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Navier-Stokes Equations for Low-Temperature One-Dimensional Quantum Fluids.

Andrew Urichuk1, Stefano Scopa1,2, Jacopo De Nardis1

  • 1Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, <a href="https://ror.org/043htjv09">CY Cergy Paris Université</a>, 95302 Cergy-Pontoise Cedex, France.

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Summary
This summary is machine-generated.

One-dimensional quantum fluids exhibit conventional viscous hydrodynamics at low temperatures. Viscosity remains relevant even at zero temperature, with universal scaling linked to quantum fluid parameters.

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Area of Science:

  • Quantum fluid dynamics
  • Low-temperature physics
  • Statistical mechanics

Background:

  • One-dimensional interacting quantum fluids, like the Lieb-Liniger gas, present unique challenges for hydrodynamic descriptions.
  • Understanding their behavior at low temperatures is crucial for fundamental physics and potential applications.

Purpose of the Study:

  • To investigate the low-temperature hydrodynamic behavior of one-dimensional interacting quantum fluids.
  • To determine the universal scaling of dynamic viscosity and its relevance at zero temperature.
  • To reconcile theoretical predictions with experimental observations of quantum fluid fluctuations.

Main Methods:

  • Computation of the low-temperature limit of generalized hydrodynamics.
  • Analysis of the Navier-Stokes equations for density, fluid velocity, and temperature.
  • Derivation of universal expressions for dynamic viscosity in terms of the Luttinger liquid parameter (K) and density.

Main Results:

  • The quantum fluid is accurately described by conventional viscous hydrodynamics at low temperatures.
  • Dynamic viscosity scales universally with temperature, Luttinger liquid parameter (K), and density.
  • A finite heating factor at zero temperature indicates the persistent relevance of viscous contributions.
  • Kinematic viscosity diverges in the semiclassical limit, aligning with Kardar-Parisi-Zhang fluctuation observations.

Conclusions:

  • Low-temperature quantum fluids exhibit universal viscous hydrodynamic behavior.
  • Viscous effects remain significant even at absolute zero temperature.
  • The study provides a unified framework for understanding quantum fluid dynamics across different temperature regimes.