Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos
By V. Khemani, D. Huse, A. Nahum. Physical review B, 2018
149 citations recorded by the source corpus.
The exponential growth or decay with time of the out-of-time-order commutator (OTOC) is one widely used diagnostic of many-body chaos in spatially extended systems. In studies of many-body classical chaos, it has been noted that one can define a velocity-dependent Lyapunov exponent, λ(v), which is the growth or decay rate along rays at that velocity. We examine the behavior of λ(v) for a variety of many-body systems, both chaotic and integrable. The so-called light cone for the spreading of operators is defined by λ(ˆnvB(ˆn))=0, with a generally direction-dependent butterfly speed vB(ˆn). In spatially local systems, λ(v) is negative outside the light cone where it takes the form λ(v)∼−(v−vB)α near vB, with the exponent α taking on various values over the range of systems we examine. The regime inside the light cone with positive Lyapunov exponents may only exist for classical, semiclassical, or large-N systems, but not for “fully quantum” chaotic systems with strong short-range interactions and local Hilbert space dimensions of order one.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/14e91f041b1b596be765ee462432627227b7bf64
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In Atomic and Molecular Physics, and Optics
- Tianci Zhou
- A. Nahum
- Matthew Fisher
- Nicholas Hunter-Jones
- J. Ruhman
- B. Skinner
- V. Khemani
- Yaodong Li
In Statistical and Nonlinear Physics
Citations in the corpus
- Emergent statistical mechanics of entanglement in random unitary circuits (2018, background): “However, the mapping of [12] shows that the function E2(v) is relevant to the scaling of the exponentially small tail of the out of time order correlator beyond the lightcone [95].”
- Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “The additional free energy cost means that, outside the lightcone, for x/t > vB , the OTOC scales as [64] C̃(x, t) ∼ e−μ(v)t, μ(v) ≡ seq (E(v)− v) .”