Soliton Gases and Generalized Hydrodynamics.

Area of Science:

• Quantum physics
• Statistical mechanics
• Classical dynamics

Background:

• Generalized hydrodynamics (GHD) describes integrable quantum systems.
• Existing models often lack efficient numerical solvers, especially with external forces.

Purpose of the Study:

• To establish a classical gas model that reproduces generalized hydrodynamics (GHD).
• To provide an efficient numerical method for GHD applicable to quantum systems.
• To demonstrate a quantum-classical equivalence in hydrodynamics.

Main Methods:

• Introducing a family of classical gases generalizing the hard-rod gas.
• Particles exhibit velocity-dependent jumps upon collision, mimicking soliton scattering.
• Developing a molecular dynamics approach for GHD.

Main Results:

• The proposed classical gas model fully reproduces GHD equations.
• A novel, efficient, and flexible numerical solver for GHD is presented.
• A direct quantum-classical equivalence is established between quantum models and their soliton-like wave packet gases.

Conclusions:

• The classical gas model offers a powerful "molecular dynamics" for GHD.
• This framework unifies the description of quantum and classical integrable systems.
• The theory has direct applications in quantum chains and cold-atom experiments (Lieb-Liniger model).