• Generalized Freud’s equation and level densities with polynomial potential

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/081/02/0189-0202

• # Keywords

Orthogonal polynomial; Freud’s equation; Dyson–Mehta method; methods of resolvents; level density.

• # Abstract

Orthogonal polynomials with weight exp[$−NV (x)$] are studied where $V (x) = \sum_{k=1}^{d} a_{2k} x^{2k}$ is a polynomial of order $2d$. The generalized Freud’s equations for $d = 3, 4$ and 5 are derived and using this $R_{\mu} = h_{\mu} / h{\mu−1}$ is obtained, where $h_{\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\mu}$ , are obtained using Freud’s equation and using this, explicit results of level densities as $N \rightarrow \infty$ are derived using the method of resolvents. The results are compared with those using Dyson–Mehta method.

• # Author Affiliations

1. The Creative School, E-791, C.R. Park, New Delhi 110 017, India

• # Pramana – Journal of Physics

Volume 96, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019