What question did this study set out to answer?

To propose and verify a novel random matrix universality class emerging from the two-body state space of three-dimensional dissipative algebra.

August 16, 2026Open Access

TDDA Quantum Chaos and a Novel Universality Class of Random MatricesTDDA 量子混沌与一类全新随机矩阵普适类

View Full Paper

Ask AI

Bookmark

Authors

ZLZhongqiang Liu

Discussion

Member takes

Implication

Numerical simulation demonstrates a novel random matrix universality class in three-dimensional dissipative algebra, revealing non-associative algebraic constraints on quantum chaotic spectra.

Key Points

To propose and verify a novel random matrix universality class emerging from the two-body state space of three-dimensional dissipative algebra.
Conducted numerical simulations on over 40,000 samples of TDDA left-multiplication operator ensembles restricted to the positive-metric physical subspace using Python, NumPy, and SymPy.
Computed nearest-neighbor energy level spacing ratios and spectral statistics for the TDDA operators as well as the first 10,000 non-trivial Riemann zeta zeros.
TDDA left-multiplication ensembles exhibited a mean nearest-neighbor spacing ratio that diverged from the classical Gaussian Orthogonal Ensemble value of 0.536 by approximately 13 standard errors.
Demonstrated that 81 matrix entries in the 9x9 operator are strictly governed by only 9 independent degrees of freedom due to non-associative multiplication constraints, with non-associative entanglement monotonically correlating with level randomness.

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a817aa1f2fb91fc834ae939 https://doi.org/10.5281/zenodo.21952864

View Full Paper

Ask AI

Bookmark

August 16, 2026Open Access

TDDA Quantum Chaos and a Novel Universality Class of Random MatricesTDDA 量子混沌与一类全新随机矩阵普适类

View Full Paper

Ask AI

Bookmark

Authors

ZLZhongqiang Liu

Discussion

Member takes

Implication

Numerical simulation demonstrates a novel random matrix universality class in three-dimensional dissipative algebra, revealing non-associative algebraic constraints on quantum chaotic spectra.

Key Points

To propose and verify a novel random matrix universality class emerging from the two-body state space of three-dimensional dissipative algebra.
Conducted numerical simulations on over 40,000 samples of TDDA left-multiplication operator ensembles restricted to the positive-metric physical subspace using Python, NumPy, and SymPy.
Computed nearest-neighbor energy level spacing ratios and spectral statistics for the TDDA operators as well as the first 10,000 non-trivial Riemann zeta zeros.
TDDA left-multiplication ensembles exhibited a mean nearest-neighbor spacing ratio that diverged from the classical Gaussian Orthogonal Ensemble value of 0.536 by approximately 13 standard errors.
Demonstrated that 81 matrix entries in the 9x9 operator are strictly governed by only 9 independent degrees of freedom due to non-associative multiplication constraints, with non-associative entanglement monotonically correlating with level randomness.

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a817aa1f2fb91fc834ae939 https://doi.org/10.5281/zenodo.21952864

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

View Full Paper

Ask AI

Bookmark