Memory through a hidden martingale process in progressive quenching.,Physical Review E

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Memory through a hidden martingale process in progressive quenching.
Physical Review E ( IF 2.2 ) Pub Date : 2020-06-24 , DOI: 10.1103/physreve.101.062139
Charles Moslonka _{1,

2} , Ken Sekimoto _{1,

3}

Affiliation

Progressive quenching (PQ) is the stochastic process in which the system's degrees of freedom are sequentially fixed. While such a 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 the 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 it. 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 by some stochastic invariance.

中文翻译：

通过逐步淬灭中的隐藏mar过程进行记忆。

渐进淬火（PQ）是随机过程，在该过程中，系统的自由度顺序固定。尽管这样的过程不能满足局部的详细平衡，但是已经发现，完整的自旋网络的某些物理可观察性表现出the属性。我们研究了系统对PQ中间阶段给出的摄动的响应。最后阶段的响应揭示了持久性记忆，我们证明了这种持久性是其背后behind过程的直接结果。不仅记忆均值响应，还记录了扰动阶段概率分布的形状。使用隐藏的mar过程，我们可以从未冻结自旋为顺磁性的状态的早期单峰分布预测最终的双峰分布。

更新日期：2020-06-24

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