Chaos and Complexity for Inverted Harmonic Oscillators
Le-Chen Qu, Jing Chen, Yu-Xiao Liu
TL;DR
This paper explores the chaotic dynamics of inverted harmonic oscillators by analyzing circuit complexity and Loschmidt echo, deriving key chaos indicators like Lyapunov exponent and scrambling time, revealing their qualitative similarities.
Contribution
It provides an analytical derivation of chaos metrics for inverted harmonic oscillators and compares the behaviors of circuit complexity and Loschmidt echo.
Findings
Lyapunov exponent derived analytically
Circuit complexity and Loschmidt echo show similar behaviors
Consistent Lyapunov exponent observed
Abstract
We investigate the circuit complexity and Loschmidt echo for the (inverted) harmonic oscillators. Focusing on the chaotic behaviors under the perturbation, we analytically derive the Lyapunov exponent and scrambling time of the inverted harmonic oscillators. We show that the circuit complexity and Loschmidt echo exhibit qualitatively similar behaviors, particularly the consistent Lyapunov exponent.
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Taxonomy
TopicsQuantum and electron transport phenomena · Quantum Computing Algorithms and Architecture · stochastic dynamics and bifurcation