Numerical simulations show that a mean-field Hamiltonian reproduces exact time evolution of a four-spin quantum system up to the scrambling time, and that the system fast-scrambles with a scrambling time growing logarithmically in system size.
Black hole holography and mean field evolution
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abstract
Holographic theories representing black holes are expected to exhibit quantum chaos. We argue if the laws of quantum mechanics are expected to hold for observers inside such black holes, then such holographic theories must have a mean field approximation valid for typical black hole states, and for timescales approaching the scrambling time. Using simple spin models as examples, we examine the predictions of such an approach for observers inside black holes, and more speculatively inside cosmological horizons.
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Black Hole Interiors via Spin Models
Numerical simulations show that a mean-field Hamiltonian reproduces exact time evolution of a four-spin quantum system up to the scrambling time, and that the system fast-scrambles with a scrambling time growing logarithmically in system size.