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Related Concept Videos

Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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Related Experiment Video

Updated: May 21, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Random reverse-cyclic matrices and screened harmonic oscillator.

Shashi C L Srivastava1, Sudhir R Jain

  • 1RIB Group, Variable Energy Cyclotron Centre, 1/AF Bidhan nagar, Kolkata 700 064, India. shashi@vecc.gov.in

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 12, 2012
PubMed
Summary
This summary is machine-generated.

We linked random matrix theory to an N-body solvable model, revealing particle correlations in a screened harmonic oscillator potential. This analysis shows unique eigenvalue distributions and spacing patterns distinct from traditional random matrix ensembles.

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Area of Science:

  • Mathematical Physics
  • Random Matrix Theory
  • Statistical Mechanics

Background:

  • Random matrix theory is crucial for understanding complex quantum systems.
  • The Gaussian orthogonal ensemble (GOE) is a standard model, but alternative ensembles are needed for diverse physical phenomena.

Purpose of the Study:

  • To calculate the joint probability distribution function for random reverse-cyclic matrices.
  • To establish a connection between these matrices and an N-body exactly solvable model.
  • To analyze the resulting eigenvalue and particle position correlations.

Main Methods:

  • Calculation of the joint probability distribution function for random reverse-cyclic matrices.
  • Identification of the connection to an N-body screened harmonic oscillator model.
  • Derivation of particle position correlations and eigenvalue density analysis.

Main Results:

  • The joint probability distribution is linked to the screened harmonic oscillator model.
  • All particle position correlations in this potential were obtained.
  • The eigenvalue density follows a Wigner form with a central hole, differing from GOE's semicircle law.
  • Spacing distributions exhibited varied forms, from Gaussian-like to Wigner.

Conclusions:

  • Random reverse-cyclic matrices provide a novel connection to exactly solvable N-body systems.
  • This framework offers insights into quantum systems with screened harmonic potentials.
  • The distinct eigenvalue and spacing distributions highlight the importance of considering diverse random matrix ensembles.