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Information-Theoretic Features of Many Fermion Systems: An Exploration Based on Exactly Solvable Models.

Angel Ricardo Plastino1, Diana Monteoliva2, Angelo Plastino3

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Information-based complexity measures reveal that systems with fewer fermions exhibit higher complexity than those with many. Complexity also increases as coupling-constant strengths decrease, highlighting the importance of low-lying energy states.

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exactly solvable modelmonopole interactionpairing interaction

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Area of Science:

  • Quantum physics
  • Many-body systems
  • Information theory

Background:

  • Finite quantum many-fermion systems are fundamental to molecular, atomic, and nuclear physics.
  • Information and complexity measures offer new insights into the structure and behavior of these systems.

Purpose of the Study:

  • Explore information-based complexity indicators in exactly soluble Lipkin models.
  • Compare structural details of different fermion systems using information theoretic tools.

Main Methods:

  • Utilized exactly soluble many-fermion models of the Lipkin kind.
  • Applied information measures and complexity indicators.
  • Analyzed the behavior of the two lowest lying energy states.

Main Results:

  • Fewer fermion systems demonstrate a higher degree of complexity than many-fermion systems.
  • Complexity increases as coupling-constant strengths decrease, without reaching zero.
  • The two lowest energy states significantly influence system complexity.

Conclusions:

  • Information-theoretic tools effectively differentiate and analyze fermion systems.
  • Lipkin models provide valuable insights into quantum many-body physics, analogous to the Hubbard model.