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Microscopic inclusion statistics in a discrete one-body spectrum.

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We introduce inclusion statistics, a new quantum statistics where particles cluster together. This contrasts with exclusion statistics and reveals unique properties in quantum systems.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics

Background:

  • Exclusion statistics governs particle behavior, preventing simultaneous occupation of quantum states.
  • Bosonic statistics allows multiple particles in the same state, but with standard statistical weights.

Purpose of the Study:

  • To formulate a microscopic theory of inclusion statistics.
  • To explore the statistical properties of quantum states under inclusion statistics.
  • To investigate the implications for a quantum gas in a harmonic potential.

Main Methods:

  • Derivation of microscopic occupation multiplicities for one-body quantum states.
  • Factorization of multiplicities into clusters of neighboring occupied states.
  • Application to a one-dimensional quantum gas in a harmonic trap.

Main Results:

  • Inclusion statistics demonstrates a tendency for particles to coalesce.
  • Occupation multiplicities exhibit enhanced statistical weights for clustered states.
  • A Calogero-like n-body inclusion spectrum emerges for the quantum gas.

Conclusions:

  • Inclusion statistics provides a novel framework contrasting with exclusion principles.
  • The derived properties offer new insights into quantum particle interactions and correlations.
  • The Calogero-like spectrum suggests potential for new physical phenomena in confined quantum systems.