2020/04/27 by Tetsuya Akutagawa, Koji Hashimoto, Toshiaki Sasaki +1 · 1 citation
Physics and Astronomy · #hep-th #cond-mat.dis-nn #cond-mat.stat-mech #nlin.CD #quant-ph
paper · pdf · doi:10.1007/jhep08(2020)013
27 pages, 14 figures. v2: analysis of level statistics improved, references and comments added
arxiv created 2020/04/27 · arxiv updated 2020/08/26
Exponential growth of thermal out-of-time-order correlator (OTOC) is an indicator of a possible gravity dual, and a simple toy quantum model showing the growth is being looked for. We consider a system of two harmonic oscillators coupled nonlinearly with each other, and numerically observe that the thermal OTOC grows exponentially in time. The system is well-known to be classically chaotic, and is a reduction of Yang-Mills-Higgs theory. The exponential growth is certified because the growth exponent (quantum Lyapunov exponent) of the thermal OTOC is well matched with the classical Lyapunov exponent, including their energy/temperature dependence. Even in the presence of the exponential growth in the OTOC, the energy level spacings are not sufficient to judge a Wigner distribution, hence the OTOC is a better indicator of quantum chaos.