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Anomalous diffusion and Noether's second theorem.

Matteo Baggioli1, Gabriele La Nave2, Philip W Phillips3

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This summary is machine-generated.

This study reveals that anomalous diffusion and heat transport stem from Lorentz-violating gauge transformations, challenging field theory principles. These transformations explain generalized Fick

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Area of Science:

  • Theoretical physics
  • Condensed matter physics
  • Quantum field theory

Background:

  • Conserved currents typically have fixed dimensions, lacking anomalous dimensions.
  • Anomalous diffusion (L∝t^γ, γ≠1/2) and heat transport (diverging thermal conductivity) violate this principle.
  • Lorentz invariance violation is a common, yet unexplained, link in these phenomena.

Purpose of the Study:

  • To identify the underlying mechanism behind anomalous transport phenomena.
  • To demonstrate how nonlocal equations of motion arise from fundamental principles.
  • To generalize Fick's and Fourier's laws for anomalous transport.

Main Methods:

  • Derivation from Noether's second theorem.
  • Application of Lorentz-violating gauge transformations.
  • Analysis of resulting generalized diffusion and heat transport equations.

Main Results:

  • Anomalous dimensions in conserved currents arise from Lorentz-violating gauge transformations.
  • Phenomenological nonlocal equations of motion are derived from these transformations.
  • Generalized forms of Fick's and Fourier's laws are established.
  • Fractional equations of motion directly lead to Goldstone modes (ω∝k^α).

Conclusions:

  • Lorentz-violating gauge transformations provide a unified framework for anomalous transport.
  • This approach reconciles observed anomalies with theoretical expectations.
  • The findings offer a new perspective on fundamental transport laws in physics.