A universal bound on Quantum Chaos from Random Matrix Theory

Abstract

In this article, using the principles of Random Matrix Theory (RMT), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two-point Out of Time Order Correlation function (OTOC) expressed in terms of square of the commutator bracket of quantum operators which are separated in time. We also provide a strict model independent bound on the measure of quantum chaos, $-1/N(1-1/\pi )\le \mathbf{SFF}\le 0$ and $0\le \mathbf{SFF}\le 1/\pi N$, valid for thermal systems with a large and small number of degrees of freedom respectively. Based on the appropriate physical arguments we give a precise mathematical derivation to establish this alternative strict bound of quantum chaos.

arXiv comment4 pages, 2 figures

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• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• Wormhole calculus without averaging from $O(N{)}^{q-1}$ tensor model
• Spectral Form Factor for Time-dependent Matrix model
• QMetrology from QCosmology: Study with Entangled Two Qubit Open Quantum System in De Sitter Space