Conjecture that the Hausdorff dimension of the frontier of the SFF random walk approaches 4/3 for chaotic Hamiltonians and 1 for integrable ones, with proofs of Gaussian statistics under Lyapunov conditions on degeneracies and exact moments for unequal-step walks.
arXiv preprint arXiv:2502.04152 , year=
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Analytical study derives conditions for ergodic infinite-temperature relaxation or robust discrete time crystal subharmonic oscillations in periodically kicked spin chains, depending on kicking protocol and initial state.
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Integrability and Chaos via fractal analysis of Spectral Form Factors: Gaussian approximations and exact results
Conjecture that the Hausdorff dimension of the frontier of the SFF random walk approaches 4/3 for chaotic Hamiltonians and 1 for integrable ones, with proofs of Gaussian statistics under Lyapunov conditions on degeneracies and exact moments for unequal-step walks.
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Ergodic and Discrete Time Crystal Phases in Periodically Kicked Many-Body Quantum Systems: An Analytical Study
Analytical study derives conditions for ergodic infinite-temperature relaxation or robust discrete time crystal subharmonic oscillations in periodically kicked spin chains, depending on kicking protocol and initial state.