Summary
The study develops an effective equation of motion for binary Bose superfluids, extending the classical Cahn-Hilliard model to quantum fluids. It reveals that domain coarsening dynamics with growth law L(t) ∼ t²/³ arises from interactions and quantum pressure, not hydrodynamics.
Highlights
- Derivation of an effective motion equation generalizing Cahn-Hilliard theory to binary Bose superfluids.
- Identification of the order parameter as the relative density difference between species.
- Demonstration that domain growth follows L(t) ∼ t²/³ due to competing interactions and quantum pressure.
- Hydrodynamic flow effects predicted to cause crossover to viscous and inertial regimes are negligible initially.
- Introduction of normalized total density and density imbalance fluctuations as key variables.
- Confirmation of Porod’s law in structure factor and characteristic interface shapes.
- Numerical simulations corroborate theoretical predictions and define the effective theory’s validity range.
Key Insights
- Effective Model Development: By reformulating the microscopic Hamiltonian into an effective equation of motion, the authors successfully extend classical phase separation frameworks to quantum superfluids, capturing essential quantum effects like quantum pressure.
- Order Parameter and Spin Variables: Choosing the relative density difference Ï• as the order parameter allows describing spinodal decomposition and phase separation dynamics with precision, highlighting the central role of the spin modes in superfluid coarsening.
- Domain Growth Law and Mechanism: The algebraic domain growth L(t) ∼ t²/³ is attributed not to fluid hydrodynamics but to a balance between interspecies interactions and quantum pressure, providing deeper insight into coarsening beyond classical fluid analogies.
- Hydrodynamic Flow Influence: While hydrodynamic flows have been hypothesized to induce asymptotic scaling crossovers in domain growth, this work shows that such effects appear only at longer timescales, with initial dynamics dominated by intrinsic quantum effects.
- Interface Properties and Scaling: The study confirms that domain interfaces obey Porod’s law in momentum space and possess well-defined tension, essential for understanding the microscopic structure during phase separation.
- Numerical Validation: Simulations using coupled Gross-Pitaevskii equations affirm the effective theory’s predictions, including the growth exponent and structural correlations, supporting the model’s robustness and practical relevance.
- Decoupling of Density and Spin Modes: The small coupling between total density fluctuations and spin dynamics validates approximations that treat these modes nearly independently, simplifying the theoretical treatment and enhancing conceptual clarity.
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Citation
Gliott, E., Piekarski, C., & Cherroret, N. (2025). Coarsening of binary Bose superfluids: an effective theory (Version 1). arXiv. http://doi.org/10.48550/ARXIV.2504.12462