Статистика Мехты Дайсона для уровней энергии для измерения спектрального отклонения от равномерного распределения

Я пытаюсь измерить статистику Дайсона-Мехты для набора собственных значений, чтобы воспроизвести рисунок 5 из этой статьи. Часть кода на Python, которую я использовал, не дает желаемых результатов, соответствующих статистике расстояния Пуассона. Я пытаюсь получить график на высоких энергиях, который примерно выглядит как прямая пунктирная линия на этом графике изображении. Код приведен ниже:
Изображение моего графика дает либо чрезвычайно большие значения, либо не приближается к прямой линии.

import numpy as np
from scipy.optimize import minimize
import matplotlib.pyplot as plt
eigenvalues = np.array([
24.4662, 24.4858, 24.4882, 24.4883, 24.494, 24.4995, 24.5262, \
24.5268, 24.5295, 24.5455, 24.5631, 24.5682, 24.5719, 24.5864, \
24.5899, 24.5937, 24.5967, 24.598, 24.6042, 24.609, 24.6123, 24.613, \
24.6393, 24.6396, 24.6486, 24.6487, 24.6508, 24.6644, 24.6677, \
24.669, 24.6714, 24.6744, 24.6807, 24.6902, 24.6972, 24.7011, \
24.7096, 24.7176, 24.7232, 24.7234, 24.7466, 24.7487, 24.7516, \
24.7656, 24.7682, 24.7735, 24.7822, 24.7836, 24.7851, 24.8083, \
24.8175, 24.8212, 24.8225, 24.838, 24.8416, 24.8417, 24.8481, \
24.8493, 24.8728, 24.8842, 24.8871, 24.8944, 24.8948, 24.9031, \
24.9035, 24.9076, 24.9117, 24.9179, 24.9226, 24.9247, 24.9252, 24.93, \
24.9306, 24.9492, 24.9557, 24.9613, 24.9633, 24.9688, 24.9771, \
24.9822, 24.9871, 24.9901, 24.9906, 24.9919, 24.992, 25.0017, \
25.0099, 25.0136, 25.0161, 25.0248, 25.0388, 25.0401, 25.0421, \
25.046, 25.0494, 25.0545, 25.0755, 25.0763, 25.0894, 25.0908, \
25.0934, 25.0943, 25.1323, 25.1326, 25.1346, 25.1378, 25.1481, \
25.1546, 25.1684, 25.1898, 25.1951, 25.202, 25.2031, 25.2035, \
25.2142, 25.2188, 25.2244, 25.2251, 25.2256, 25.2295, 25.2324, \
25.2337, 25.2345, 25.2456, 25.2517, 25.2607, 25.261, 25.2642, \
25.2779, 25.2864, 25.2896, 25.2924, 25.2938, 25.3032, 25.3062, \
25.3179, 25.3196, 25.3243, 25.3379, 25.3543, 25.3659, 25.3712, \
25.374, 25.3852, 25.3934, 25.3955, 25.3991, 25.402, 25.4201, 25.4232, \
25.4299, 25.4299, 25.4316, 25.4408, 25.4439, 25.4519, 25.4641, \
25.4701, 25.4711, 25.4749, 25.4749, 25.4959, 25.4971, 25.5046, \
25.5046, 25.5048, 25.5218, 25.5261, 25.5363, 25.5407, 25.5524, \
25.553, 25.555, 25.5568, 25.5606, 25.5608, 25.5648, 25.5761, 25.5805, \
25.5811, 25.5825, 25.5873, 25.5935, 25.6024, 25.615, 25.6205, \
25.6281, 25.6287, 25.6298, 25.6334, 25.647, 25.6561, 25.6591, \
