Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas

Abstract: Shear viscosity is a measure of the amount of dissipation in a simple fluid. In kinetic theory shear viscosity is related to the rate of momentum transport by quasi-particles, and the uncertainty relation suggests that the ratio of shear viscosity eta to entropy density s in units of hbar/k_B is bounded by a constant. Here, hbar is Planck's constant and k_B is Boltzmann's constant. A specific bound has been proposed on the basis of string theory where, for a large class of theories, one can show that eta/s is greater or equal to hbar/(4 pi k_B). We will refer to a fluid that saturates the string theory bound as a perfect fluid. In this review we summarize theoretical and experimental information on the properties of the three main classes of quantum fluids that are known to have values of eta/s that are smaller than hbar/k_B. These fluids are strongly coupled Bose fluids, in particular liquid helium, strongly correlated ultracold Fermi gases, and the quark gluon plasma. We discuss the main theoretical approaches to transport properties of these fluids: kinetic theory, numerical simulations based on linear response theory, and holographic dualities. We also summarize the experimental situation, in particular with regard to the observation of hydrodynamic behavior in ultracold Fermi gases and the quark gluon plasma.

• The paper demonstrates that nearly perfect fluidity emerges in quantum systems as shear viscosity approaches the universal minimum predicted by holographic and kinetic theories.
• It employs kinetic theory, numerical simulations, and holographic dualities to model the low η/s ratios in ultracold Fermi gases, liquid helium, and quark-gluon plasma.
• The study offers key insights into superfluidity and collective behavior, bridging quantum mechanics with macroscopic fluid dynamics across diverse systems.

Overview of Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas

The paper by Thomas Schaefer and Derek Teaney provides a comprehensive study of nearly perfect fluidity, examining the ratio of shear viscosity ($\eta$) to entropy density ($s$) across different types of quantum fluids: strongly coupled Bose fluids like liquid helium, ultracold Fermi gases, and the quark-gluon plasma (QGP). These systems are particularly interesting due to their low values of the $\eta/s$ ratio, approaching the conjectured lower bound derived from string theory and holography, $\hbar/(4\pi k_B)$.

Key Insights

The authors explore the theoretical and experimental understanding of quantum fluids, focusing on their transport properties. The idea that such fluids can be almost ideal, with shear viscosity nearly saturating the string theory bound, is an important theme.

• Quantum Fluids of Interest: The fluids examined include:
  • Liquid Helium: Known for its superfluid properties and low viscosity below the lambda point.
  • Ultracold Atomic Fermi Gases: These gases near a Feshbach resonance demonstrate strong interactions and pair formation, resembling both BEC and BCS states.
  • Quark-Gluon Plasma: Created in heavy-ion collisions, this state of matter exhibits collective behavior and low viscosity, indicative of nearly perfect fluidity.
• Theoretical Approaches:
  • Kinetic Theory: Provides a framework for understanding the shear viscosity in terms of momentum transport by quasi-particles.
  • Numerical Simulations: Used to model fluid dynamics and compute transport properties in quantum gases.
  • Holographic Dualities: These provide a novel approach to computing transport properties in strongly coupled quantum fluids, utilizing the AdS/CFT correspondence to derive $\eta/s$.
• Experimental Observations:
  • Ultracold Atomic Gases: Evidence of hydrodynamic behavior is observed via damping of collective modes and elliptic flow.
  • Heavy Ion Collisions: Resulting in QGP, these experiments display behavior consistent with hydrodynamic models that predict a low shear viscosity.

Implications and Future Directions

The findings in the paper have both practical and theoretical implications. The researchers highlight the universality of the minimum $\eta/s$ across different systems, suggesting a profound connection between quantum mechanics and fluid dynamics. From a practical perspective, understanding these fluids can lead to advances in fields ranging from superconductivity to cosmology.

Looking forward, there are several avenues for further exploration:

1. Refining Theoretical Methods: Developing more accurate theoretical models and simulations, particularly those that bridge kinetic theory and holographic techniques, could enhance our understanding of strongly coupled systems.
2. Advanced Experimental Techniques: Improving experimental capabilities in ultracold atoms and heavy-ion physics could provide deeper insights, particularly around the quantum-to-classical transition in these fluids.
3. Novel Quantum Fluids: Exploring new materials and conditions that might host nearly perfect fluidity, potentially shedding light on other branches of condensed matter and high energy physics.

In conclusion, Schaefer and Teaney's paper significantly contributes to the understanding of nearly perfect fluids, bringing together concepts from a variety of fields. The unifying theme of low $\eta/s$ values across vastly different quantum systems is indicative of a broader phenomenological foundation potentially rooted in the principles of quantum mechanics and information theory.