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arXiv · 1905.13534

Chaos and Complexity in Quantum Mechanics

Tibra Ali·Arpan Bhattacharyya·S. Shajidul Haque·Eugene H. Kim·Nathan Moynihan·Jeff Murugan
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Abstract

We propose a new diagnostic for quantum chaos. We show that 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 behaviour.

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Tibra Ali, Arpan Bhattacharyya, S. Shajidul Haque, Eugene H. Kim, Nathan Moynihan, Jeff Murugan. 2020-01-14. Chaos and Complexity in Quantum Mechanics. https://doi.org/10.1103/physrevd.101.026021

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