Out-of-time-order correlators in finite open systems.

@article{Syzranov2018OutoftimeorderCI,
  title={Out-of-time-order correlators in finite open systems.},
  author={S V Syzranov and Alexey V. Gorshkov and Victor M. Galitski},
  journal={Physical review. B},
  year={2018},
  volume={97}
}
We study out-of-time-order correlators (OTOCs) of the form 〈 A ^ ( t ) B ^ ( 0 ) C ^ ( t ) D ^ ( 0 ) 〉 for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially ∝Σa i e -t/τi + const to a constant value at t → ∞, in contrast with… 

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References

SHOWING 1-10 OF 30 REFERENCES
Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
The idea of the out-of-time-order correlator (OTOC) has recently emerged in the study of both condensed matter systems and gravitational systems. It not only plays a key role in investigating the
Measurement of many-body chaos using a quantum clock
There has been recent progress in understanding chaotic features in many-body quantum systems. Motivated by the scrambling of information in black holes, it has been suggested that the time
Scrambling and thermalization in a diffusive quantum many-body system
Out-of-time ordered (OTO) correlation functions describe scrambling of information in correlated quantum matter. They are of particular interest in incoherent quantum systems lacking well defined
Quasiprobability behind the out-of-time-ordered correlator
Two topics, evolving rapidly in separate fields, were combined recently: the out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD)
Exact out-of-time-ordered correlation functions for an interacting lattice fermion model
Exact solutions for local equilibrium and nonequilibrium out-of-time-ordered correlation (OTOC) functions are obtained for a lattice fermion model with on-site interactions, namely the
Slow scrambling in disordered quantum systems
Recent work has studied the growth of commutators as a probe of chaos and information scrambling in quantum many-body systems. In this work we study the effect of static disorder on the growth of
Out‐of‐time‐ordered correlators in many‐body localized systems
In many‐body localized systems, propagation of information forms a light cone that grows logarithmically with time. However, local changes in energy or other conserved quantities typically spread
...
...