记忆通过一个隐鞅过程的渐进淬火
Memory Through a Hidden Martingale Process in Progressive Quenching
摘要：
渐进淬火（PQ）是系统的自由度顺序固定的随机过程。虽然这一过程不满足局部细致平衡，但已发现一个完备自旋网络的某些物理观测量具有鞅性质。我们研究了系统对PQ中间阶段扰动的响应。在最后阶段的反应揭示了持久的记忆，我们表明，这种持久性是后面的鞅过程的直接后果。不仅平均响应，在扰动阶段的概率分布的形状也被记住。使用隐鞅过程，我们可以预测最终的双峰分布从早期的单峰分布的制度，其中解冻自旋是顺磁性的。本文提出了鞅性质是一个随机守恒定律的观点，它是由某种随机不变性支持的。
英文摘要：
Progressive quenching (PQ) is the stochastic process in which the system's degrees of freedom are sequentially fixed. While such process does not satisfy the local detailed balance, it has been found that the some physical observable of a complete spin network exhibits the martingale property. We studied system's response to the perturbation given at intermediate stages of the PQ. The response at the final stage reveals the persistent memory, and we show that this persistence is a direct consequence of the martingale process behind. Not only the mean response, the shape of the probability distribution at the stage of perturbation is also memorized. Using the hidden martingale process we can predict the final bimodal distribution from the early-stage unimodal distribution in the regime where the unfrozen spins are paramagnetic. We propose a viewpoint that the martingale property is a stochastic conservation law which is supported behind by some stochastic invariance.
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