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Single-particle entropy in (1+2)-body random matrix ensembles.

V K B Kota1, R Sahu

  • 1Physical Research Laboratory, Ahmedabad 380 009, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 9, 2002
PubMed
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Embedded Gaussian orthogonal ensembles (EGOE(1+2)) predict a Gaussian energy dependence for single-particle entropy in chaotic systems. Numerical calculations confirm this theory, showing consistency with interacting Fermi systems.

Area of Science:

  • Nuclear Physics
  • Quantum Chaos
  • Statistical Mechanics

Background:

  • Random matrix theory is crucial for understanding complex quantum systems.
  • Entropy measures disorder and information content in quantum states.
  • Interacting Fermi systems exhibit complex energy level structures.

Purpose of the Study:

  • To theoretically predict and numerically verify the energy dependence of entropy in chaotic quantum systems.
  • To investigate the applicability of embedded Gaussian orthogonal ensembles (EGOE(1+2)) to Fermi systems.
  • To compare different entropy definitions within the EGOE(1+2) framework.

Main Methods:

  • Development of EGOE(1+2) models incorporating one-body and two-body interactions.
  • Numerical calculations of entropy using single-particle occupation numbers.

Related Experiment Videos

  • Comparison of theoretical predictions with numerical results and known data for Fermi systems.

    • Main Results:

    • EGOE(1+2) models predict a one-parameter Gaussian energy dependence for single-particle entropy in the chaotic regime.
    • Numerical EGOE(1+2) calculations validate the predicted Gaussian form.
    • The study demonstrates that single-particle, thermodynamic, and information entropies align with established results for interacting Fermi systems.

    Conclusions:

    • The EGOE(1+2) framework provides a successful theoretical description of entropy in chaotic quantum systems.
    • The findings offer insights into the statistical properties of complex quantum systems, particularly interacting Fermi systems.
    • This work bridges theoretical predictions from random matrix theory with numerical simulations and experimental observations.