用耦合激光测量Wishart随机矩阵的最大特征值分布
Measuring maximal eigenvalue distribution of Wishart random matrices with coupled lasers
摘要：
我们确定了25个耦合光纤激光器的组合输出功率的概率分布，并表明它与Wishart随机矩阵最大特征值的Tracy-Widom，Majumdar-Vergassola和Vivo-Majumdar-Bohigas分布很好地吻合，没有拟合参数。这是通过对光纤激光器的组合输出功率的$500,000$测量来实现的，该组合输出功率随着光纤激光器长度的变化而连续变化。我们的实验表明，对于小偏差的组合输出功率超过其平均值的Tracy-Widom分布是正确的，而大偏差的Majumdar-Vergassola和Vivo-Majumdar-Bohigas分布是正确的。
英文摘要：
We determined the probability distribution of the combined output power from twenty five coupled fiber lasers and show that it agrees well with the Tracy-Widom, Majumdar-Vergassola and Vivo-Majumdar-Bohigas distributions of the largest eigenvalue of Wishart random matrices with no fitting parameters. This was achieved with $500,000$ measurements of the combined output power from the fiber lasers, that continuously changes with variations of the fiber lasers lengths. We show experimentally that for small deviations of the combined output power over its mean value the Tracy-Widom distribution is correct, while for large deviations the Majumdar-Vergassola and Vivo-Majumdar-Bohigas distributions are correct.
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