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A system at equilibrium is in a state of dynamic balance, with forward and reverse reactions taking place at equal rates. If an equilibrium system is subjected to a change in conditions that affects these reaction rates differently (a stress), then the rates are no longer equal and the system is not at equilibrium. The system will subsequently experience a net reaction in the direction of a greater rate (a shift) that will re-establish the equilibrium. This phenomenon is summarized by Le...
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Related Experiment Video

Updated: Sep 30, 2025

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Corrections to reaction-diffusion dynamics above the upper critical dimension.

Johannes Hofmann1

  • 1Department of Physics, Gothenburg University, 41296 Gothenburg, Sweden.

Physical Review. E
|March 16, 2022
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Summary

This study reveals that corrections to reaction-diffusion scaling are determined by complex memory effects, not simple rate changes. These findings advance understanding of k-particle annihilation processes in statistical physics.

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Area of Science:

  • Statistical physics
  • Chemical kinetics
  • Quantum gas dynamics

Background:

  • Reaction-diffusion models are fundamental in statistical physics for describing chemical reaction dynamics.
  • Mean-field theory typically governs the leading-order late-time scaling of k-particle annihilation processes (kA→∅) above the upper critical dimension.

Purpose of the Study:

  • To investigate corrections to the late-time scaling of k-particle annihilation processes above the upper critical dimension.
  • To determine the nature of memory effects influencing these reaction dynamics.

Main Methods:

  • Utilizing a Bose gas representation to map real-time reactant dynamics to imaginary-time evolution.
  • Applying methods from ultracold quantum gases and nuclear physics to compute corrections.
  • Analyzing higher-order correlation functions to capture subcluster memory effects.

Main Results:

  • Leading corrections to scaling are not due to simple renormalization of the reaction rate.
  • Corrections are dictated by higher-order correlation functions reflecting subcluster memory effects.
  • Exact computations of these corrections were performed for various annihilation processes with k>2.

Conclusions:

  • The study refines the understanding of scaling corrections in reaction-diffusion systems.
  • Identifies complex memory effects as crucial for accurate modeling of k-particle annihilation.
  • Provides a framework for analyzing similar processes in statistical and quantum physics.