Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves

By I. Aleiner, L. Faoro, L. Ioffe. 2016

260 citations recorded by the source corpus.

We extend the Keldysh technique to enable the computation of out-of-time order correlators. We show that the behavior of these correlators is described by equations that display initially an exponential instability which is followed by a linear propagation of the decoherence between two initially identically copies of the quantum many body systems with interactions. At large times the decoherence propagation (quantum butterfly effect) is described by a diffusion equation with non-linear dissipation known in the theory of combustion waves. The solution of this equation is a propagating non-linear wave moving with constant velocity despite the diffusive character of the underlying dynamics. Our general conclusions are illustrated by the detailed computations for the specific models describing the electrons interacting with bosonic degrees of freedom (phonons, two-level-systems etc.) or with each other.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e73e418758c2616d129f6b14996c21778afdc4cf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Brian Swingle
3. V. Khemani
4. Matthew Fisher
5. S. Sachdev
6. Shenglong Xu
7. D. Huse
8. D. Stanford

In Statistical and Nonlinear Physics

1. A. Nahum
2. D. Stanford
3. S. Sachdev
4. Brian Swingle
5. S. Hartnoll
6. V. Khemani
7. Xiao-Liang Qi
8. Andrew Lucas

Citations in the corpus

• Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “[29] Igor L Aleiner, Lara Faoro, and Lev B Ioffe.”
• Power-law out of time order correlation functions in the SYK model (2017, background): “at s = 0, and the time ordering is along the contour [29] shown in Fig.”
• Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, background): “[38] also yields a form with λ(v) = 0 inside the lightcone and linear behaviour α = 1 outside the lightcone.”
• Operator growth in the SYK model (2018, methodology): “This type of intuition was used in early discussions of scrambling by quantum circuits [15], and it is related to the kinetic equation method used for the OTOC in weakly coupled theories in [4].”
• A quantum hydrodynamical description for scrambling and many-body chaos (2017, methodology): “one should still be able to formulate the Lyapunov behavior and butterfly spreading using an effective chaotic mode as, for example, in [22].”
• Quantum Butterfly Effect in Weakly Interacting Diffusive Metals (2017, unknown): “Computing f(t,x) involves defining the action on a complex-time contour with real time folds separated by i /2 [44, 48, 50, 51].”
• Locality, Quantum Fluctuations, and Scrambling (2018, background): “Section II describes in detail the notions of operator dynamics used throughout the paper and their relations to OTOCs.”
• Random Quantum Circuits (2022, methodology): “More precisely, most physical observables are expressed as “multi-sheet” path integrals (19, 127, 128), or rather multi-layer circuits (an example is shown in Fig.”