Random reverse-cyclic matrices and screened harmonic oscillator.
We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic oscillator. The connection enables us to obtain all the correlations among the particle positions moving in a screened harmonic potential. The density of nontrivial eigenvalues of this ensemble is found to be of the Wigner form and admits a hole at the origin, in contrast to the semicircle law of the Gaussian orthogonal ensemble of random matrices. The spacing distributions assume different forms ranging from Gaussian-like to Wigner.
RIB Group, Variable Energy Cyclotron Centre, 1/AF Bidhan nagar, Kolkata 700 064, India. shashi@vecc.gov.in
Shashi C L
SC
Srivastava
Sudhir R
SR
Jain
D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical; D009991:Oscillometry / Q000379:methods*
D003102:Colloids