退相干指数：稳定相位噪声与客观态约化的约束
The Decoherence Exponent: Stable Phase Noise and Constraints on Objective State Reduction
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中文总结 AI 辅助
该研究推导退相干指数的形式，分析稳定相位噪声对客观态约化的约束，通过数值验证边界，探讨不同噪声机制下的态约化特性及双时间几何的可行性。
中文摘要 AI 辅助
设$L_u$为代表未观测相位提升的对称莱维过程，通过电荷$Q$与量子系统耦合。对$e^{iL_uQ}$取平均得到完全正的退相位半群。若特征指数缺乏本征电荷标度，莱维-辛钦定理要求$\u03b7(\u03be)=D | \u03be |^{\u03b1}$（$0<\u03b1\u22642$），因此相干性以$\u0393_{ab}=D | q_a-q_b |^{\u03b1}$衰减。对于整数电荷差，该过程降至包裹变量$\u0398_u=L_u\bmod 2\u03c0$；对于实电荷，提升为相关相位。舍恩伯格定理保证当$0<\u03b1\u22642$时任意有限实谱的完全正性，而$\u03b1>2$会产生解析障碍，该边界是精确的，此处通过数值验证。高斯积分相位给出二次电荷依赖，但有色高斯噪声不一定产生马尔可夫半群。分析了两种理想化非高斯机制：逆幂泊松散粒噪声（$\u03b1=d/p$）和布朗相位经$\u03b1/2$稳定时钟的博赫纳次从属。对于有界约化游走，我们证明每个对称有界提议律的玻恩概率。截断稳定律（$\u03b1=0.5,1,1.5,2$）的模拟证实了该律独立性。在连续时间中，$\u03b1$稳定驱动无法约化：精确流（马库斯）方程振荡，朴素伊藤跳跃方程无法保持态。对于高斯白噪声，伊藤模型坍缩为玻恩概率，而精确流（斯特拉托诺维奇）模型无阈值时不坍缩且产生非玻恩出射概率。二次情形恢复米尔本的小步极限，而非其精确泊松动力学。最后，研究双时间几何作为可能的紧致相位源，但闭合类时曲线、非幺正演化及不稳定模塔阻碍了一致场论实现。
英文摘要
Let $L_u$ be a symmetric Levy process representing an unobserved phase lift, coupling to a quantum system via charge $Q$. Averaging $e^{iL_uQ}$ gives a completely positive dephasing semigroup. If the characteristic exponent lacks an intrinsic charge scale, the Levy-Khintchine theorem forces $η(ξ)=D | ξ|^α$ ($0<α\le2$), so coherences decay at $Γ_{ab}=D | q_a-q_b |^α$. For integer charge differences, the process descends to the wrapped variable $Θ_u=L_u\bmod 2π$; for real charges, the lift is the relevant phase. Schoenberg's theorem ensures complete positivity for any finite real spectrum when $0<α\le2$, while $α>2$ yields an analytic obstruction. This boundary is exact, verified numerically here. A Gaussian integrated phase gives quadratic charge dependence, though colored Gaussian noise need not yield a Markov semigroup. Two idealized non-Gaussian mechanisms are analyzed: inverse-power Poisson shot noise ($α=d/p$) and Bochner subordination of Brownian phase by an $α/2$-stable clock. For a bounded reduction walk, we prove Born probabilities for every symmetric bounded proposal law. Simulations of truncated stable laws ($α=0.5,1,1.5,2$) confirm this law-independence. In continuous time, $α$-stable drivers fail to reduce: the exact-flow (Marcus) equation oscillates, and the naive Ito jump equation fails to preserve state. For Gaussian white noise, the Itô model collapses to Born probabilities, whereas the exact-flow (Stratonovich) model does not collapse without a threshold and yields non-Born exit probabilities. The quadratic case recovers Milburn's small-step limit, not his exact Poisson dynamics. Finally, a bi-temporal geometry is examined as a possible compact phase source, but closed timelike curves, nonunitary evolution, and an unstable mode tower prevent a consistent field-theoretic realization.
