Freezing transition in decaying Burgers turbulence and random matrix dualities
Freezing transition in decaying Burgers turbulence and random matrix dualities
复制标题
衰减伯格斯湍流中的冻结转变和随机矩阵对偶性
DOI：
10.1209/0295-5075/90/60004
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Alberto Rosso
中科院分区：
文献类型：
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作者：
Y. Fyodorov;P. Doussal;Alberto Rosso
本文揭示了一维衰减Burgers型湍流中初速服从正态分布的幂相关随机分布的相变，在νc>；0时，ν=νc>；0处的相变粘性降低。低粘度相呈现出连续依赖于ν的非高斯单点速度概率密度，反映了相关统计力学问题中的自发一步复制对称破缺。我们解析地得到了低阶累积量。我们的结果是基于对随机对数势中冻结转变机制的洞察和最近在随机矩阵理论中发现的对偶关系的扩展而得到的，并得到了数值检验。它们本质上是非平均场，数值计算的冲击波大小分布也证明了这一点，这与短程相关的KIDA模型不同。我们还对后一种模型中速度的有限粘性行为提供了一些见解。
We reveal a phase transition with decreasing viscosity ν at ν=νc>0 in one-dimensional decaying Burgers turbulence with a power-law–correlated random profile of Gaussian-distributed initial velocities . The low-viscosity phase exhibits non-Gaussian one-point probability density of velocities, continuously dependent on ν, reflecting a spontaneous one-step replica symmetry breaking (RSB) in the associated statistical-mechanics problem. We obtain the low orders cumulants analytically. Our results, which are checked numerically, are based on combining insights in the mechanism of the freezing transition in random logarithmic potentials with an extension of duality relations discovered recently in the random matrix theory. They are essentially non–mean-field in nature as also demonstrated by the shock size distribution computed numerically and different from the short-range–correlated Kida model. We also provide some insights for the finite-viscosity behaviour of velocities in the latter model.