offering a possible probe of the microscopic quantum structure of the horizon.
Commentsv2: 53 pages. 4 appendices. add comments on black hole S-matrix. typos corrected
