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Published on: December 4, 2017
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Navier-Stokes Equations for Nearly Integrable Quantum Gases.
1University of Warsaw, Faculty of Physics, Pasteura 5, 02-093 Warsaw, Poland.
Physical Review Letters
|February 6, 2025
Summary
This study demonstrates how Navier-Stokes equations emerge from quantum many-body systems. It reveals two distinct fluid regimes with unique viscous properties, derived from microscopic interactions.
Area of Science:
- Quantum many-body physics
- Hydrodynamics
- Statistical mechanics
Background:
- The Navier-Stokes equations are fundamental to fluid dynamics.
- Understanding their microscopic origins in quantum systems is a key challenge.
- Integrable quantum systems offer a tractable framework for studying emergent hydrodynamics.
Purpose of the Study:
- To derive the Navier-Stokes equations from the microscopic dynamics of nearly integrable 1D quantum many-body systems.
- To investigate the role of non-integrable interactions in shaping hydrodynamic behavior.
- To compute transport coefficients and identify different fluid regimes.
Main Methods:
- Extension of hydrodynamics for integrable models to include non-integrable interactions.
- Analysis of the effective Boltzmann equation with a detailed collision integral.
- Computation of transport coefficients for specific quantum many-body systems.
Main Results:
- The Navier-Stokes equations are shown to emerge from the studied quantum systems.
- Two distinct hydrodynamic regimes with differing viscous properties were identified.
- Transport coefficients were computed for coupled 1D cold-atomic gases, an experimentally relevant system.
Conclusions:
- The work provides a microscopic foundation for Navier-Stokes hydrodynamics in a quantum context.
- The findings highlight the importance of non-integrable interactions in determining fluid properties.
- The developed method offers a pathway to study hydrodynamics in various complex quantum systems.
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