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Julian J Riccardo1, Jose L Riccardo1, Antonio J Ramirez-Pastor1

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This study introduces a new particle distribution for correlated states, extending Haldane

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Existing particle distribution models often assume independent particle states.
  • Correlated states introduce complexities in particle exclusion, particularly multiple exclusions.

Purpose of the Study:

  • To develop a novel particle distribution accounting for correlated states and multiple exclusions.
  • To introduce an exclusion spectrum function G(n) for occupation-dependent exclusion.

Main Methods:

  • Utilizing an ansatz for multiple exclusion in spatially correlated states.
  • Applying Haldane's state counting framework.
  • Introducing and analyzing the exclusion spectrum function G(n).

Main Results:

  • The new distribution recovers Haldane's statistics and Wu's distribution in the limit of noncorrelated states.
  • Thermodynamic and state occupation results are presented for ideal lattice gases of k-mers.
  • Demonstrated remarkable agreement with grand-canonical Monte Carlo simulations for k=2 to 10.

Conclusions:

  • The proposed distribution accurately models systems with multiple particle exclusions.
  • The model shows strong performance for increasing particle sizes (k-mers) where multiple exclusion is dominant.
  • This work provides a robust framework for understanding correlated particle systems.