25.6643, 25.6677, 25.6716, 25.672, 25.6924, 25.693, 25.6945, 25.7022, \
25.706, 25.7087, 25.7094, 25.7132, 25.7207, 25.7257, 25.7478, \
25.7594, 25.7746, 25.7884, 25.8006, 25.8021, 25.8052, 25.8145, \
25.8178, 25.829, 25.8355, 25.8411, 25.8513, 25.86, 25.8604, 25.8613, \
25.8646, 25.8725, 25.8802, 25.8815, 25.8885, 25.8958, 25.897, \
25.9051, 25.9104, 25.9186, 25.9188, 25.9225, 25.9234, 25.9298, \
25.9299, 25.9338, 25.9396, 25.9444, 25.9567, 25.9633, 25.9784, \
25.9804, 25.9812, 25.9841, 25.9899, 25.9907, 25.9962, 26., 26.0089, \
26.0109, 26.0153, 26.037, 26.0381, 26.0403, 26.0442, 26.0592, \
26.0667, 26.0674, 26.0815, 26.0854, 26.0888, 26.0933, 26.0972, \
26.1009, 26.102, 26.1139, 26.1141, 26.1297, 26.1364, 26.1381, \
26.1405, 26.1476, 26.1496, 26.1517, 26.1588, 26.1618, 26.165, \
26.1652, 26.1705, 26.1706, 26.1741, 26.1745, 26.1895, 26.1998, \
26.2001, 26.2003, 26.2271, 26.2306, 26.2478, 26.2518, 26.2566, \
26.2566, 26.2621, 26.2695, 26.2776, 26.2868, 26.2888, 26.3012, \
26.3081, 26.3283, 26.3325, 26.3363, 26.3414, 26.3472, 26.3571, \
26.3638, 26.3754, 26.3783, 26.3802, 26.3803, 26.3877, 26.3982, \
26.4058, 26.4137, 26.4196, 26.4235, 26.4239, 26.4274, 26.4352, \
26.4374, 26.4455, 26.4457, 26.4524, 26.4576, 26.4576, 26.4576, \
26.4661, 26.4854, 26.4927, 26.4947, 26.5062, 26.512, 26.5181, 26.525, \
26.5341, 26.5415, 26.5448, 26.5536, 26.5581, 26.5626, 26.5637, \
26.5685, 26.5723, 26.5745, 26.5752, 26.5758, 26.5851, 26.5913, \
26.5923, 26.5956, 26.6004, 26.6032, 26.6044, 26.613, 26.6212, 26.644, \
26.6443, 26.6599, 26.666, 26.6688, 26.6698, 26.671, 26.6768, 26.6804, \
26.6959, 26.6962, 26.6991, 26.7014, 26.7083, 26.7113, 26.7148, \
26.7211, 26.7345, 26.7389, 26.7506, 26.7679, 26.7731, 26.7762, 26.78, \
26.79, 26.792, 26.808, 26.8097, 26.81, 26.8122, 26.8146, 26.8218, \
26.8305, 26.8378, 26.8445, 26.8504, 26.8538, 26.8614, 26.8651, \
26.8731, 26.8767, 26.8791, 26.8805, 26.8834, 26.8897, 26.8974, \
26.8995, 26.9033, 26.927, 26.931, 26.9325, 26.9328, 26.9555, 26.9637, \
26.9665, 26.9683, 26.9739, 26.9778, 26.9787, 26.9895, 26.9932, \
27.0047, 27.0057, 27.0099, 27.012, 27.0131, 27.0151, 27.0194, \
27.0208, 27.0227, 27.048, 27.0528, 27.0631, 27.0674, 27.0682, \
27.0723, 27.0762, 27.0813, 27.0867, 27.0987, 27.1, 27.1024, 27.1033, \
27.106, 27.1274, 27.1354, 27.1429, 27.1478, 27.1492, 27.1497, \
27.1516, 27.1538, 27.1539, 27.1599, 27.1681, 27.1735, 27.1801, \
27.1938, 27.2243, 27.2251, 27.2286, 27.2293, 27.2345, 27.2379, \
27.2394, 27.2446, 27.262, 27.2661, 27.2688, 27.2699, 27.2806, \
