Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics, and spiked random matrices: Pinning and localization.
Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics, and spiked random matrices: Pinning and localization.
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具有柱状和点无序的倾斜弹性线、非厄米量子力学和尖峰随机矩阵：钉扎和定位。
DOI：
10.1103/physreve.103.042120
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
N. O’Connell
中科院分区：
文献类型：
--
作者：
Alexandre Krajenbrink;P. Le Doussal;N. O’Connell
我们重新审视的问题的弹性线（如超导体中的涡旋线）受到两个柱状无序和点无序的尺寸d=1+1。在施加横向场时，预期会发生离域转变，超过该转变，线宏观上会倾斜。我们调查这种过渡中的固定倾斜角合奏和“单向”模型，向后跳跃被忽略。从最近的结果定向聚合物在数学文献中，和他们的连接到随机矩阵理论，我们发现，对于一个单一的线和一个单一的强缺陷，在点无序的存在下，这种转变与Baik-Ben Arous-Péché（BBP）转变相一致的外观中的光谱的扰动随机矩阵的高斯酉系综的离群值。这种转变是方便地描述在聚合物图片通过变分计算。在离域阶段，基态能量表现出Tracy-Widom涨落。在定域相中，我们用变分计算表明，占据长度沿着柱状缺陷的涨落可用f_{KPZ}来描述，这是一个普遍存在于Kardar-Parisi-Zhang普适类中的分布。然后，我们考虑一个光滑的柱状缺陷能量密度。取决于该密度如何在其下边缘消失，我们发现（i）仅离域相或（ii）具有离域过渡的局域相。我们分析了这个过渡，这是一个无限秩的扩展的BBP过渡。在本地化阶段的一个单一的弹性线的基态能量的波动（对于固定的柱状缺陷能量）所描述的Fredholm行列式的基础上的一个新的内核，密切相关的内核描述的最大真实的本征值的真实的Ginibre合奏。许多列和许多不相交的线，相关的玻色玻璃相的研究的情况下，也进行了分析。基态能量由自由几率和Burgers方程得到。最近的结果的广义罗森茨威格-波特模型的连接表明，本地化的许多聚合物逐渐增加其长度。
We revisit the problem of an elastic line (such as a vortex line in a superconductor) subject to both columnar disorder and point disorder in dimension d=1+1. Upon applying a transverse field, a delocalization transition is expected, beyond which the line is tilted macroscopically. We investigate this transition in the fixed tilt angle ensemble and within a "one-way" model where backward jumps are neglected. From recent results about directed polymers in the mathematics literature, and their connections to random matrix theory, we find that for a single line and a single strong defect this transition in the presence of point disorder coincides with the Baik-Ben Arous-Péché (BBP) transition for the appearance of outliers in the spectrum of a perturbed random matrix in the Gaussian unitary ensemble. This transition is conveniently described in the polymer picture by a variational calculation. In the delocalized phase, the ground state energy exhibits Tracy-Widom fluctuations. In the localized phase we show, using the variational calculation, that the fluctuations of the occupation length along the columnar defect are described by f_{KPZ}, a distribution which appears ubiquitously in the Kardar-Parisi-Zhang universality class. We then consider a smooth density of columnar defect energies. Depending on how this density vanishes at its lower edge we find either (i) a delocalized phase only or (ii) a localized phase with a delocalization transition. We analyze this transition which is an infinite-rank extension of the BBP transition. The fluctuations of the ground state energy of a single elastic line in the localized phase (for fixed columnar defect energies) are described by a Fredholm determinant based on a new kernel, closely related to the kernel describing the largest real eigenvalues of the real Ginibre ensemble. The case of many columns and many nonintersecting lines, relevant for the study of the Bose glass phase, is also analyzed. The ground state energy is obtained using free probability and the Burgers equation. Connections with recent results on the generalized Rosenzweig-Porter model suggest that the localization of many polymers occurs gradually upon increasing their lengths.
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10.1007/s00023-019-00809-z
发表时间：
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期刊：
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影响因子：
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作者：
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DOI：
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发表时间：
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影响因子：
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影响因子：
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DOI：
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发表时间：
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期刊：
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