Chaos and complexity in quantum mechanics
Tibra Ali, Arpan Bhattacharyya, S. Shajidul Haque, Eugene H. Kim, Nathan Moynihan, Jeff Murugan
Abstract
We propose a new diagnostic for quantum chaos. We show that the time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order correlators. Moreover, for systems that can be switched from a regular to unstable (chaotic) regime by a tuning of the coupling constant of the interaction Hamiltonian, we find that the complexity defines a new time scale. We interpret this time scale as recording when the system makes the transition from regular to chaotic behavior.
Topics & Concepts
ScramblingLyapunov exponentChaoticQuantum chaosStatistical physicsQuantumSynchronization of chaosHamiltonian (control theory)PhysicsMathematicsQuantum mechanicsComputer scienceQuantum dynamicsControl theory (sociology)AlgorithmArtificial intelligenceControl (management)Mathematical optimizationQuantum chaos and dynamical systemsQuantum many-body systemsNonlinear Dynamics and Pattern Formation