Severe slowing-down and universality of the dynamics in disordered interacting many-body systems: ageing and ultraslow diffusion
Severe slowing-down and universality of the dynamics in disordered interacting many-body systems: ageing and ultraslow diffusion
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DOI：
10.1088/1367-2630/16/11/113050
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发表时间：
2013-11
影响因子：
3.3
通讯作者：
Lloyd P. Sanders;M. A. Lomholt;L. Lizana;Karl Fogelmark;R. Metzler;T. Ambjörnsson
中科院分区：
文献类型：
--
作者：
Lloyd P. Sanders;M. A. Lomholt;L. Lizana;Karl Fogelmark;R. Metzler;T. Ambjörnsson
低维多体系统通常具有超慢动力学的特点。我们研究了在强烈无序环境中具有核心相互作用的相同粒子的通用系统中的标记粒子。这种紊乱表现为单颗粒水平上具有无标度粘附时间的间歇运动。虽然对于非相互作用粒子，我们发现均方位移为 0 的幂律形式 ⟨ x 2 ( t ) ⟩ ≃ t ?> 的异常扩散，但我们在此证明无序环境与多体相互作用的结合会导致超慢的对数动力学 ⟨ x 2 ( t ) ⟩ ≃ log 1 / 2 t ?> 具有通用 1 / 2 ?> 指数。即使存在特征粘着时间但粘着时间的波动发散，我们观察到均方位移 ⟨ x 2 ( t ) ⟩ ≃ t γ ?> 为 0 ，这比著名的哈里斯定律 ⟨ x 2 ( t ) ⟩ ≃ t 1 / 2 ?> 无序慢。我们根据计数过程的从属关系来合理化结果，其中每个转换都由老化连续时间过程的前向等待时间主导。
Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form ⟨ x 2 ( t ) ⟩ ≃ t ?> of the mean squared displacement with 0 , we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics ⟨ x 2 ( t ) ⟩ ≃ log 1 / 2 t ?> with a universal 1 / 2 ?> exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement ⟨ x 2 ( t ) ⟩ ≃ t γ ?> with 0 , that is slower than the famed Harris law ⟨ x 2 ( t ) ⟩ ≃ t 1 / 2 ?> without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process.