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Random coupling model of turbulence as a classical Sachdev-Ye-Kitaev model
Xu-Yao Hu1, Vladimir Rosenhaus2
1Center for Cosmology and Particle Physics, Department of Physics, New York University, 726 Broadway, New York, New York 10003, USA.
Physical Review. E
|December 20, 2023
Summary
A classical model of turbulence, the random coupling model, is analogous to the Sachdev-Ye-Kitaev (SYK) model. This connection offers new insights into quantum chaos and turbulence research.
Area of Science:
- * Physics
- * Fluid Dynamics
- * Quantum Mechanics
Background:
- * The Sachdev-Ye-Kitaev (SYK) model is a solvable model of quantum many-body chaos.
- * Classical turbulence is often described by the Navier-Stokes and nonlinear Schrödinger equations.
- * The random coupling model, a classical analog studied in turbulence, involves Gaussian-random couplings between many modes.
Purpose of the Study:
- * To establish a connection between the classical random coupling model and the quantum SYK model.
- * To derive the effective action for the random coupling model using path integral techniques.
- * To explore potential new physical realizations and turbulence models.
Main Methods:
- * Utilizing path integral methods to derive the effective action.
- * Applying large-N saddle point approximation to obtain an integral equation.
- * Comparing the derived equation with the SYK model's corresponding equation.
Main Results:
- * The path integral derivation yields an effective action for the random coupling model.
- * The large-N saddle point approximation results in an integral equation for the two-point function.
- * This equation closely resembles the equation found in the SYK model.
Conclusions:
- * A significant analogy exists between the classical random coupling model and the quantum SYK model.
- * This connection may facilitate new physical contexts for realizing the SYK model.
- * It also suggests novel models and analytical techniques for studying turbulence.
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