On the Hydrodynamics of Unstable Excitations

Abstract: The generalized hydrodynamic (GHD) approach has been extremely successful in describing the out-of-equilibrium properties of a great variety of integrable many-body quantum systems. It naturally extracts the large-scale dynamical degrees of freedom of the system, and is thus a particularly good probe for emergent phenomena. One such phenomenon is the presence of unstable particles, traditionally seen via special analytic structures of the scattering matrix. Because of their finite lifetime and energy threshold, these are especially hard to study. In this paper we apply the GHD approach to a model possessing both unstable excitations and quantum integrability. The largest family of relativistic integrable quantum field theories known to have these features are the homogeneous sine-Gordon models. We consider the simplest non-trivial example of such theories and investigate the effect of an unstable excitation on various physical quantities, both at equilibrium and in the non-equilibrium state arising from the partitioning protocol. The hydrodynamic approach sheds new light onto the physics of the unstable particle, going much beyond its definition via the analytic structure of the scattering matrix, and clarifies its effects both on the equilibrium and out-of-equilibrium properties of the theory. Crucially, within this dynamical perspective, we identify unstable particles as finitely-lived bound states of co-propagating stable particles of different types, and observe how stable populations of unstable particles emerge in large-temperature thermal baths.

• The paper analyzes an integrable quantum field theory model with unstable particle excitations using generalized hydrodynamics (GHD).
• The inclusion of unstable particles significantly alters the hydrodynamic profile and contributes to distinct non-equilibrium dynamics, including parity breaking.
• The study's insights extend GHD techniques to systems with instabilities, potentially impacting condensed matter and cold atom physics.

On the Hydrodynamics of Unstable Excitations: An Expert Overview

The paper, "On the Hydrodynamics of Unstable Excitations," presents a comprehensive analysis of a unique integrable model within quantum field theory (QFT), focusing on the interplay between generalized hydrodynamics (GHD) and unstable particle excitations. Utilizing the $SU(3)_2$-homogeneous sine-Gordon (HSG) model, the researchers explore the implications of introducing unstable particles into a theoretically integrable system. The study offers novel insights into dynamical behaviors both in equilibrium and out-of-equilibrium, driven by the generalized hydrodynamic framework.

Key Observations and Results

1. Generalized Hydrodynamics and Integrable Systems: The paper builds upon the GHD framework, which effectively describes transport phenomena in integrable quantum systems. Through GHD, the researchers capture the impact of unstable excitations on dynamical observables, substantially advancing the understanding of non-equilibrium steady states (NESS).
2. Impact of Unstable Particles: The analysis reveals that the inclusion of unstable particles markedly alters the hydrodynamic profile. Despite being dynamically realized through complex scattering processes, these particles behave like long-lived bound states, providing a richer spectrum that influences particle density, currents, and thermodynamic properties.
3. Parity Breaking and Non-Equilibrium Dynamics: The $SU(3)_2$ model exhibits parity breaking, where the scattering matrix asymmetry leads to distinct transport and relaxation properties. This feature contributes to distinct non-equilibrium behaviors, emphasizing the profound effect of unstable excitations on the transport characteristics.
4. Temperature-Dependent Behavior: The study explores various temperature regimes, revealing a crossover between distinct hydrodynamic behaviors. At low temperatures, the system behaves like a dual free Majorana fermion model. As temperature increases, it transitions to a regime where the unstable excitation significantly contributes, effectively altering the RG flow towards an interacting CFT with a larger central charge.
5. Spectral Densities and Effective Velocities: The researchers provide a detailed account of effective velocities and spectral densities across temperature scales. Notably, the dynamics reflect a sophisticated interaction between stable and unstable particles, with effective velocities illustrating how scattering influences macroscopic observables like current and energy distributions.
6. Practical Implications and Future Directions: The insights from the HSG model lay groundwork for exploiting integrable structures in unexplored domains of condensed matter and atomic physics. By extending GHD techniques to systems with inherent instabilities, new experimental setups and theoretical models can be envisioned, enhancing the understanding of complex many-body dynamics.

Theoretical and Practical Implications

This research advances the theoretical frontiers of integrable systems by integrating GHD with models containing unstable particles. The ability to dynamically characterize such systems may find applications in designing robust transport mechanisms in quantum materials or analyzing cold atom setups where integrability plays a crucial role. Moreover, the approach devises a path toward resolving long-standing questions regarding the coexistence of stability and instability in one-dimensional quantum systems.

The paper essentially bridges two seemingly disparate realms: the exact solvability of integrable systems and the chaotic dynamics induced by instabilities. While integrable systems traditionally rely on stability, this study challenges and extends this paradigm. Future explorations may involve more complex multi-species models or studying dynamics near critical points, further enriching the dialogue between theoretical predictions and experimental realizations.

In summary, the study offers a compelling narrative of how unstable particle excitations within integrable quantum field theories can be systematically analyzed using generalized hydrodynamics. Such work enhances the theoretical toolbox available to physicists exploring quantum dynamics on both microscopic and macroscopic scales.