{'fraction_non_alphanumeric': 0.020569620253164556, 'fraction_numerical': 0.0, 'mean_word_length': 5.912568306010929, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Regularity versus randomness in matrix-element distributions in quantum nonintegrable Hamiltonian systems.

The relationship between matrix-element correlations and level-spacing properties is analyzed for typical Hamiltonian systems by introducing both global and local statistical measures. Two-dimensional two-point correlation functions and higher-order traces for Hamiltonian matrices are introduced for abstracting global properties of matrix-element distributions. The global behavior of correlation patterns for Hamiltonian matrices is shown to be markedly different from that for \ensuremath{\delta}-correlated random matrices, which suggests that the Wigner-type spacing characteristic is not a property specific of the standard random matrix but a property of a more general class of nonrandom matrices. A technique of site randomization for matrix elements is introduced for exploring the local property of matrix-element correlations. It is demonstrated that level-spacing distributions for a class of statistically most-realizable matrix element configurations, constructed by a local site randomization from a given Hamiltonian matrix, generally do not coincide with that for a matrix-element configuration of the original Hamiltonian matrix itself.