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Topological phases in population dynamics with rock-paper-scissors interactions.

Jinfeng Liang1, Qionglin Dai1, Hancheng Li1

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This study explores topological phases in non-quantum systems using Lotka-Volterra dynamics. Researchers identified distinct edge-localization states and a topological transition, offering new insights into topological phenomena.

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Area of Science:

  • Non-equilibrium physics
  • Complex systems dynamics
  • Topological matter

Background:

  • Topological phases are primarily studied in quantum systems.
  • The existence and characterization of topological phases in non-quantum systems remain an active research area.
  • Understanding boundary phenomena in complex systems is crucial.

Purpose of the Study:

  • To investigate topological phases in a non-quantum system.
  • To analyze edge-localization states in an antisymmetric Lotka-Volterra model.
  • To characterize the transition between different edge states.

Main Methods:

  • Modeling an antisymmetric Lotka-Volterra dynamics on a two-site cell chain with open boundary conditions.
  • Transforming population dynamics into a non-Hermitian quantum system.
  • Applying generalized topological band theory and winding number for analysis.

Main Results:

  • Discovery of two distinct edge-localization states: left and right.
  • Observation of exponential decay in mass distribution within boundary regions.
  • Identification of a sharp, topological transition between the two edge states.

Conclusions:

  • Topological phases can manifest in non-quantum systems like Lotka-Volterra dynamics.
  • The study successfully distinguishes and characterizes edge-localization states using topological concepts.
  • The findings contribute to a broader understanding of topological phenomena beyond quantum mechanics.