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Kinetic theory for classical and quantum many-body chaos
Sašo Grozdanov1, Koenraad Schalm2, Vincenzo Scopelliti2
1Center for Theoretical Physics, MIT, Cambridge, Massachusetts 02139, USA.
Physical Review. E
|February 21, 2019
Summary
Quantum chaos in field theories connects to Boltzmann-type kinetic equations. This reveals that particle exchange dynamics govern chaotic behavior and Lyapunov exponents in systems like dilute gases.
Area of Science:
- Quantum Field Theory
- Statistical Mechanics
- Chaos Theory
Background:
- Out-of-time-ordered correlators (OTOCs) are key measures of quantum chaos.
- Deriving chaotic many-body dynamics from fundamental principles remains a challenge.
- Kinetic equations describe particle transport but their connection to chaos is complex.
Purpose of the Study:
- To establish a precise connection between quantum chaos measures and kinetic equations.
- To provide a concrete derivation for chaotic dynamics from first principles.
- To elucidate the role of particle exchange in chaotic systems.
Main Methods:
- Analysis of the late-time limit of out-of-time-ordered correlation functions.
- Equating OTOCs to a Boltzmann-type kinetic equation for gross particle exchange.
- Identifying the Lyapunov exponent with exponential growth in particle exchange.
Main Results:
- The out-of-time-ordered correlation function in the late-time limit equals a Boltzmann-type kinetic equation.
- This kinetic equation describes total gross particle exchange, weighted by energy.
- The Lyapunov exponent is determined by the exponential growth of this gross exchange.
Conclusions:
- This work provides a mathematically rigorous link between quantum chaos and kinetic theory.
- The physics of transport and scrambling in dilute gases are unified by the same scattering processes.
- The derivation offers a concrete framework for understanding chaotic dynamics in many-body systems.
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