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Many-Body Chaos in Thermalized Fluids
Sugan D Murugan1, Dheeraj Kumar1,2, Subhro Bhattacharjee1
1International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India.
Physical Review Letters
|October 1, 2021
Summary
Researchers linked temperature (T) and chaos (Lyapunov exponents, λ) in many-body systems. They found chaos scales with the square root of temperature (λ∝√T) in thermalized flows, suggesting universal behavior.
Area of Science:
- Statistical Mechanics
- Nonlinear Dynamics
- Condensed Matter Physics
Background:
- Understanding the relationship between thermodynamic variables and chaos is crucial for many-body systems.
- Lyapunov exponents (λ) quantify chaos, while temperature (T) is a key thermodynamic variable.
Purpose of the Study:
- To investigate the scaling relationship between Lyapunov exponents and temperature in thermalized flows.
- To explore the universality of this relationship across different dimensions and system types.
Main Methods:
- Utilized nonlinear fluid equations in one and three dimensions.
- Analyzed thermalized flow dynamics to calculate Lyapunov exponents.
Main Results:
- Demonstrated a direct proportionality between Lyapunov exponents and the square root of temperature (λ∝√T) in thermalized flows.
- Observed agreement with findings from frustrated spin systems, indicating potential universality.
- Reconciled the effects of many-body chaos on both equilibrium and non-equilibrium systems.
Conclusions:
- The study provides strong evidence for the conjectured thermal scaling of Lyapunov exponents.
- The findings suggest an underlying universal mechanism linking thermodynamic temperature and chaos in diverse many-body systems.
- Dynamical flow structures are key to relating chaos and temperature, unifying concepts of equilibration and non-equilibrium dynamics.
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