27.3013, 27.3059, 27.3079, 27.3107, 27.311, 27.3178, 27.3204, \
27.3229, 27.326, 27.3421, 27.3421, 27.3595, 27.3722, 27.3793, \
27.3825, 27.3849, 27.386, 27.3915, 27.3926, 27.3976, 27.4053, \
27.4098, 27.4172, 27.4214, 27.426, 27.4395, 27.4421, 27.4435, \
27.4448, 27.446, 27.4572, 27.4673, 27.4771, 27.4814, 27.4862, 27.493, \
27.4939, 27.4941, 27.4974, 27.5033, 27.5073, 27.5101, 27.5107, \
27.5113, 27.512, 27.5178, 27.5329, 27.536, 27.5432, 27.5447, 27.5684, \
27.5751, 27.5776, 27.5796, 27.5832, 27.5926, 27.6163, 27.62, 27.623, \
27.6262, 27.6327, 27.6384, 27.6408, 27.6471, 27.6623, 27.6625, \
27.6634, 27.6724, 27.6749, 27.6817, 27.6848, 27.6875, 27.6957, \
27.6965, 27.6968, 27.7215, 27.7235, 27.725, 27.7343, 27.7384, 27.739, \
27.7467, 27.7555, 27.76, 27.7607, 27.7755, 27.7764, 27.7864, 27.8037, \
27.804, 27.8075, 27.8086, 27.8136, 27.8149, 27.8193, 27.8234, \
27.8282, 27.8304, 27.8372, 27.8526, 27.8722, 27.8728, 27.8823, \
27.8847, 27.8855, 27.8871, 27.8874, 27.8887, 27.8939, 27.9003, \
27.9134, 27.923, 27.9279, 27.9311, 27.9348, 27.9358, 27.9433, \
27.9569, 27.9721, 27.9724, 27.9731, 27.9771, 27.9831, 27.9847, \
27.9859, 27.9873, 27.9887, 27.9919, 28.0041, 28.0075, 28.0152, \
28.0279, 28.028, 28.0445, 28.048, 28.0586, 28.0591, 28.0697, 28.0736, \
28.0749, 28.0857, 28.0866, 28.0904, 28.0918, 28.0945, 28.1149, \
28.1178, 28.1208, 28.1362, 28.1424, 28.147, 28.1473, 28.1519, \
28.1542, 28.1577, 28.1645, 28.1685, 28.1685, 28.1693, 28.1749, \
28.1797, 28.1797, 28.1834, 28.1947, 28.2029, 28.2163, 28.2219, \
28.2312, 28.2324, 28.251, 28.2514, 28.2552, 28.2568, 28.2581, \
28.2709, 28.2804, 28.2809, 28.2877, 28.2895, 28.2981, 28.3005, \
28.3088, 28.3099, 28.3112, 28.3136, 28.3169, 28.3294, 28.3316, \
28.3413, 28.3424, 28.3425, 28.3552, 28.361, 28.3632, 28.366, 28.3708, \
28.3742, 28.3758, 28.386, 28.3982, 28.4315, 28.4333, 28.4341, \
28.4372, 28.4478, 28.4491, 28.4573, 28.4681, 28.4819, 28.4867, \
28.4921, 28.4966, 28.4987, 28.4995, 28.5003, 28.5004, 28.5033, \
28.5234, 28.526, 28.5269, 28.543, 28.5442, 28.5457, 28.5472, 28.5513, \
28.552, 28.5523, 28.554, 28.5654, 28.5664, 28.5669, 28.5765, 28.588, \
28.5882, 28.6025, 28.61, 28.6247, 28.6264, 28.6273, 28.6276, 28.6368, \
28.6374, 28.6466, 28.6476, 28.648, 28.65, 28.6636, 28.6709, 28.6828, \
28.6859, 28.6918, 28.7055, 28.713, 28.7186, 28.7313, 28.7313, \
28.7318, 28.7326, 28.733, 28.735, 28.7413, 28.7436, 28.7466, 28.7535, \
28.759, 28.7619, 28.7651, 28.773, 28.7731, 28.7781, 28.7886, 28.7907, \
28.7942, 28.8101, 28.8312, 28.8395, 28.8399, 28.8437, 28.848, \
