Kinetic theory for classical and quantum many-body chaos

Grozdanov, Sašo; Schalm, Koenraad; Scopelliti, Vincenzo

doi:10.1103/PhysRevE.99.012206

Title: Kinetic theory for classical and quantum many-body chaos

Journal Article · Tue Jan 08 00:00:00 EST 2019 · Physical Review. E

DOI:https://doi.org/10.1103/PhysRevE.99.012206· OSTI ID:1637335

Grozdanov, Sašo ^[1]; Schalm, Koenraad ^[2]; Scopelliti, Vincenzo ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Leiden Univ. (Netherlands)

For perturbative scalar field theories, the late-time-limit of the out-of-time-ordered correlation function that measures (quantum) chaos is shown to be equal to a Boltzmann-type kinetic equation that measures the total gross (instead of net) particle exchange between phase-space cells, weighted by a function of energy. This derivation gives a concrete form to numerous attempts to derive chaotic many-body dynamics from ad hoc kinetic equations. A period of exponential growth in the total gross exchange determines the Lyapunov exponent of the chaotic system. Physically, the exponential growth is a front propagating into an unstable state in phase space. As in conventional Boltzmann transport, which follows from the dynamics of the net particle number density exchange, the kernel of this kinetic integral equation for chaos is also set by the 2-to-2 scattering rate. This provides a mathematically precise statement of the known fact that in dilute weakly coupled gases, transport and scrambling (or ergodicity) are controlled by the same physics.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0011090

OSTI ID:: 1637335

Alternate ID(s):: OSTI ID: 1489861; OSTI ID: 1611575

Journal Information:: Physical Review. E, Vol. 99, Issue 1; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 24 works

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Recent Developments in the Holographic Description of Quantum Chaos Jahnke, Viktor Advances in High Energy Physics, Vol. 2019 https://doi.org/10.1155/2019/9632708	journal	March 2019
Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions Keselman, Anna; Nie, Laimei; Berg, Erez arXiv https://doi.org/10.48550/arxiv.2009.10104	text	January 2020
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