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

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.

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Genre: Journal Article

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Creators:
Choudhury, Sayantan1, Author
Mukherjee, Arkaprava, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014

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Free keywords: High Energy Physics - Theory, hep-th, Condensed Matter, Statistical Mechanics, cond-mat.stat-mech,General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Phenomenology, hep-ph,Quantum Physics, quant-ph
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.

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Dates: 2018-11-022019
Publication Status: Published in print
Pages: 4 pages, 2 figures
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Rev. Method: -
Identifiers: arXiv: 1811.01079
URI: http://arxiv.org/abs/1811.01079
DOI: 10.1007/JHEP05(2019)149
Degree: -

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Title: Journal of High Energy Physics
Source Genre: Journal
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Pages: - Volume / Issue: 2019 (5) Sequence Number: 149 Start / End Page: - Identifier: -