Relevant OTOC operators: footprints of the classical dynamics
arXiv:2008.00046 · doi:10.1103/PhysRevE.102.052133
Abstract
The out-of-time order correlator (OTOC) has recently become relevant in different areas where it has been linked to scrambling of quantum information and entanglement. It has also been proposed as a good indicator of quantum complexity. In this sense, the OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. Here we have studied the OTOC-RE correspondence on physically meaningful bases like the ones constructed with the Pauli, reflection, and translation operators. The evolution is given by a paradigmatic bi-partite system consisting of two perturbed and coupled Arnold cat maps with different dynamics. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy and hence to reveal the character of the dynamics, up to a time t 0 . In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time. When represented in phase space, each one of these sets reveals the classical dynamical footprints with different depth according to the chosen base.
arXiv comment8 pages, 10 figures
References in corpus (23)
- A bound on chaos
- Black holes and the butterfly effect
- Chaos in quantum channels
- Out-of-Time-Order Correlation for Many-Body Localization
- Out-of-time-ordered correlators in many-body localized systems
- Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
- Scrambling and entanglement spreading in long-range spin chains
- Out-of-time-order correlations in many-body localized and thermal phases
- Chaos signatures in the short and long time behavior of the out-of-time ordered correlator
- Thermodynamics of quantum information scrambling
- Reversible quantum information spreading in many-body systems near criticality
- The Weyl representation on the torus
- Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems
- Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems
- Out-of-time-order correlator in coupled harmonic oscillators
- Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest time-scale
- Out-of-time-ordered correlator in the quantum bakers map and truncated unitary matrices
- Signatures of quantum chaos transition in short spin chains
- OTOC, complexity and entropy in bi-partite systems
- Emergence of correlations in the process of thermalization of interacting bosons
- Wigner separability entropy and complexity of quantum dynamics
- Semi-classical Scar functions in phase space
- Quantum and classical complexity in coupled maps