Chaos and complexity for inverted harmonic oscillators
Le-Chen Qu, Jing Chen, Yu-Xiao Liu
Abstract
We investigate the circuit complexity and Loschmidt echo for the (inverted) harmonic oscillators. Using a perturbative approach, 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.
Topics & Concepts
Lyapunov exponentScramblingHarmonicCHAOS (operating system)ExponentPhysicsStatistical physicsMathematicsControl theory (sociology)Computer scienceQuantum mechanicsNonlinear systemAlgorithmLinguisticsControl (management)Computer securityPhilosophyArtificial intelligencestochastic dynamics and bifurcationQuantum and electron transport phenomenaQuantum chaos and dynamical systems