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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Area of Science:

  • Condensed matter physics
  • Quantum field theory
  • High-energy physics

Background:

  • Charge diffusion is crucial in understanding transport phenomena in various physical systems.
  • Nonlinear self-interactions and diffusive fluctuations can significantly alter charge transport dynamics.
  • Previous models often simplified these interactions, limiting their applicability.

Purpose of the Study:

  • To develop a more comprehensive effective field theory (EFT) for charge diffusion.
  • To investigate the impact of nonlinear self-interactions and the slowest ultraviolet (UV) mode on charge diffusion.
  • To explore the implications for experimental systems like bad metals and the quark-gluon plasma.

Main Methods:

  • Construction of a UV-regulated effective field theory (EFT).
  • Inclusion of the slowest ultraviolet (UV) mode within the EFT framework.
  • Analysis of the retarded density-density Green's function and its properties.

Main Results:

  • The relaxation time of the UV mode is found to be protected from renormalization.
  • This finding is consistent with experimental observations in bad metal systems.
  • The retarded density-density Green's function exhibits four branch points, extending the theory's applicability.

Conclusions:

  • The developed EFT provides a robust framework for studying charge diffusion with nonlinearities.
  • The protected relaxation time offers a key insight into the behavior of diffusive systems.
  • The results have potential implications for understanding heavy-ion collisions and the quark-gluon plasma.