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Scaling and Localization in Multipole-Conserving Diffusion.

Jung Hoon Han1, Ethan Lake2,3, Sunghan Ro2

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We investigate particle diffusion with conserved center of mass, revealing boundary localization and unique scaling behaviors. This study explores nonlinear diffusion equations and quantum analogs like Fermi surfaces and Bose-Einstein condensation.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Nonlinear Dynamics

Background:

  • Diffusion is a fundamental transport process.
  • Conserved quantities significantly impact system dynamics.
  • Classical and quantum systems exhibit distinct behaviors.

Purpose of the Study:

  • To explore diffusion in systems with conserved total center of mass.
  • To classify phenomena using nonlinear diffusion equations.
  • To investigate quantum analogs in fermionic and bosonic systems.

Main Methods:

  • Analysis of classical particle dynamics with conserved center of mass.
  • Derivation and classification of nonlinear diffusion equations.
  • Investigation of quantum fermionic and bosonic systems.

Main Results:

  • Equilibrium distributions show exponential localization at boundaries in finite systems.
  • An unusual approach to equilibrium exhibits scaling with dynamical exponent z=4+d.
  • Quantum systems display real-space Fermi surfaces and Bose-Einstein condensation analogs.

Conclusions:

  • Conserved center of mass dynamics leads to unique diffusion behaviors.
  • Nonlinear diffusion equations provide a framework for classifying these phenomena.
  • Quantum analogs reveal rich emergent phenomena in analogous systems.