摘要翻译：
我们研究了最近提出的一个非马尔可夫随机游动模型，其特征是最近过去的记忆丢失和遗忘诱导的持久性。我们给出了由四个相组成的完整相图：(i)经典非持久性，(ii)经典持久性，(iii)对数周期非持久性和(iv)负反馈驱动的对数周期持久性。前两个相具有连续的尺度不变对称性，而对数周期破坏了这种对称性。相反，对数周期运动满足离散尺度不变对称性，具有复杂而非真实的分形维数。对于对数周期持久性，我们不仅发现了统计上的自相似性，而且还发现了几何上的自相似性。
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英文标题：
《Spontaneous symmetry breaking in amnestically induced persistence》
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作者：
Marco Antonio Alves da Silva, A. S. Ferreira, G. M. Viswanathan and J.
  C. Cressoni
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of 4 phases, for this system: (i) classical nonpersistence, (ii) classical persistence (iii) log-periodic nonpersistence and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.
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PDF链接：
https://arxiv.org/pdf/708.3102