A theory of first order dissipative superfluid dynamics (1105.3733v2)

Abstract: We determine the most general form of the equations of relativistic superfluid hydrodynamics consistent with Lorentz invariance, time-reversal invariance, the Onsager principle and the second law of thermodynamics at first order in the derivative expansion. Once parity is violated, either because the $U(1)$ symmetry is anomalous or as a consequence of a different parity-breaking mechanism, our results deviate from the standard textbook analysis of superfluids. Our general equations require the specification of twenty parameters (such as the viscosity and conductivity). In the limit of small relative superfluid velocities we find a seven parameter set of equations. In the same limit, we have used the AdS/CFT correspondence to compute the parity odd contributions to the superfluid equations of motion for a generic holographic model and have verified that our results are consistent.

Overview of "A Theory of First Order Dissipative Superfluid Dynamics"

The paper, "A Theory of First Order Dissipative Superfluid Dynamics," by Bhattacharya et al. provides a comprehensive exploration of the equations governing relativistic superfluid hydrodynamics, integrating dissipative effects at the first order of a gradient expansion. This paper is essential in understanding superfluid behavior beyond the ideal assumptions, which typically neglect dissipative terms. The authors establish a general framework that incorporates Lorentz invariance, time-reversal invariance, the Onsager principle, and the second law of thermodynamics, while accommodating parity violation and triangle anomalies.

Key Contributions

1. General Formulation: The paper systematically derives the most general form for the hydrodynamic equations governing a 3+1 dimensional superfluid. These equations are consistent with fundamental symmetries and thermodynamic constraints.
2. Dissipative Dynamics: By extending the Landau-Tisza framework, the authors incorporate dissipative corrections, thereby illuminating processes such as viscosity and conductivity that are pivotal in real-world superfluid flows.
3. Lorentz and Time-Reversal Invariance: The paper crucially maintains Lorentz invariance and adheres to the Onsager principle, ensuring that the formulation is applicable to both relativistic and non-relativistic limits.
4. Influence of Anomalies: A distinctive feature here is the consideration of parity violation mechanisms, notably triangle anomalies. These elements lead to divergence from traditional analyses and introduce novel transport coefficients.
5. Entropy Current Analysis: The researchers depart from canonical forms of the entropy current, a vital aspect for ensuring the theory adheres to the second law of thermodynamics universally. This approach reveals restrictions on transport coefficients in flat spacetime derived from curved backgrounds.

Numerical and Theoretical Insights

• Parameterized Equations: The equations necessitate 20 parameters in total, with distinct parametric sets for parity-preserving and parity-violating scenarios. Notably, the authors delineate a pathway where a limiting case with small superfluid velocities reduces this parameter space to seven.
• AdS/CFT Correspondence Validation: In assessing holographic models via AdS/CFT correspondence, the authors confirm consistency with their theoretical framework. This provides an external validation to the derived superfluid dynamics, illustrating the coherence between theoretical and string-theory-based descriptions.

Implications and Future Directions

The paper sets a robust theoretical basis for understanding superfluid dynamics in various contexts, including astrophysical scenarios and laboratory superfluids like helium. The insights regarding transport coefficients and parity violation may contribute to designing experiments aiming to probe these specific aspects in superfluid systems.

• Experimental Applications: The framework could be crucial in the analysis of non centro symmetric superconductors, potentially unveiling subtle effects overlooked under traditional models.
• Extensions to Higher Dimensions: The work opens up channels to investigate superfluid dynamics in dimensions beyond 3+1, which could harbor new phenomena under similar dissipative frameworks.
• Entropy Considerations: Future explorations might explore entropic contributions in non-equilibrium conditions within superfluids, using the newly proposed formulations.

Conclusion

Bhattacharya et al.'s work on superfluid dynamics offers pivotal insights into a complex interplay of dissipative processes in a relativistic framework. It stands out by accounting for anomalies, maintaining rigorous thermodynamic consistency, and projecting a path for future experimental and theoretical investigations in both fluid and high-energy physics contexts.