Complexity of quantum motion and quantum-classical correspondence: A phase-space approach
arXiv:1912.07043 · doi:10.1103/PhysRevResearch.2.043178
Abstract
We discuss the connection between the out-of-time-ordered correlator and the number of harmonics of the phase-space Wigner distribution function. In particular, we show that both quantities grow exponentially for chaotic dynamics, with a rate determined by the largest Lyapunov exponent of the underlying classical dynamics, and algebraically -- linearly or quadratically -- for integrable dynamics. It is then possible to use such quantities to detect in the time domain the integrability to chaos crossover in many-body quantum systems.
arXiv comment6 pages, 3 figures
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