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Undular Diffusion in Nonlinear Sigma Models.

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Charge transport in non-Abelian theories reveals two distinct diffusion laws upon symmetry breaking. Unconventional diffusion emerges in transversal sectors, differing from normal diffusion in Cartan fields.

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Area of Science:

  • * Theoretical physics
  • * Condensed matter physics
  • * Quantum field theory

Background:

  • * Explores charge transport in nonrelativistic classical field theories.
  • * Focuses on theories invariant under non-Abelian unitary Lie groups.
  • * Investigates grand-canonical ensembles at finite charge densities (polarized ensembles).

Purpose of the Study:

  • * To examine the full structure of two-point dynamical correlation functions.
  • * To understand charge transport laws upon explicit breaking of non-Abelian symmetry.
  • * To characterize diffusion in both unbroken and broken symmetry sectors.

Main Methods:

  • * Analysis of two-point dynamical correlation functions.
  • * Examination of grand-canonical ensembles at finite charge densities.
  • * Theoretical analysis of symmetry breaking in non-Abelian field theories.

Main Results:

  • * Two distinct transport laws with dynamical exponent z=2 emerge upon symmetry breaking.
  • * Cartan fields exhibit normal diffusion in the unbroken symmetry sector.
  • * Transversal sectors show unconventional diffusion with a complex diffusion constant and undulating spatiotemporal correlations.

Conclusions:

  • * Unconventional diffusion in transversal sectors is governed by nonlinear Goldstone modes.
  • * The imaginary component of the diffusion constant depends on polarization strength.
  • * Higher rank symmetry models demonstrate an absence of dynamical correlations among distinct transversal sectors.