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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
Abstract:
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.
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