AI 中文总结
该研究通过推导惯性朗之万系统的相空间协方差界，结合有限温度规范理论，表明热对齐可决定可计算的后期轴子暗物质态，而非仅均匀位移。
AI 中文摘要
仅从轴子平均值无法推断热对齐，因为消除初始位移的耗散浴也会制备场和动量涨落。我们推导了相空间协方差界，该界在完整惯性朗之万系统中量化了这种记忆与噪声的关系。随后，一个可重整化的有限温度规范理论通过一个标量转变，将瞬时 susceptibility（磁化率）、陈-西蒙斯浴、浴终止以及稳定的后期势关联起来。求解耦合的平均值与协方差演化表明，入射态被消除，产生因果红外谱，并在转变区间内将完整的相空间分布捕获为轴子暗物质。因此，热对齐决定了可计算的后期轴子态，而非仅均匀位移。
英文摘要
Thermal alignment cannot be inferred from the axion mean alone because the dissipative bath that erases the initial displacement also prepares field and momentum fluctuations. We derive a phase space covariance bound that quantifies this memory and noise relation in the full inertial Langevin system. A renormalizable finite temperature gauge theory then links the temporary susceptibility, the Chern-Simons bath, bath termination, and the stable late potential through one scalar transition. Solving the coupled mean and covariance evolution demonstrates erasure of the incoming state, release of a causal infrared spectrum, and capture of the full phase space distribution as axion dark matter across the transition interval. Thermal alignment therefore determines a calculable late axion state rather than a homogeneous displacement alone.
Comments10 pages, 6 figures
