2018/03/31 by Vedika Khemani, David A. Huse, Adam Nahum · 4 citations
Physics and Astronomy · #Classical mechanics #Hilbert space #Integrable system #Lyapunov exponent #Mathematical physics #Method of quantum characteristics #Nonlinear system #Opinion Dynamics and Social Influence #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Semiclassical physics #Statistical physics #cond-mat.stat-mech #cond-mat.str-el #hep-th #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physrevb.98.144304
published as Phys. Rev. B 98, 144304 (2018) · Published version
openalex publication_date 2018/10/16 · arxiv created 2018/10/19 · arxiv updated 2018/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It has been a long-standing challenge to expand the notion of exponential sensitivity to small perturbations in the initial conditions from the realm of classical chaos to that of many-body quantum systems. Recently, exponential growth in a measure known as the out-of-time-order commutator (OTOC) has been proposed as a diagnostic of chaos in the setting of many-body quantum systems. The authors examine the behavior of the OTOC along rays of different velocities for a variety of spatially local extended many-body quantum systems, both integrable and nonintegrable. They find that the velocity-dependent Lyapunov exponents are negative for velocities greater than a characteristic ``butterfly speed'', which defines the light cone for the spreading of operators. It is demonstrated that a regime with well-defined positive Lyapunov exponents inside the light-cone may only exist for classical, semiclassical, weakly interacting, or large-N systems, but not for fully quantum systems with strong short-range interactions and local Hilbert space dimensions of order one.