Detecting few-body quantum chaos: out-of-time ordered correlators at
saturation
- URL: http://arxiv.org/abs/2202.09443v3
- Date: Sun, 29 May 2022 16:16:19 GMT
- Title: Detecting few-body quantum chaos: out-of-time ordered correlators at
saturation
- Authors: Dragan Markovi\'c and Mihailo \v{C}ubrovi\'c
- Abstract summary: We study numerically and analytically the time dependence and saturation of out-of-time ordered correlators (OTOC) in chaotic few-body quantum-mechanical systems.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study numerically and analytically the time dependence and saturation of
out-of-time ordered correlators (OTOC) in chaotic few-body quantum-mechanical
systems: quantum Henon-Heiles system (weakly chaotic), BMN matrix quantum
mechanics (strongly chaotic) and Gaussian random matrix ensembles. The growth
pattern of quantum-mechanical OTOC is complex and nonuniversal, with no clear
exponential regime at relevant timescales in any of the examples studied (which
is not in contradiction to the exponential growth found in the literature for
many-body systems, i.e. fields). On the other hand, the plateau (saturated)
value of OTOC reached at long times decreases with temperature in a simple and
universal way: $\exp(\mathrm{const.}/T^2)$ for strong chaos (including random
matrices) and $\exp(\mathrm{const.}/T)$ for weak chaos. For small matrices and
sufficiently complex operators, there is also another, high-temperature regime
where the saturated OTOC grows with temperature. Therefore, the plateau OTOC
value is a meaningful indicator of few-body quantum chaos. We also discuss some
general consequences of our findings for the AdS/CFT duality.
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