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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Theoretical Physics

Background:

  • The behavior of systems with conserved quantities is crucial in statistical mechanics.
  • Understanding transport properties like ballistic and diffusive motion is key to characterizing physical systems.
  • Stochastic perturbations can significantly alter the dynamics and integrability of physical models.

Purpose of the Study:

  • To investigate the emergence of diffusive hydrodynamics in a 1D hard-rod gas model.
  • To analyze the impact of stochastic backscattering on transport properties.
  • To derive exact expressions for transport matrices and structure factors in the presence of noise.

Main Methods:

  • Analysis of the one-dimensional hard-rod gas model.
  • Introduction of stochastic backscattering as a perturbation.
  • Derivation of exact expressions in the small noise limit.
  • Calculation of diffusion and structure factor matrices.

Main Results:

  • The system exhibits a crossover from ballistic to diffusive transport.
  • Infinitely many conserved quantities are preserved, related to even velocity moments.
  • Diffusion and structure factor matrices generically possess off-diagonal components.
  • The particle density structure factor is non-Gaussian and singular at the origin.
  • Return probability shows logarithmic deviations from pure diffusion.

Conclusions:

  • Stochastic backscattering in the 1D hard-rod gas leads to diffusive hydrodynamics while preserving some integrability.
  • The derived off-diagonal components and non-Gaussian structure factor highlight complex emergent behavior.
  • Logarithmic deviations in return probability offer a unique signature of this system's dynamics.