28.8605, 28.8705, 28.8739, 28.8765, 28.8769, 28.8848, 28.8865, \
28.8903, 28.9095, 28.913, 28.9145, 28.9146, 28.9172, 28.9373, \
28.9374, 28.9421, 28.945, 28.9571, 28.9621, 28.9644, 28.9722, \
28.9723, 28.9723, 28.9759, 28.9785, 28.9806, 28.9867, 28.993, \
28.9995, 28.9995, 29.0024, 29.0064, 29.008, 29.0225, 29.0237, \
29.0273, 29.0282, 29.0434, 29.0505, 29.0551, 29.0606, 29.0612, \
29.0672, 29.0699, 29.07, 29.0724, 29.077, 29.0823, 29.085, 29.0881, \
29.092, 29.0947, 29.1019, 29.116, 29.1308, 29.1365, 29.1385, 29.1415, \
29.1418, 29.1425, 29.1579, 29.1598, 29.1609, 29.1774, 29.184, \
29.1909, 29.1975, 29.2035, 29.2096, 29.2122, 29.2197, 29.2252, \
29.2291, 29.2329, 29.2363, 29.2386, 29.2443, 29.2644, 29.27, 29.276, \
29.277, 29.2803, 29.2827, 29.2893, 29.2912, 29.2939, 29.2981, \
29.3085, 29.3112, 29.3123, 29.3166, 29.3203, 29.3236, 29.3286, \
29.3477, 29.3512, 29.3538, 29.3581, 29.3645, 29.3835, 29.3863, \
29.3872, 29.393, 29.3992, 29.4108, 29.4127, 29.4192, 29.4222, \
29.4265, 29.4296, 29.4462, 29.4463, 29.4464, 29.4555, 29.4603, \
29.4616, 29.4627, 29.4658, 29.4708, 29.4721, 29.4784, 29.4804, \
29.4815, 29.4877, 29.5132, 29.5196, 29.5215, 29.5222, 29.5256, \
29.5314, 29.5472, 29.5476, 29.5554, 29.5645, 29.5728, 29.5739, \
29.5788, 29.5805, 29.589, 29.5924, 29.5963, 29.5968, 29.6046, \
29.6075, 29.609, 29.6098, 29.6179, 29.6203, 29.631, 29.6328, 29.6377, \
29.6417, 29.6495, 29.6515, 29.6553, 29.6589, 29.6658, 29.6685, \
29.6689, 29.6714, 29.6838, 29.6843, 29.6866, 29.6881, 29.7094, \
29.7121, 29.7134, 29.7138, 29.7146, 29.7189, 29.7265, 29.7292, \
29.7342, 29.7376, 29.7389, 29.7511, 29.7554, 29.7765, 29.7792, \
29.7828, 29.7832, 29.7882, 29.7941, 29.7969, 29.8036, 29.8191, \
29.8197, 29.834, 29.8371, 29.8521, 29.8534, 29.8589, 29.8595, \
29.8598, 29.86, 29.8649, 29.8732, 29.8823, 29.9062, 29.9083, 29.9089, \
29.9109, 29.9138, 29.9139, 29.9158, 29.9219, 29.9313, 29.9344, \
29.9404, 29.9428, 29.9516, 29.9517, 29.9536, 29.9545, 29.9627, \
29.9703, 29.9767, 29.9781, 29.9797, 29.9916, 29.9956, 30.0071, \
30.0153, 30.0155, 30.0165, 30.0183, 30.0296, 30.0397, 30.0432, \
30.0432, 30.0524, 30.0531, 30.0535, 30.0536, 30.0553, 30.0668, \
30.0732, 30.0874, 30.0942, 30.0947, 30.1018, 30.1032, 30.1051, \
30.1082, 30.1103, 30.1121, 30.1122, 30.124, 30.131, 30.1364, 30.1385, \
30.1473, 30.1508, 30.1512, 30.1569, 30.1604, 30.1615, 30.1713, \
30.1722, 30.1785, 30.1863, 30.1888, 30.2022, 30.2028, 30.2043, \
30.2071, 30.2114, 30.2121, 30.2159, 30.2214, 30.224, 30.2281, \
