Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator
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Abstract Out-of-time-ordered correlators (OTOCs) have been suggested as a means to study quantum chaotic behavior in various systems. In this work, I calculate OTOCs for the quantum mechanical anharmonic oscillator with quartic potential, which is classically integrable and has a Poisson-like energy-level distribution. For low temperature, OTOCs are periodic in time, similar to results for the harmonic oscillator and the particle in a box. For high temperature, OTOCs exhibit a rapid (but power-like) rise at early times, followed by saturation consistent with 2〈x2〉T〈p2〉T at late times. At high temperature, the spectral form factor decreases at early times, bounces back and then reaches a plateau with strong fluctuations.
1991 ◽
Vol 95
(6)
◽
pp. 4201-4214
◽
2007 ◽
Vol 2007
(suppl_26)
◽
pp. 333-338
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