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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In gapped random matrix systems with parametrically many degenerate ground states, the spectral form factor at low temperatures is dominated by the disconnected contribution at all times, while the connected form factor depends only on the non-degenerate eigenvalues.
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.
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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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Spectral Form Factor of Gapped Random Matrix Systems
In gapped random matrix systems with parametrically many degenerate ground states, the spectral form factor at low temperatures is dominated by the disconnected contribution at all times, while the connected form factor depends only on the non-degenerate eigenvalues.
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Quantum chaotic systems: a random-matrix approach
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.