30.2309, 30.248, 30.2584, 30.2769, 30.2773, 30.2818, 30.2833, \
30.2959, 30.2971, 30.298, 30.3045, 30.3131, 30.3195, 30.3223, \
30.3344, 30.335, 30.3385, 30.3422, 30.343, 30.3438, 30.3469, 30.347, \
30.3626, 30.3761, 30.3784, 30.3784, 30.379, 30.3829, 30.3917, \
30.4073, 30.4108, 30.4126, 30.4128, 30.4208, 30.4219, 30.4295, \
30.4371, 30.4477, 30.4492, 30.4537, 30.4565, 30.4688, 30.469, 30.478, \
30.4787, 30.4794, 30.4797, 30.4807, 30.4882, 30.4884, 30.4963, \
30.5069, 30.5094, 30.514, 30.5285, 30.5321, 30.5355, 30.5381, \
30.5387, 30.5494, 30.5579, 30.5586, 30.5623, 30.5694, 30.5708, \
30.602, 30.6024, 30.6199, 30.62, 30.6201, 30.6202, 30.6236, 30.625, \
30.6266, 30.633, 30.6373, 30.6374, 30.6377, 30.6381, 30.6437, \
30.6508, 30.6521, 30.6548, 30.6576, 30.6583, 30.67, 30.6706, 30.6713, \
30.6837, 30.6863, 30.6897, 30.6913, 30.6916, 30.7017, 30.7025, \
30.7031, 30.7042, 30.7135, 30.721, 30.7214, 30.7219, 30.7233, \
30.7421, 30.7425, 30.7524, 30.7531, 30.7563, 30.7694, 30.7734, \
30.7791, 30.8048, 30.8154, 30.8194, 30.8202, 30.825, 30.8381, \
30.8456, 30.8469, 30.8566, 30.8618, 30.8619, 30.8623, 30.8633, \
30.8675, 30.8681, 30.8706, 30.8758, 30.8937, 30.9024, 30.9162, \
30.9188, 30.9193, 30.9204, 30.9258, 30.9309, 30.9358, 30.9409, \
30.9435, 30.9446, 30.9531, 30.9552, 30.9572, 30.9587, 30.9588, \
30.959, 30.9736, 30.9797, 30.9897, 30.9927, 31.0047, 31.0061, \
31.0117, 31.0207, 31.0207, 31.0285, 31.0352, 31.0363, 31.0392, \
31.0399, 31.046, 31.0502, 31.0547, 31.0548, 31.0559, 31.0561, \
31.0589, 31.0722, 31.0728, 31.0794, 31.0906, 31.0974, 31.0985, \
31.1092, 31.1158, 31.1211, 31.132, 31.1331, 31.1339, 31.1362, \
31.1378, 31.1401, 31.1408, 31.1554, 31.1563, 31.1585, 31.1587, \
31.1599, 31.1605, 31.1607, 31.1707, 31.1778, 31.1784, 31.1929, \
31.1932, 31.1983, 31.1993, 31.2065, 31.2115, 31.2115, 31.2176, \
31.2225, 31.2252, 31.2267, 31.2453, 31.248, 31.2485, 31.2504, \
31.2571, 31.259, 31.2696, 31.2771, 31.2778, 31.285, 31.2892, 31.2933, \
31.2948, 31.2968, 31.3007, 31.3046, 31.3127, 31.316, 31.3209, \
31.3238, 31.33, 31.3639, 31.3665, 31.3717, 31.3742, 31.3777, 31.3784, \
31.3841, 31.3922, 31.3995, 31.4028, 31.4056, 31.4062, 31.4067, \
31.4147, 31.4203, 31.425, 31.4296, 31.4306, 31.431, 31.4354, 31.4379, \
31.4384, 31.4445, 31.4548, 31.4563, 31.4584, 31.46, 31.46, 31.4759, \
31.4796, 31.4802, 31.4861, 31.4864, 31.5026, 31.5028, 31.5183, \
31.5202, 31.5339, 31.5452, 31.5554, 31.5597, 31.5711, 31.5818, \
31.5849, 31.5899, 31.5945, 31.6062, 31.6128, 31.6149])

