A bound on quantum chaos from Random Matrix Theory with Gaussian Unitary 
Ensemble

Choudhury, Sayantan; Mukherjee, Arkaprava

doi:10.1007/JHEP05(2019)149

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A bound on quantum chaos from Random Matrix Theory with Gaussian Unitary Ensemble

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Choudhury, Sayantan
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Choudhury, S., & Mukherjee, A. (2019). A bound on quantum chaos from Random Matrix Theory with Gaussian Unitary Ensemble. Journal of High Energy Physics, 2019(5): 149. doi:10.1007/JHEP05(2019)149.

Cite as: https://hdl.handle.net/21.11116/0000-0002-82B9-A

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, $-1/N(1-1/\pi)\leq {\bf SFF}\leq 0$ and $0\leq
{\bf SFF}\leq 1/\pi N$, 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.