Quantum Generalized Hydrodynamics

Area of Science:

• Quantum Many-Body Physics
• Statistical Mechanics
• Condensed Matter Theory

Background:

• Classical Euler hydrodynamic equations describe many-particle quantum systems at low frequencies and long wavelengths.
• Generalized Hydrodynamics (GHD) extends this framework to one-dimensional quantum integrable models.
• Standard GHD, however, neglects quantum fluctuations, limiting its accuracy for certain quantum effects.

Purpose of the Study:

• To incorporate quantum fluctuation effects into the generalized hydrodynamics framework.
• To develop a more comprehensive theory for one-dimensional quantum systems, particularly those with zero entropy.
• To describe quantum fluctuations in truly nonequilibrium scenarios where conventional theories are insufficient.

Main Methods:

• Quantization of the generalized hydrodynamics (GHD) framework.
• Focus on one-dimensional Bose gas with delta repulsion and zero entropy states.
• Utilizing the thermodynamic Bethe ansatz to determine effective parameters.

Main Results:

• Developed a theory of quantum GHD that accounts for quantum fluctuations.
• The quantum GHD theory is equivalent to a multicomponent Luttinger liquid theory.
• Effective parameters are determined by the thermodynamic Bethe ansatz.

Conclusions:

• Quantum GHD successfully describes quantum fluctuations in one-dimensional quantum systems.
• This new framework extends the applicability of GHD to nonequilibrium systems.
• The theory provides a more accurate description of quantum many-body dynamics beyond classical hydrodynamic limits.