Holographic complexity measures show universal linear growth followed by late-time saturation, proven necessary and sufficient via pole structures in the energy basis using the residue theorem, arising from random matrix statistics.
Quantum chaos, integrability, and late times in the Krylov basis,
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Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.
Finite-loop truncations of the planar dilatation operator in N=4 SYM exhibit GOE-like level statistics at large coupling for two- and four-loops (but not three), with eigenvector and Krylov diagnostics indicating weak integrability breaking and multifractality.
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
citing papers explorer
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Universal Time Evolution of Holographic and Quantum Complexity
Holographic complexity measures show universal linear growth followed by late-time saturation, proven necessary and sufficient via pole structures in the energy basis using the residue theorem, arising from random matrix statistics.
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Controlled Chaos in 4D SCFTs
Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.
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Probing weak chaos in $\mathcal N=4$ super Yang-Mills and long-range spin chains
Finite-loop truncations of the planar dilatation operator in N=4 SYM exhibit GOE-like level statistics at large coupling for two- and four-loops (but not three), with eigenvector and Krylov diagnostics indicating weak integrability breaking and multifractality.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.