Hydrodynamic properties in soliton field theory

TL;DR

This work establishes a deep correspondence between hydrodynamic instabilities and soliton field theory by showing that soliton formation can proceed via a sound-mode instability driven by thermodynamic instability, leading to phase-separated two-phase configurations with interfaces that act as fluid membranes. It derives a Rayleigh–Plateau–like membrane instability for soliton interfaces in the thin-wall limit, confirming that soliton boundaries behave like surface-tension–carrying membranes and can undergo topological transitions to reduce surface area. The analysis identifies three key instabilities—tachyonic, sound-mode, and membrane—and elaborates the resulting evolution pathways, including phase separation into solitons or vacuum bubbles and fragmentation of string-like solitons into multiple Q-balls. The framework offers a unified, field-theoretic description of interfacial hydrodynamics with potential applications to cosmology, holographic fluids, and gravitational systems, where soliton fluids can model phase transitions and horizon-like membranes.

Abstract

The crucial role of hydrodynamic instabilities in soliton field theory is revealed. We demonstrate that the essential of soliton formation mechanism is the sound mode instability induced by thermodynamic instability. This instability triggers phase separation, where new thermal phases are generated to produce solitons. These solitons can be regarded as a coexistence state composed of a matter phase and a vacuum phase, with an interface providing surface tension to maintain dynamical equilibrium. The phase separation mechanism naturally allows the existence of vacuum bubbles, characterized by a vacuum phase surrounded by a matter phase with negative pressure. Furthermore, we show that the soliton interface resembles a fluid membrane, whose interface pressure satisfies a Young-Laplace-type relation, resulting in the emergence of the membrane instability induced by surface tension. In the thin-wall limit, the dispersion relation is analytically derived. This instability triggers topological transition of the interface, splitting a cylindrical interface into multiple spheres with a smaller total surface area. Such results highlight the duality between solitons and fluids, providing a field theory description for hydrodynamics with interfaces.

Figures (10)

• Figure 1: The tidal surge of the Qiantang River. During this process, the tidal bore maintains its shape as it propagates across the river surface, leaving behind a raised water level, resembling the motion of a one-dimensional soliton.
• Figure 2: Phase diagrams of holographic fluids with a thermal first-order phase transition: free energy density (a) and entropy density (b) as functions of temperature.
• Figure 3: Schematic diagram of the Rayleigh-Plateau model with a water column of length $L$ and radius $R$ being affected by a perturbation of wavelength $\lambda$. $R_{1}$ and $R_{2}$ denote the principal radii of curvature in the cross-sectional and axial directions of the cylinder, respectively.
• Figure 4: The physical properties in the case of the scalar potential $V_{1}$. (a, b): The derivative of the scalar potential $V'$ and the effective potential $U$ as functions of the squared scalar field $\phi^{2}$, with parameter $\kappa=0.5$. (c, d): The grand potential $\mathcal{F}$ and the squared effective mass $m^{2}_{V}$ as functions of the squared frequency $\omega^{2}$.
• Figure 5: The physical properties in the case of the scalar potential $V_{2}$. (a, b): The derivative of the scalar potential $V'$ and the effective potential $U$ as functions of the squared scalar field $\phi^{2}$, with parameter $K=-0.1$. (c, d): The grand potential $\mathcal{F}$ and the squared effective mass $m^{2}_{V}$ as functions of the squared frequency $\omega^{2}$.