Quantum Mechanical Out-Of-Time-Ordered-Correlators for the Anharmonic
(Quartic) Oscillator
- URL: http://arxiv.org/abs/2008.06056v3
- Date: Tue, 1 Dec 2020 07:24:43 GMT
- Title: Quantum Mechanical Out-Of-Time-Ordered-Correlators for the Anharmonic
(Quartic) Oscillator
- Authors: Paul Romatschke
- Abstract summary: Out-of-time-ordered correlators (OTOCs) have been suggested as a means to study quantum chaotic behavior in various systems.
I calculate OTOCs for the quantum mechanical anharmonic oscillator with quartic potential.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 $2\langle x^2\rangle_T \langle
p^2\rangle_T$ at late times. At high temperature, the spectral form factor
decreases at early times, bounces back and then reaches a plateau with strong
fluctuations.
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