# Определить ступенчатую функцию N(E) для конкретного интервала собственных значений
def staircase_N(E, interval_eigenvalues):
    return np.sum(interval_eigenvalues <= E)

# Определить расчет статистики Дайсона-Мехты Δ3(L; epsilon) с линейной поправкой
def dyson_mehta(epsilon, L, num_intervals=100):
    # Выбрать собственные значения только в интервале [epsilon, epsilon + L]
    interval_eigenvalues = eigenvalues[(eigenvalues >= epsilon) & (eigenvalues <= epsilon + L)]

    # Пропустить, если в интервале нет собственных значений
    if len(interval_eigenvalues) == 0:
        return 0

    # Сгенерировать кумулятивную N(E) для этого интервала
    E_values = np.linspace(epsilon, epsilon + L, num_intervals)
    N_E_values = np.array([staircase_N(E, interval_eigenvalues) for E in E_values])

    # Рассчитать линию наилучшего соответствия для N(E) в этом интервале
    linear_fit = np.polyfit(E_values, N_E_values, 1)
    A, B = linear_fit

    # Определить функцию линейной поправки
    def linear_fit_function(E):
        return A * E + B

    # Рассчитать среднеквадратичное отклонение и приближенную интеграл
    delta3_sum = np.sum(((N_E_values - linear_fit_function(E_values)) ** 2)/100)
    delta3_integral = delta3_sum /L
    return delta3_integral

# Определить диапазон значений L для тестирования
L_values = np.arange(1, 16, 1)  # Выбрать диапазон от 0.5 до 5 раз среднего расстояния уровней
average_delta3_values = []

# Рассчитать среднее значение Δ3(L) для каждого значения L
for L in L_values:
    epsilon_min = eigenvalues.min()
    epsilon_max = eigenvalues.max() - L
    epsilon_increment = 0.1* (eigenvalues.max() - eigenvalues.min()) / len(eigenvalues)  # Доля среднего расстояния

    # Сгенерировать значения epsilon в интервале [epsilon_min, epsilon_max]
    epsilon_values = np.arange(epsilon_min, epsilon_max, epsilon_increment)

    # Рассчитать Δ3(L; epsilon) для каждого epsilon и усреднить
    delta3_values = [dyson_mehta(epsilon, L) for epsilon in epsilon_values]
    average_delta3 = np.mean(delta3_values)
    average_delta3_values.append(average_delta3)

# Построить результаты и эталонную линию L/15

plt.plot(L_values, average_delta3_values , marker="o", color="blue", label=r'$\Delta_3(L)$')
plt.plot(L_values, L_values / 15, linestyle="--", color="orange", label=r'$L/15$')
plt.xlabel('Длина окна (L)')
plt.ylabel(r'Среднее $\Delta_3(L)$')
plt.title(r'Статистика Дайсона-Мехты $\Delta_3(L)$ для различных длин окон')
plt.grid(True)
plt.legend()
plt.show()

Какие изменения я должен внести в код, чтобы он выглядел похоже на данный график?