Introduces a universal dimensionless instability parameter based on quantum-state evolution speed versus spectral-gap protection, plus a self-limitation theorem for nonlinear regulators in driven quantum systems.
Riemannian structure on mani- folds of quantum states
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QRSI spans degenerate quantum eigenspaces almost surely by conjugating the Hamiltonian with random unitaries on g parallel branches and using subspace estimation, while exactly preserving the spectral gap.
Establishes bound relations between electronic properties in magnetic crystals, including a new lower bound on susceptibility for Chern insulators and generalization of Chern bounds to three dimensions.
Berry Phase Rate and other geometric observables from learned spectral embeddings of equity-index returns detect financial regime shifts with competitive out-of-sample performance and lower false-alarm rates than supervised baselines.
Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.
The AMT parameter equals the squared Fubini-Study speed of the driven state and the tt-component of the quantum geometric tensor, supplying a strictly local criterion for nonadiabatic instability that an occupation-dependent nonlinear regulator U can suppress to produce bounded low-occupancy bosonic
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Geometric Observables for Financial Regime Detection
Berry Phase Rate and other geometric observables from learned spectral embeddings of equity-index returns detect financial regime shifts with competitive out-of-sample performance and lower false-alarm rates than supervised baselines.