Kinetic theory for classical and quantum many-body chaos
Abstract
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.
- Authors:
-
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Leiden Univ. (Netherlands)
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1637335
- Alternate Identifier(s):
- OSTI ID: 1489861; OSTI ID: 1611575
- Grant/Contract Number:
- SC0011090
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. E
- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 1; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; finite temperature field theory; kinetic theory; quantum chaos; quantum field theory; quantum transport; Physics
Citation Formats
Grozdanov, Sašo, Schalm, Koenraad, and Scopelliti, Vincenzo. Kinetic theory for classical and quantum many-body chaos. United States: N. p., 2019.
Web. doi:10.1103/PhysRevE.99.012206.
Grozdanov, Sašo, Schalm, Koenraad, & Scopelliti, Vincenzo. Kinetic theory for classical and quantum many-body chaos. United States. https://doi.org/10.1103/PhysRevE.99.012206
Grozdanov, Sašo, Schalm, Koenraad, and Scopelliti, Vincenzo. Tue .
"Kinetic theory for classical and quantum many-body chaos". United States. https://doi.org/10.1103/PhysRevE.99.012206. https://www.osti.gov/servlets/purl/1637335.
@article{osti_1637335,
title = {Kinetic theory for classical and quantum many-body chaos},
author = {Grozdanov, Sašo and Schalm, Koenraad and Scopelliti, Vincenzo},
abstractNote = {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.},
doi = {10.1103/PhysRevE.99.012206},
journal = {Physical Review. E},
number = 1,
volume = 99,
place = {United States},
year = {Tue Jan 08 00:00:00 EST 2019},
month = {Tue Jan 08 00:00:00 EST 2019}
}
Web of Science
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