Exact Large-Scale Fluctuations of the Phase Field in the Sine-Gordon Model

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory

Background:

• The sine-Gordon model is a fundamental model in quantum field theory and condensed matter physics.
• Understanding large-scale phase fluctuations is crucial for describing the behavior of various physical systems.

Purpose of the Study:

• To develop an exact theory and analytical formulas for large-scale phase fluctuations in the sine-Gordon model.
• To provide a framework valid for all regimes, temperatures, and interaction strengths.

Main Methods:

• Combining ballistic fluctuation theory with generalized hydrodynamics.
• Extending the phenomenological soliton-gas picture using generalized hydrodynamics modes.
• Utilizing Monte Carlo methods for numerical verification in the classical regime.

Main Results:

• First exact theory and analytical formulas for sine-Gordon model phase fluctuations.
• Demonstrated that stable quasiparticles exhibit coherent ballistic propagation, not diffusive spreading.
• Extensive numerical checks confirm analytical predictions in the classical regime.

Conclusions:

• The developed theory offers a qualitatively new understanding of phase fluctuations in the sine-Gordon model.
• Results are directly applicable to experimental systems like tunnel-coupled quasicondensates.